essay about mathematics

Essays About Math: Top 10 Examples and Writing Prompts

Love it or hate it, an understanding of math is said to be crucial to success. So, if you are writing essays about math, read our top essay examples.

Mathematics is the study of numbers, shapes, and space using reason and usually a special system of symbols and rules for organizing them . It can be used for a variety of purposes, from calculating a business’s profit to estimating the mass of a black hole. However, it can be considered “controversial” to an extent.

Most students adore math or regard it as their least favorite. No other core subject has the same infamy as math for generating passionate reactions both for and against it. It has applications in every field, whether basic operations or complex calculus problems. Knowing the basics of math is necessary to do any work properly.

If you are writing essays about Math, we have compiled some essay examples for you to get started.

1. Mathematics: Problem Solving and Ideal Math Classroom by Darlene Gregory

2. math essay by prasanna, 3. short essay on the importance of mathematics by jay prakash.

4. Math Anxiety by Elias Wong

5. Why Math Isn’t as Useless as We Think by Murtaza Ali

1. mathematics – do you love or hate it, 2. why do many people despise math, 3. how does math prepare you for the future, 4. is mathematics an essential skill, 5. mathematics in the modern world.

“The trait of the teacher that is being strict is we know that will really help the students to change. But it will give a stress and pressure to students and that is one of the causes why students begin to dislike math. As a student I want a teacher that is not so much strict and giving considerations to his students. A teacher that is not giving loads of things to do and must know how to understand the reasons of his students.”

Gregory discusses the reasons for most students’ hatred of math and how teachers handle the subject in class. She says that math teachers do not explain the topics well, give too much work, and demand nothing less than perfection. To her, the ideal math class would involve teachers being more considerate and giving less work.

You might also be interested in our ordinal number explainer.

“Math is complicated to learn, and one needs to focus and concentrate more. Math is logical sometimes, and the logic needs to be derived out. Maths make our life easier and more straightforward. Math is considered to be challenging because it consists of many formulas that have to be learned, and many symbols and each symbol generally has its significance.”

In her essay, Prasanna gives readers a basic idea of what math is and its importance. She additionally lists down some of the many uses of mathematics in different career paths, namely managing finances, cooking, home modeling and construction, and traveling. Math may seem “useless” and “annoying” to many, but the essay gives readers a clear message: we need math to succeed.

“In this modern age of Science and Technology, emphasis is given on Science such as Physics, Chemistry, Biology, Medicine and Engineering. Mathematics, which is a Science by any criterion, also is an efficient and necessary tool being employed by all these Sciences. As a matter of fact, all these Sciences progress only with the aid of Mathematics. So it is aptly remarked, ‘Mathematics is a Science of all Sciences and art of all arts.’”

As its title suggests, Prakash’s essay briefly explains why math is vital to human nature. As the world continues to advance and modernize, society emphasizes sciences such as medicine, chemistry, and physics. All sciences employ math; it cannot be studied without math. It also helps us better our reasoning skills and maximizes the human mind. It is not only necessary but beneficial to our everyday lives.

4. Math Anxiety by Elias Wong

“Math anxiety affects different not only students but also people in different ways. It’s important to be familiar with the thoughts you have about yourself and the situation when you encounter math. If you are aware of unrealistic or irrational thoughts you can work to replace those thoughts with more positive and realistic ones.”

Wong writes about the phenomenon known as “math anxiety.” This term is used to describe many people’s hatred or fear of math- they feel that they are incapable of doing it. This anxiety is caused mainly by students’ negative experiences in math class, which makes them believe they cannot do well. Wong explains that some people have brains geared towards math and others do not, but this should not stop people from trying to overcome their math anxiety. Through review and practice of basic mathematical skills, students can overcome them and even excel at math.

“We see that math is not an obscure subject reserved for some pretentious intellectual nobility. Though we may not be aware of it, mathematics is embedded into many different aspects of our lives and our world — and by understanding it deeply, we may just gain a greater understanding of ourselves.”

Similar to some of the previous essays, Ali’s essay explains the importance of math. Interestingly, he tells a story of the life of a person name Kyle. He goes through the typical stages of life and enjoys typical human hobbies, including Rubik’s cube solving. Throughout this “Kyle’s” entire life, he performed the role of a mathematician in various ways. Ali explains that math is much more prevalent in our lives than we think, and by understanding it, we can better understand ourselves.

Writing Prompts on Essays about Math

Math is a controversial subject that many people either passionately adore or despise. In this essay, reflect on your feelings towards math, and state your position on the topic. Then, give insights and reasons as to why you feel this way. Perhaps this subject comes easily to you, or perhaps it’s a subject that you find pretty challenging. For an insightful and compelling essay, you can include personal anecdotes to relate to your argument.

$Essays about Math: Why do many people despise math?$

It is well-known that many people despise math. In this essay, discuss why so many people do not enjoy maths and struggle with this subject in school. For a compelling essay, gather interview data and statistics to support your arguments. You could include different sections correlating to why people do not enjoy this subject.

In this essay, begin by reading articles and essays about the importance of studying math. Then, write about the different ways that having proficient math skills can help you later in life. Next, use real-life examples of where maths is necessary, such as banking, shopping, planning holidays, and more! For an engaging essay, use some anecdotes from your experiences of using math in your daily life.

Many people have said that math is essential for the future and that you shouldn’t take a math class for granted. However, many also say that only a basic understanding of math is essential; the rest depends on one’s career. Is it essential to learn calculus and trigonometry? Choose your position and back up your claim with evidence.

Prasanna’s essay lists down just a few applications math has in our daily lives. For this essay, you can choose any activity, whether running, painting, or playing video games, and explain how math is used there. Then, write about mathematical concepts related to your chosen activity and explain how they are used. Finally, be sure to link it back to the importance of math, as this is essentially the topic around which your essay is based.

If you are interested in learning more, check out our essay writing tips !

For help with your essays, check out our round-up of the best essay checkers

Martin is an avid writer specializing in editing and proofreading. He also enjoys literary analysis and writing about food and travel.

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Essay on Importance of Mathematics in our Daily Life in 100, 200, and 350 words.

Updated on
Dec 22, 2023

Essay on Importance of Mathematics in our Daily Life

Mathematics is one of the core aspects of education. Without mathematics, several subjects would cease to exist. It’s applied in the science fields of physics, chemistry, and even biology as well. In commerce accountancy, business statistics and analytics all revolve around mathematics. But what we fail to see is that not only in the field of education but our lives also revolve around it. There is a major role that mathematics plays in our lives. Regardless of where we are, or what we are doing, mathematics is forever persistent. Let’s see how maths is there in our lives via our blog essay on importance of mathematics in our daily life.

Table of Contents

1 Essay on Importance of Mathematics in our Daily life in 100 words
2 Essay on Importance of Mathematics in our Daily life in 200 words
3 Essay on Importance of Mathematics in our Daily Life in 350 words

Essay on Importance of Mathematics in our Daily life in 100 words

Mathematics is a powerful aspect even in our day-to-day life. If you are a cook, the measurements of spices have mathematics in them. If you are a doctor, the composition of medicines that make you provide prescription is made by mathematics. Even if you are going out for just some groceries, the scale that is used for weighing them has maths, and the quantity like ‘dozen apples’ has maths in it. No matter the task, one way or another it revolves around mathematics. Everywhere we go, whatever we do, has maths in it. We just don’t realize that. Maybe from now on, we will, as mathematics is an important aspect of our daily life.

Essay on Importance of Mathematics in our Daily life in 200 words

Mathematics, as a subject, is one of the most important subjects in our lives. Irrespective of the field, mathematics is essential in it. Be it physics, chemistry, accounts, etc. mathematics is there. The use of mathematics proceeds in our daily life to a major extent. It will be correct to say that it has become a vital part of us. Imagining our lives without it would be like a boat without a sail. It will be a shock to know that we constantly use mathematics even without realising the same.

From making instalments to dialling basic phone numbers it all revolves around mathematics.

Let’s take an example from our daily life. In the scenario of going out shopping, we take an estimate of hours. Even while buying just simple groceries, we take into account the weight of vegetables for scaling, weighing them on the scale and then counting the cash to give to the cashier. We don’t even realise it and we are already counting numbers and doing calculations.

Without mathematics and numbers, none of this would be possible.

Hence we can say that mathematics helps us make better choices, more calculated ones throughout our day and hence make our lives simpler.

Essay on Importance of Mathematics in our Daily Life in 350 words

Mathematics is what we call a backbone, a backbone of science. Without it, human life would be extremely difficult to imagine. We cannot live even a single day without making use of mathematics in our daily lives. Without mathematics, human progress would come to a halt.

Maths helps us with our finances. It helps us calculate our daily, monthly as well as yearly expenses. It teaches us how to divide and prioritise our expenses. Its knowledge is essential for investing money too. We can only invest money in property, bank schemes, the stock market, mutual funds, etc. only when we calculate the figures. Let’s take an example from the basic routine of a day. Let’s assume we have to make tea for ourselves. Without mathematics, we wouldn’t be able to calculate how many teaspoons of sugar we need, how many cups of milk and water we have to put in, etc. and if these mentioned calculations aren’t made, how would one be able to prepare tea?

In such a way, mathematics is used to decide the portions of food, ingredients, etc. Mathematics teaches us logical reasoning and helps us develop problem-solving skills. It also improves our analytical thinking and reasoning ability. To stay in shape, mathematics helps by calculating the number of calories and keeping the account of the same. It helps us in deciding the portion of our meals. It will be impossible to think of sports without mathematics. For instance, in cricket, run economy, run rate, strike rate, overs bowled, overs left, number of wickets, bowling average, etc. are calculated. It also helps in predicting the result of the match. When we are on the road and driving, mathetics help us keep account of our speeds, the distance we have travelled, the amount of fuel left, when should we refuel our vehicles, etc.

We can go on and on about how mathematics is involved in our daily lives. In conclusion, we can say that the universe revolves around mathematics. It encompasses everything and without it, we cannot imagine our lives.

Deepansh Gautam

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What Students Are Saying About the Value of Math

We asked teenagers: Do you see the point in learning math? The answer from many was “yes.”

By The Learning Network

“Mathematics, I now see, is important because it expands the world,” Alec Wilkinson writes in a recent guest essay . “It is a point of entry into larger concerns. It teaches reverence. It insists one be receptive to wonder. It requires that a person pay close attention.”

In our writing prompt “ Do You See the Point in Learning Math? ” we wanted to know if students agreed. Basic arithmetic, sure, but is there value in learning higher-level math, such as algebra, geometry and calculus? Do we appreciate math enough?

The answer from many students — those who love and those who “detest” the subject alike — was yes. Of course math helps us balance checkbooks and work up budgets, they said, but it also helps us learn how to follow a formula, appreciate music, draw, shoot three-pointers and even skateboard. It gives us different perspectives, helps us organize our chaotic thoughts, makes us more creative, and shows us how to think rationally.

Not all were convinced that young people should have to take higher-level math classes all through high school, but, as one student said, “I can see myself understanding even more how important it is and appreciating it more as I get older.”

Thank you to all the teenagers who joined the conversation on our writing prompts this week, including students from Bentonville West High School in Centerton, Ark, ; Harvard-Westlake School in Los Angeles ; and North High School in North St. Paul, Minn.

Please note: Student comments have been lightly edited for length, but otherwise appear as they were originally submitted.

“Math is a valuable tool and function of the world.”

As a musician, math is intrinsically related to my passion. As a sailor, math is intertwined with the workings of my boat. As a human, math is the building block for all that functions. When I was a child, I could very much relate to wanting a reason behind math. I soon learned that math IS the reason behind all of the world’s workings. Besides the benefits that math provides to one’s intellect, it becomes obvious later in life that math is a valuable tool and function of the world. In music for example, “adolescent mathematics” are used to portray functions of audio engineering. For example, phase shifting a sine wave to better project sound or understanding waves emitted by electricity and how they affect audio signals. To better understand music, math is a recurring pattern of intervals between generating pitches that are all mathematically related. The frets on a guitar are measured precisely to provide intervals based on a tuning system surrounding 440Hz, which is the mathematically calculated middle of the pitches humans can perceive and a string can effectively generate. The difference between intervals in making a chord are not all uniform, so guitar frets are placed in a way where all chords can sound equally consonant and not favor any chord. The power of mathematics! I am fascinated by the way that math creeps its way into all that I do, despite my plentiful efforts to keep it at a safe distance …

— Renan, Miami Country Day School

“Math isn’t about taking derivatives or solving for x, it’s about having the skills to do so and putting them to use elsewhere in life.”

I believe learning mathematics is both crucial to the learning and development of 21st century students and yet also not to be imposed upon learners too heavily. Aside from the rise in career opportunity in fields centered around mathematics, the skills gained while learning math are able to be translated to many facets of life after a student’s education. Learning mathematics develops problem solving skills which combine logic and reasoning in students as they grow. The average calculus student may complain of learning how to take derivatives, arguing that they will never have to use this after high school, and in that, they may be right. Many students in these math classes will become writers, musicians, or historians and may never take a derivative in their life after high school, and thus deem the skill to do so useless. However, learning mathematics isn’t about taking derivatives or solving for x, it’s about having the skills to do so and putting them to use elsewhere in life. A student who excels at calculus may never use it again, but with the skills of creativity and rational thinking presented by this course, learning mathematics will have had a profound effect on their life.

— Cam, Glenbard West

“Just stop and consider your hobbies and pastimes … all of it needs math.”

Math is timing, it’s logic, it’s precision, it’s structure, and it’s the way most of the physical world works. I love math — especially algebra and geometry — as it all follows a formula, and if you set it up just right, you can create almost anything you want in at least two different ways. Just stop and consider your hobbies and pastimes. You could be into skateboarding, basketball, or skiing. You could be like me, and sit at home for hours on end grinding out solves on a Rubik’s cube. Or you could be into sketching. Did you know that a proper drawing of the human face places the eyes exactly halfway down from the top of the head? All of it needs math. Author Alec Wilkinson, when sharing his high school doubting view on mathematics, laments “If I had understood how deeply mathematics is embedded in the world …” You can’t draw a face without proportions. You can’t stop with your skis at just any angle. You can’t get three points without shooting at least 22 feet away from the basket, and get this: you can’t even ride a skateboard if you can’t create four congruent wheels to put on it.

— Marshall, Union High School, Vancouver, WA

“Math gives us a different perspective on everyday activities.”

Even though the question “why do we even do math?” is asked all the time, there is a deeper meaning to the values it shares. Math gives us a different perspective on everyday activities, even if those activities in our routine have absolutely nothing to do with mathematical concepts itself. Geometry, for instance, allows us to think on a different level than simply achieving accuracy maintains. It trains our mind to look at something from various viewpoints as well as teaching us to think before acting and organizing chaotic thoughts. The build up of learning math can allow someone to mature beyond the point where if they didn’t learn math and thought through everything. It paves a way where we develop certain characteristics and traits that are favorable when assisting someone with difficult tasks in the future.

— Linden, Harvard-Westlake High School, CA

“Math teaches us how to think.”

As explained in the article, math is all around us. Shapes, numbers, statistics, you can find math in almost anything and everything. But is it important for all students to learn? I would say so. Math in elementary school years is very important because it teaches how to do simple calculations that can be used in your everyday life; however middle and high school math isn’t used as directly. Math teaches us how to think. It’s far different from any other subject in school, and truly understanding it can be very rewarding. There are also many career paths that are based around math, such as engineering, statistics, or computer programming, for example. These careers are all crucial for society to function, and many pay well. Without a solid background in math, these careers wouldn’t be possible. While math is a very important subject, I also feel it should become optional at some point, perhaps part way through high school. Upper level math classes often lose their educational value if the student isn’t genuinely interested in learning it. I would encourage all students to learn math, but not require it.

— Grey, Cary High School

“Math is a valuable tool for everyone to learn, but students need better influences to show them why it’s useful.”

Although I loved math as a kid, as I got older it felt more like a chore; all the kids would say “when am I ever going to use this in real life?” and even I, who had loved math, couldn’t figure out how it benefits me either. This was until I started asking my dad for help with my homework. He would go on and on about how he used the math I was learning everyday at work and even started giving me examples of when and where I could use it, which changed my perspective completely. Ultimately, I believe that math is a valuable tool for everyone to learn, but students need better influences to show them why it’s useful and where they can use it outside of class.

— Lilly, Union High School

“At the roots of math, it teaches people how to follow a process.”

I do believe that the math outside of arithmetic, percentages, and fractions are the only math skills truly needed for everyone, with all other concepts being only used for certain careers. However, at the same time, I can’t help but want to still learn it. I believe that at the roots of math, it teaches people how to follow a process. All mathematics is about following a formula and then getting the result of it as accurately as possible. It teaches us that in order to get the results needed, all the work must be put and no shortcuts or guesses can be made. Every equation, number, and symbol in math all interconnect with each other, to create formulas that if followed correctly gives us the answer needed. Everything is essential to getting the results needed, and skipping a step will lead to a wrong answer. Although I do understand why many would see no reason to learn math outside of arithmetic, I also see lessons of work ethics and understanding the process that can be applied to many real world scenarios.

— Takuma, Irvine High School

“I see now that math not only works through logic but also creativity.”

A story that will never finish resembling the universe constantly expanding, this is what math is. I detest math, but I love a never-ending tale of mystery and suspense. If we were to see math as an adventure it would make it more enjoyable. I have often had a closed mindset on math, however, viewing it from this perspective, I find it much more appealing. Teachers urge students to try on math and though it seems daunting and useless, once you get to higher math it is still important. I see now that math not only works through logic but also creativity and as the author emphasizes, it is “a fundamental part of the world’s design.” This view on math will help students succeed and have a more open mindset toward math. How is this never-ending story of suspense going to affect YOU?

— Audrey, Vancouver, WA union high school

“In some word problems, I encounter problems that thoroughly interest me.”

I believe math is a crucial thing to learn as you grow up. Math is easily my favorite subject and I wish more people would share my enthusiasm. As Alec Wilkinson writes, “Mathematics, I now see, is important because it expands the world.” I have always enjoyed math, but until the past year, I have not seen a point in higher-level math. In some of the word problems I deal with in these classes, I encounter problems that thoroughly interest me. The problems that I am working on in math involve the speed of a plane being affected by wind. I know this is not riveting to everyone, but I thoroughly wonder about things like this on a daily basis. The type of math used in the plane problems is similar to what Alec is learning — trigonometry. It may not serve the most use to me now, but I believe a thorough understanding of the world is a big part of living a meaningful life.

— Rehan, Cary High School

“Without high school classes, fewer people get that spark of wonder about math.”

I think that math should be required through high school because math is a use-it-or-lose-it subject. If we stop teaching math in high school and just teach it up to middle school, not only will many people lose their ability to do basic math, but we will have fewer and fewer people get that spark of wonder about math that the author had when taking math for a second time; after having that spark myself, I realized that people start getting the spark once they are in harder math classes. At first, I thought that if math stopped being required in high school, and was offered as an elective, then only people with the spark would continue with it, and everything would be okay. After thinking about the consequences of the idea, I realized that technology requires knowing the seemingly unneeded math. There is already a shortage of IT professionals, and stopping math earlier will only worsen that shortage. Math is tricky. If you try your best to understand it, it isn’t too hard. However, the problem is people had bad math teachers when they were younger, which made them hate math. I have learned that the key to learning math is to have an open mind.

— Andrew, Cary High School

“I think math is a waste of my time because I don’t think I will ever get it.”

In the article Mr. Wilkinson writes, “When I thought about mathematics at all as a boy it was to speculate about why I was being made to learn it, since it seemed plainly obvious that there was no need for it in adult life.” His experience as a boy resonates with my experience now. I feel like math is extremely difficult at some points and it is not my strongest subject. Whenever I am having a hard time with something I get a little upset with myself because I feel like I need to get everything perfect. So therefore, I think it is a waste of my time because I don’t think I will ever get it. At the age of 65 Mr. Wilkinson decided to see if he could learn more/relearn algebra, geometry and calculus and I can’t imagine myself doing this but I can see myself understanding even more how important it is and appreciating it more as I get older. When my dad was young he hated history but, as he got older he learned to appreciate it and see how we can learn from our past mistakes and he now loves learning new things about history.

— Kate, Cary High School

“Not all children need to learn higher level math.”

The higher levels of math like calculus, algebra, and geometry have shaped the world we live in today. Just designing a house relates to math. To be in many professions you have to know algebra, geometry, and calculus such as being an economist, engineer, and architect. Although higher-level math isn’t useful to some people. If you want to do something that pertains to math, you should be able to do so and learn those high levels of math. Many things children learn in math they will never use again, so learning those skills isn’t very helpful … Children went through so much stress and anxiety to learn these skills that they will never see again in their lives. In school, children are using their time learning calculus when they could be learning something more meaningful that can prepare them for life.

— Julyssa, Hanover Horton High School

“Once you understand the basics, more math classes should be a choice.”

I believe that once you get to the point where you have a great understanding of the basics of math, you should be able to take more useful classes that will prepare you for the future better, rather than memorizing equations after equations about weird shapes that will be irrelevant to anything in my future. Yes, all math levels can be useful to others’ futures depending on what career path they choose, but for the ones like me who know they are not planning on encountering extremely high level math equations on the daily, we should not have to take math after a certain point.

— Tessa, Glenbard West High School

“Math could shape the world if it were taught differently.”

If we learned how to balance checkbooks and learn about actual life situations, math could be more helpful. Instead of learning about rare situations that probably won’t come up in our lives, we should be learning how to live on a budget and succeed money-wise. Since it is a required class, learning this would save more people from going into debt and overspending. In schools today, we have to take a specific class that doesn’t sound appealing to the average teenager to learn how to save and spend money responsibly. If it was required in math to learn about that instead of how far Sally has to walk then we would be a more successful nation as a whole. Math could shape the world differently but the way it is taught in schools does not have much impact on everyday life.

— Becca, Bentonville West High School

“To be honest, I don’t see the point in learning all of the complicated math.”

In a realistic point of view, I need to know how to cut a cake or a piece of pie or know how to divide 25,000 dollars into 10 paychecks. On the other hand, I don’t need to know the arc and angle. I need to throw a piece of paper into a trash can. I say this because, in all reality and I know a lot of people say this but it’s true, when are we actually going to need this in our real world lives? Learning complicated math is a waste of precious learning time unless you desire to have a career that requires these studies like becoming an engineer, or a math professor. I think that the fact that schools are still requiring us to learn these types of mathematics is just ignorance from the past generations. I believe that if we have the technology to complete these problems in a few seconds then we should use this technology, but the past generations are salty because they didn’t have these resources so they want to do the same thing they did when they were learning math. So to be honest, I don’t see the point in learning all of the complicated math but I do think it’s necessary to know the basic math.

— Shai, Julia R Masterman, Philadelphia, PA

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Math Essay Ideas for Students: Exploring Mathematical Concepts

Are you a student who's been tasked with writing a math essay? Don't fret! While math may seem like an abstract and daunting subject, it's actually full of fascinating concepts waiting to be explored. In this article, we'll delve into some exciting math essay ideas that will not only pique your interest but also impress your teachers. So grab your pens and calculators, and let's dive into the world of mathematics!

The Beauty of Fibonacci Sequence

Have you ever wondered why sunflowers, pinecones, and even galaxies exhibit a mesmerizing spiral pattern? It's all thanks to the Fibonacci sequence! Explore the origin, properties, and real-world applications of this remarkable mathematical sequence. Discuss how it manifests in nature, art, and even financial markets. Unveil the hidden beauty behind these numbers and show how they shape the world around us.

The Mathematics of Music

Did you know that music and mathematics go hand in hand? Dive into the relationship between these two seemingly unrelated fields and develop your writing skills . Explore the connection between harmonics, frequencies, and mathematical ratios. Analyze how musical scales are constructed and why certain combinations of notes create pleasant melodies while others may sound dissonant. Explore the fascinating world where numbers and melodies intertwine.

The Geometry of Architecture

Architects have been using mathematical principles for centuries to create awe-inspiring structures. Explore the geometric concepts that underpin iconic architectural designs. From the symmetry of the Parthenon to the intricate tessellations in Islamic art, mathematics plays a crucial role in creating visually stunning buildings. Discuss the mathematical principles architects employ and how they enhance the functionality and aesthetics of their designs.

Fractals: Nature's Infinite Complexity

Step into the mesmerizing world of fractals, where infinite complexity arises from simple patterns. Did you know that the famous Mandelbrot set , a classic example of a fractal, has been studied extensively and generated using computers? In fact, it is estimated that the Mandelbrot set requires billions of calculations to generate just a single image! This showcases the computational power and mathematical precision involved in exploring the beauty of fractal geometry.

Explore the beauty and intricacy of fractal geometry, from the famous Mandelbrot set to the Sierpinski triangle. Discuss the self-similarity and infinite iteration that define fractals and how they can be found in natural phenomena such as coastlines, clouds, and even in the structure of our lungs. Examine how fractal mathematics is applied in computer graphics, art, and the study of chaotic systems. Let the captivating world of fractals unfold before your eyes.

The Game Theory Revolution

Game theory isn't just about playing games; it's a powerful tool used in various fields, from economics to biology. Dive into the world of strategic decision-making and explore how game theory helps us understand human behavior and predict outcomes. Discuss in your essay classic games like The Prisoner's Dilemma and examine how mathematical models can shed light on complex social interactions. Explore the cutting-edge applications of game theory in diverse fields, such as cybersecurity and evolutionary biology. If you still have difficulties choosing an idea for a math essay, find a reliable expert online. Ask them to write me an essay or provide any other academic assistance with your math assignments.

Chaos Theory and the Butterfly Effect

While writing an essay, explore the fascinating world of chaos theory and how small changes can lead to big consequences. Discuss the famous Butterfly Effect and how it exemplifies the sensitive dependence on initial conditions. Delve into the mathematical principles behind chaotic systems and their applications in weather forecasting, population dynamics, and cryptography. Unravel the hidden order within apparent randomness and showcase the far-reaching implications of chaos theory.

The Mathematics Behind Cryptography

In an increasingly digital world, cryptography plays a vital role in ensuring secure communication and data protection. Did you know that the global cybersecurity market is projected to reach a staggering $248.26 billion by 2023? This statistic emphasizes the growing importance of cryptography in safeguarding sensitive information.

Explore the mathematical foundations of cryptography and how it allows for the creation of unbreakable codes and encryption algorithms. Discuss the concepts of prime numbers, modular arithmetic, and public-key cryptography. Delve into the fascinating history of cryptography, from ancient times to modern-day encryption methods. In your essay, highlight the importance of mathematics in safeguarding sensitive information and the ongoing challenges faced by cryptographers.

Writing a math essay doesn't have to be a daunting task. By choosing a captivating topic and exploring the various mathematical concepts, you can turn your essay into a fascinating journey of discovery. Whether you're uncovering the beauty of the Fibonacci sequence, exploring the mathematical underpinnings of music, or delving into the game theory revolution, there's a world of possibilities waiting to be explored. So embrace the power of mathematics and let your creativity shine through your words!

Remember, these are just a few math essay ideas to get you started. Feel free to explore other mathematical concepts that ignite your curiosity. The world of mathematics is vast, and each concept has its own unique story to tell. So go ahead, unleash your inner mathematician, and embark on an exciting journey through the captivating realm of mathematical ideas!

Tobi Columb, a math expert, is a dedicated educator and explorer. He is deeply fascinated by the infinite possibilities of mathematics. Tobi's mission is to equip his students with the tools needed to excel in the realm of numbers. He also advocates for the benefits of a gluten-free lifestyle for students and people of all ages. Join Tobi on his transformative journey of mathematical mastery and holistic well-being.

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Mathematics: Discovered or Created? Essay (Critical Writing)

Mathematics is a branch of science that has had far-reaching impacts on many spheres of life. Through mathematics, man has made remarkable advances in technology and other fields of life. Mathematics also provides us with a logical order for describing the various prototypes and structures that comprise nature. Mathematics is also responsible for some of the greatest breakthroughs that have been made by humanity so far.

For instance, mathematics has played a hand in humanity’s foray into the cosmos and it has been responsible for the modern internet advancements. Albert Einstein once asked, “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?” (Ernest 9). This question is part of a big debate on whether math is a product of human creation or human discovery. Consequently, if math is part of human discovery what are some of the laws and notions that are subject to this discovery? This paper explores the issues surrounding the debate on whether math is a product of human creation or human discovery.

First, it is important to note that math acts like the outline to our universe. Many mathematicians agree that the universe is governed by a singular order that is defined using mathematical principles. Consequently, even if the universe ceased to exist, all mathematical principles would still be true. Therefore, like other aspects of human nature, mathematics is part of human discovery. Furthermore, there are several mathematical principles that are yet to be discovered. When these principles are discovered, they “will then assist us in building models that will give us predictive power and understanding of the physical phenomena we seek to control” (Ernest 10). Therefore, math is a natural concept that is to be discovered and used by humanity. This argument is common among lovers of mathematics.

Another viable explanation of the existence of mathematics is that it is merely part of the human creation. The argument about math being part of the intricate web of nature could be easily refuted by the view that human beings invented mathematics as a tool that could aid in the description of the physical world. Therefore, mathematics is only popular among human beings because it suits their needs when they are exploring the world.

It is also true that some mathematical concepts have been changed and altered for them to be palatable to human beings. Furthermore, if the universe ceased to exist, there would be no need for mathematics and it would not exist. Mathematics has been made possible by geography, astronomy, and physics among other areas of universal studies. Mathematics exists solely to satisfy the needs of studying and understanding the universe but it is not part of these studies. Therefore, mathematics is not something that is discovered but it is a human creation.

These two arguments form the basis of our understanding of the institution of mathematics. However, in my understanding, mathematics is a human creation. The argument for mathematics being part of human discovery is far-fetched and fanatical. For instance, mathematics only describes certain variables of the physical universe. There are several other factors of the universe that cannot be defined or explained by mathematical concepts. Therefore, the argument about mathematics being part of human discovery can be nullified by the idea that there are discoveries that are outside of the mathematical realm. In my view, when discoveries about the physical world are made, man proceeds to create mathematical concepts that can help him analyze and explain these new discoveries.

Works Cited

Ernest, Paul. “Is mathematics discovered or invented.” Philosophy of Mathematics Education Journal 12.1 (2009): 9-13. Print.

Albert Einstein’s Contributions to Science
Albert Einstein, His Life and Career
Women Mathematicians: Maria Agnesi, Sophie Germain
Statistical Thinking and Collection of Information
Quantitative Approach to Research
Statistics: Chi-Square Test and Regression Analysis
P-Value Definition and Role
Statistical Process in Data Analysis
Chicago (A-D)
Chicago (N-B)

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How mathematical practices can improve your writing

Writing is similar to three specific mathematical practices: modelling, problem-solving and proving, writes Caroline Yoon. Here, she gives some tips on how to use these to improve academic writing

Caroline Yoon

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I feel for my students when I hand them their first essay assignment. Many are mathematicians, students and teachers who chose to study mathematics partly to avoid writing. But in my mathematics education courses, and in the discipline more generally, academic writing is part of our routine practice.

Mathematicians face some challenging stereotypes when it comes to writing. Writing is seen as ephemeral, subjective and context-dependent, whereas mathematics is seen as enduring, universal and context-free. Writing reflects self, but mathematics transcends it: they are distinct from each other.

This is a false dichotomy that can discourage mathematicians from writing. It suggests writing is outside the natural skill set of the mathematician, and that one’s mathematics training not only neglects one’s development as a writer but actively prevents it. Rather than capitulate to this false dichotomy, I propose we turn it around to examine how writing is similar to three specific mathematical practices: modelling, problem-solving and proving.

Three mathematical practices that can improve your writing

Mathematical modelling.

Let us consider a hypothetical mathematics education student who has spent weeks thinking, reading and talking about her essay topic, but only starts writing it the night before it is due. She writes one draft only – the one she hands in – and is disappointed with the low grade her essay receives.

She wishes she had started earlier but she was still trying to figure out what she wanted to say up until the moment she started writing. It was only the pressure of the deadline that forced her to start; without it, she would have spent even more time thinking and reading to develop her ideas. After all, she reasons, there is no point writing when you do not know what to write about!

This “think first, write after” approach, sometimes known as the “writing up” model is a dangerous trap many students fall into, and is at odds with the way writing works. The approach allows no room for imperfect drafts that are a necessary part of the writing process . Writing experts trade on the generative power of imperfect writing; they encourage writers to turn off their internal critics and allow themselves to write badly as a way of overcoming writing inertia and discovering new ideas. The “shitty first draft” is an ideal (and achievable) first goal in the writing process. Anyone can produce a sketchy first draft that generates material that can be worked on, improved and eventually rewritten into a more sharable form.

Mathematical modelling offers a compelling metaphor for the generative power of imperfect writing. Like polished writing, polished mathematical models are seldom produced in the first attempt. A modeller typically begins with some understanding of the real situation to be modelled. The modeller considers variables and relationships from his or her understanding of the real situation and writes them into an initial mathematical model.

The model is his or her mathematical description of the situation, written in mathematical notation, and the modeller who publishes a mathematical model has typically created and discarded multiple drafts along the way, just as the writer who publishes a piece of writing has typically written and discarded multiple drafts along the way.

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One write way to student success in mathematics

Problem-solving

Writing an original essay is like trying to solve a mathematics problem. There is no script to follow; it must be created by simultaneously determining one’s goals and figuring out how to achieve them. In both essay writing and mathematical problem-solving, getting stuck is natural and expected. It is even a special kind of thrill.

This observation might come as a surprise to mathematicians who do not think of their problem-solving activity as writing. But doing mathematics, the ordinary everyday act of manipulating mathematical relationships and objects to notice new levels of structure and pattern, involves scratching out symbols and marks, and moving ideas around the page or board.

Why do I care that mathematicians acknowledge their natural language of symbols and signs as writing? Quite frankly because they are good at it. They have spent years honing their ability to use writing to restructure their thoughts, to dissect their ideas, identify new arguments. They possess an analytic discipline that most writers struggle with.

Yet few of my mathematics education students take advantage of this in their academic writing. They want their writing to come out in consecutive, polished sentences and become discouraged when it does not. They do not use their writing to analyse and probe their arguments as they do when they are stuck on mathematical problems. By viewing writing only as a medium for communicating perfectly formed thoughts, they deny themselves their own laboratories, their own thinking tools.

I am not suggesting that one’s success in solving mathematical problems automatically translates into successful essay writing. But the metaphor of writing as problem-solving might encourage a mathematics education student not to give up too easily when she finds herself stuck in her writing.

Our hypothetical student now has a good draft that she is happy with. She is satisfied it represents her knowledge of the subject matter and has read extensively to check the accuracy of its content. A friend reads the draft and remarks that it is difficult to understand. Our student is unperturbed. She puts it down to her friend’s limited knowledge of the subject and is confident her more knowledgeable teacher will understand her essay.

But the essay is not an inert record judged on the number of correct facts it contains. It is also a rhetorical act that seeks to engage the public. It addresses an audience, it tries to persuade, to inspire some response or action.

Mathematical proofs are like expository essays in this regard; they must convince an audience. When undergraduate mathematics students learn to construct proofs of their own, a common piece of advice is to test them on different audiences. The phrase “Convince yourself, convince a friend, convince an enemy” becomes relevant in this respect.

Mathematicians do not have to see themselves as starting from nothing when they engage in academic writing. Rather, they can use mathematical principles they have already honed in their training, but which they might not have formerly recognised as tools for improving their academic writing.

Practical tips for productive writing beliefs and behaviours

Writing can generate ideas. Free writing is a good way to start. Set a timer and write continuously for 10 minutes without editing. These early drafts will be clumsy, but there will also be some gold that can be mined and developed.
Writing can be used to analyse and organise ideas. When stuck, try to restructure your ideas. Identify the main point in each paragraph and play around with organising their flow.
Writing is a dialogue with the public. Seek out readers’ interpretations of your writing and listen to their impressions. Read your writing out loud to yourself: you will hear it differently!

Caroline Yoon is an associate professor of mathematics at the University of Auckland.

This is an edited version of the journal article “The writing mathematician” by Caroline Yoon, published in For the Learning of Mathematics and collected in The Best Writing on Mathematics , edited by Mircea Pitici (Princeton University Press).

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How to Write a Math Essay

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Students often wonder why they have to write in math class. In fact, the purpose of a math essay is for students to demonstrate their understanding of mathematical ideas and concepts. Both high school and college students have to write math essays. Though it is a specific type of writing, you can follow many of the same guidelines for writing used in other subjects.

The first step to writing a math essay is choosing a topic. One option is to choose a mathematical concept you find interesting, such as one which you discussed in class but want to explore further. Alternatively, choose a problem that you've solved. For this type of essay, you state the problem and solution and explain how you arrived at the answer. For either type of essay, brainstorm what about the topic or problem intrigues you. For example, consider why you chose to delve deeper into that particular concept or explain the math for that specific equation.

Just like essays in other subjects, math essays require you to consider your audience. Mathematician P.R. Halmos suggests in his article, "How to Write Mathematics," thinking of a particular person when writing, especially one whose math ways "can stand mending." Therefore, unless directed otherwise, write as if your audience has the same basic level of math skills as you. Though you are writing a math essay to explain an idea or solution, you also want to persuade your reader that your methodology is the best one. Keep in mind your professor or teacher is not the main audience member as he already understands the concept.

Concept Essay Organization

A math essay about a concept looks similar to essays in other classes; it is, in fact, an expository essay. For this, you investigate a mathematical concept, develop further ideas about the theory based on research and make a claim in the form of a thesis statement. To write the essay, start with an introduction by stating the topic and its import. The introduction includes your claim about the theory. Develop the claim in subsequent paragraphs using evidence from your research as support. Conclude by tying up any loose ends and readdressing the theory in light of the information you provided.

Equation Essay Organization

For an equation essay, state the problem and solution directly in the introduction; explain the significance of the problem and your rationale for solving it as you did. The significance and rationale are similar to a thesis statement, providing the basis for your argument. Write a paragraph clearly explaining how you approach the problem, thus giving the reader a guide to follow. For a complex problem, include a graph that helps demonstrate the result of your equation, explaining explicitly what the graph shows. Similarly, define variables precisely with phrases such as "Let n be any real number." Describe your method for solving the problem, guiding your reader through the formulas you used and your reasons for using them.

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Oregon State University: How to Write a Math Essay
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Nadia Archuleta has a B.A. in English writing. She spent five years working abroad and has traveled extensively. She has worked as an English as a Foreign/Second Language teacher for 12 years.

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ESSAY SAUCE

FOR STUDENTS : ALL THE INGREDIENTS OF A GOOD ESSAY

Mathematics essays

Our free mathematics essay examples include popular topics such as algorithms, applied mathematics, calculus, knot theory, linear algebra, and more.

Euler’s identity

Euler’s identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as “the most beautiful equation.” It is a special case of a foundational equation in complex arithmetic called Euler’s Formula, which the late great physicist Richard Feynman called in his lectures “our jewel” and “the most remarkable formula in … Read more

The Banach-Tarski paradox

Mathematics is seen by many as a mysterious and often unsettling subject. Answers often hide behind layers and layers of complicated equations, formulas and ciphers, the application of advanced concepts to real life is limited and I often find myself more confused after class than when I first entered. However, the real beauty of Mathematics … Read more

Pascal’s triangle, binomial theorem

What is Pascal’s Triangle? Pascal’s Triangle was named after Blaise Pascal. Pascal’s triangle starts with the number 1 and goes down the scale. When you start with one, add more numbers in a triangular shape, like a pyramid of some sort. All the numbers on the surrounding right and left sides of the triangle are … Read more

My journey of teaching and learning mathematics since embarking on a PGCE Mathematics course

Before I came to study a Post Graduate Certificate (PGCE) Mathematics course at University College London Institute of Education (UCL IOE), I had been working as an Academic Tutor at a behavioural centre, linked to a mainstream secondary school for the past 7 months. Students placed here had either learning difficulties or behaviour issues experienced … Read more

Aircraft – mathematics

Math SL Internal Assessment Lift and Drag Introduction When you look at aircrafts, they look like they shouldn’t be able to leave the ground because of how big they are. I always watched aircrafts, take off and land, over and over. According to Newton’s Third Law, every action has an equal and opposite reaction, lift … Read more

The World of Mathematics

Mathematics is often considered a useless discipline because people think they do not use advanced math in their life. It is a misunderstanding. Not using advanced math does not mean it is not vital. If you trade stocks, you will read many stock analysis reports. These reports use mathematical knowledge. Many students in the United … Read more

The history of algebra

We all use algebra. Even if it’s for the simple stuff, we use some form of algebra in our everyday lives. While reading chapters 1-10, I came across the word algebra and became quite curious about the subject for I have never really understood nor cared for it honestly, I just figured it’s the usual … Read more

Mathematics introduction

Mathematics belongs to the science discourse community. The word science means knowledge and comes from the Latin “Scientia”. In university, science is made up of a lot of discourse communities, such as Mathematics, Physics, and Chemistry. By searching the definition of science in Webster’s New Collegiate Dictionary, science is “knowledge covering general truths of the … Read more

Niels Henrik Abel

For over two centuries, mathematicians had trouble in finding a solution to the quintic equation, that is until Niels Henrik Abel formulated a theory. Abel was a Norwegian mathematician born on August 5, 1802, and his talent and potential in the field of mathematics was already present at a young age, leading him to become … Read more

The narrative of zero

Numbers surround us. They stamp our days, light our evenings, foresee our climate, and keep us on course. They drive business and support human progress. The beginning of the numerals makes disarray between the historical backdrop of mathematics and the historical backdrop of our modern numerals. The narrative of zero alludes to something can be … Read more

Emmy Noether

She was more than a mathematician to the people she met and to the people she inspired. She even has managed to inspire people long after she has passed. Emmy Noether was born on March 23, 1882 in Bavaria Germany. Growing up she wanted to go to college but back then women weren’t allowed to … Read more

Bitopological Approximation Space with Application to Data Reduction in Multivalued Information Systems

Abstract: In this work we generalize Pawlak approximation space to bitopological approximation space. One binary relation can define two subbases of two topological spaces. Membership, equillity and inclusion relations using rough approximations are defined and studied in bitopological aapproximation space. Some new measures that measure the accuracy and the quality of approximations are defined and … Read more

Statistics overview

Statistics is a form of mathematical analysis that uses quantified models, representations and synopses for a given set of experimental data or real life studies. Statistical analysis involves the process of gathering and evaluating data and then summarizing the data into a mathematical form. Statistics is a term used to summarize a process that a … Read more

Numerical Weather Prediction

You turn on the television, and often the first channel that pops up is the weather. It’s going 24/7 with predictions that go from weekly all the way down to hourly, with conditions that go from humidity to temperature. But what goes on behind the scenes is heavily entrenched in mathematics– meteorology’s backbone is a … Read more

The Mathematics of Our Universe

Abstract In this report, we start by defining key aspects of classical Lagrangian mechanics including the principle of least action and how one can use this to derive the Euler-Lagrange equations. Momentum and Conservation laws shall also be introduced, deriving relations between position, momenta and the Lagrangian of a given system. Following this, we develop … Read more

Ideas for your next mathematics essay

Stuck for a title for your next essay? Here are some ideas to inspire you:

The Mathematics of Music: Exploring the Relationship between Mathematics and Music – This essay would examine the connections between music and mathematics, including the use of mathematical concepts in musical composition and the study of the mathematics of sound.
The Golden Ratio: A Mathematical and Aesthetic Marvel – This essay would discuss the concept of the golden ratio and its applications in art, architecture, and design. It would explore the beauty and symmetry of this mathematical principle.
Mathematics in Sports: Analyzing the Numbers Behind Athletic Performance – This essay would explore the use of mathematics in sports, including the use of statistics and analytics to analyze athletic performance and predict outcomes.
Chaos Theory: The Science of Nonlinear Systems – This essay would discuss the concept of chaos theory and its applications in various fields, such as meteorology, physics, and economics. It would explore the idea that small changes in initial conditions can have a significant impact on the final outcome of a system.
The Mathematics of Cryptography: Securing Information in the Digital Age – This essay would examine the use of mathematics in cryptography, including the principles of encryption and decryption, and how these concepts are applied to secure information in the digital age.
Fractals: The Beauty of Infinite Complexity – This essay would explore the concept of fractals and their applications in art, nature, and science. It would discuss the beauty and complexity of these repeating patterns found in nature and how they are used in various fields of study.
Mathematical Models in Biology: Understanding the Complexities of Life – This essay would discuss the use of mathematical models in biology, including the modeling of population growth, the spread of disease, and the behavior of organisms. It would explore how these models help scientists understand the complex systems that make up living organisms.
The Mathematics of Finance: Analyzing Investments and Markets – This essay would examine the use of mathematics in finance, including the principles of financial analysis, investments, and risk management. It would explore how mathematics is used to understand and predict market trends.
Geometry in Art: The Intersection of Math and Creativity – This essay would discuss the use of geometry in art, including the use of shapes, patterns, and symmetry. It would explore how artists use mathematical concepts to create beautiful and compelling works of art.
The History of Mathematics: From Ancient Times to Modern-Day Advances – This essay would trace the history of mathematics, from its origins in ancient civilizations to modern-day advancements in the field. It would explore the contributions of key mathematicians throughout history and the evolution of mathematical concepts and principles over time.

Extended Essay: Group 5: Mathematics

General Timeline
Group 1: English Language and Literature
Group 2: Language Acquisition
Group 3: Individuals and Societies
Group 4: Sciences
Group 5: Mathematics
Group 6: The Arts
Interdisciplinary essays
Six sub-categories for WSEE
IB Interdisciplinary EE Assessment Guide
Brainstorming
Pre-Writing
Research Techniques
The Research Question
Paraphrasing, Summarising and Quotations
Writing an EE Introduction
Writing the main body of your EE
Writing your EE Conclusion
Sources: Finding, Organising and Evaluating Them
Conducting Interviews and Surveys
Citing and Referencing
Check-in Sessions
First Formal Reflection
Second Formal Reflection
Final Reflection (Viva Voce)
Researcher's Reflection Space (RRS) Examples
Information for Supervisors
How is the EE Graded?
EE Online Resources
Stavanger Public Library
Exemplar Essays
Extended Essay Presentations
ISS High School Academic Honesty Policy

Mathematics

An extended essay (EE) in mathematics is intended for students who are writing on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Essays in this group are divided into six categories:

the applicability of mathematics to solve both real and abstract problems
the beauty of mathematics—eg geometry or fractal theory
the elegance of mathematics in the proving of theorems—eg number theory
the history of mathematics: the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds or thousands of years
the effect of technology on mathematics:
in forging links between different branches of mathematics,
or in bringing about a new branch of mathematics, or causing a particular branch to flourish.

These are just some of the many different ways that mathematics can be enjoyable or useful, or, as in many cases, both.

For an Introduction in a Mathematics EE look HERE .

Choice of topic

The EE may be written on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself.

Students may choose mathematical topics from fields such as engineering, the sciences or the social sciences, as well as from mathematics itself.

Statistical analyses of experimental results taken from other subject areas are also acceptable, provided that they focus on the modeling process and discuss the limitations of the results; such essays should not include extensive non-mathematical detail.

A topic selected from the history of mathematics may also be appropriate, provided that a clear line of mathematical development is demonstrated. Concentration on the lives of, or personal rivalries between, mathematicians would be irrelevant and would not score highly on the assessment criteria.

It should be noted that the assessment criteria give credit for the nature of the investigation and for the extent that reasoned arguments are applied to an appropriate research question.

Students should avoid choosing a topic that gives rise to a trivial research question or one that is not sufficiently focused to allow appropriate treatment within the requirements of the EE.

Students will normally be expected either to extend their knowledge beyond that encountered in the Diploma Programme mathematics course they are studying or to apply techniques used in their mathematics course to modeling in an appropriately chosen topic.

However, it is very important to remember that it is an essay that is being written, not a research paper for a journal of advanced mathematics, and no result, however impressive, should be quoted without evidence of the student’s real understanding of it.

Example and Treatment of Topic

Examples of topics

These examples are just for guidance. Students must ensure their choice of topic is focused (left-hand column) rather than broad (right-hand column

Treatment of the topic

Whatever the title of the EE, students must apply good mathematical practice that is relevant to the

chosen topic, including:

• data analysed using appropriate techniques

• arguments correctly reasoned

• situations modeled using correct methodology

• problems clearly stated and techniques at the correct level of sophistication applied to their solution.

Research methods

Students must be advised that mathematical research is a long-term and open-ended exploration of a set of related mathematical problems that are based on personal observations.

The answers to these problems connect to and build upon each other over time.

Students’ research should be guided by analysis of primary and secondary sources.

A primary source for research in mathematics involves:

• data-gathering

• visualization

• abstraction

• conjecturing

• proof.

A secondary source of research refers to a comprehensive review of scholarly work, including books, journal articles or essays in an edited collection.

A literature review for mathematics might not be as extensive as in other subjects, but students are expected to demonstrate their knowledge and understanding of the mathematics they are using in the context of the broader discipline, for example how the mathematics they are using has been applied before, or in a different area to the one they are investigating.

Writing the essay

Throughout the EE students should communicate mathematically:

• describing their way of thinking

• writing definitions and conjectures

• using symbols, theorems, graphs and diagrams

• justifying their conclusions.

There must be sufficient explanation and commentary throughout the essay to ensure that the reader does not lose sight of its purpose in a mass of mathematical symbols, formulae and analysis.

The unique disciplines of mathematics must be respected throughout. Relevant graphs and diagrams are often important and should be incorporated in the body of the essay, not relegated to an appendix.

However, lengthy printouts, tables of results and computer programs should not be allowed to interrupt the development of the essay, and should appear separately as footnotes or in an appendix. Proofs of key results may be included, but proofs of standard results should be either omitted or, if they illustrate an important point, included in an appendix.

Examples of topics, research questions and suggested approaches

Once students have identified their topic and written their research question, they can decide how to

research their answer. They may find it helpful to write a statement outlining their broad approach. These

examples are for guidance only.

An important note on “double-dipping”

Students must ensure that their EE does not duplicate other work they are submitting for the Diploma Programme. For example, students are not permitted to repeat any of the mathematics in their IA in their EE, or vice versa.

The mathematics EE and internal assessment

An EE in mathematics is not an extension of the internal assessment (IA) task. Students must ensure that they understand the differences between the two.

The EE is a more substantial piece of work that requires formal research
The IA is an exploration of an idea in mathematics.

It is not appropriate for a student to choose the same topic for an EE as the IA. There would be too much danger of duplication and it must therefore be discouraged.

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The Best Writing on Mathematics 12

Mircea pitici, series editor.

This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics makes mathematical writing available to a wide audience.

The year’s finest mathematical writing from around the world

The year's finest mathematical writing from around the world

The year's finest mathematics writing from around the world

The year's finest writing on mathematics from around the world

The year's finest writing on mathematics from around the world, with a foreword by Nobel Prize – winning physicist Roger Penrose

The year’s most memorable writing on mathematics

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Essay Samples on Mathematics in Everyday Life

Math: the efficient and effective methods to study math.

Math is everywhere; it should be one of the wonders of the world. In a way, Math is a fundamental part of who I am. It’s always been there for me. Yes, a bit strange coming from a high school student. Usually students despise quadratic...

Mathematics in Everyday Life

Math Discovery and Mathematical Patterns in Standard of Living

Mathematics is literally defined as the study of numbers, quantities, formulas and patterns but in my own understanding, it is the world of numbers and with that it is how the world works. Mathematics is also the study of things, the relationships between things, and...

Problem Solving: Use of Math in Our Everyday Life

What I say about math is that I really don’t like it, but at the end of the day through high school math I have learned how to solve problems and not give up when I don’t fully understand something. I dislike math, but I do need it. The reason why I dislike math is that...

Problem Solving

Doubt as a Key to Mathematical Knowledge

In my arabic culture, doubt, especially when directed at supperiors, is considered extremely disrespectful. In contrast the proverb, “Doubt is the key to knowledge” indicates that doubt should be looked at in a positive light and specifically as a way of knowing. However doubt is...

The Application of Persistence and Perseverance in Mathematics

All children can benefit from studying and developing strong skills in mathematics. Primarily, learning mathematics improves problem-solving skills, and working through problems can teach persistence and perseverance. Mathematics is essential in daily life for such activities as counting, cooking, managing money, and building things. Beyond...

Persistence

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The Essence of Mathematics and Its Significance Towards the Behavior of Nature

Mathematics plays an integral part in our daily living, because everything we see, touch, and feel you can’t hide the fact that there is a math involved. Earth doesn’t appear how it looks today if scientists, don’t compute or used mathematics in making our world...

Mathematical Predictions

The Power of Mathematics: Unveiling its Influence on Nature and Phenomena

Introduction Mathematics plays an integral part in our daily living, because everything we see, touch, and feel you can’t hide the fact that there is a math involved. Earth doesn’t appear how it looks today if scientists, don’t compute or used mathematics in making our...

Role of Education

The Meaning of Application of Principles in Real Life

The realm of mathematics have a variety of implications on many real word activities that take place in today’s society. From the construction of a buildings to the usage of models in stocks and investment, math has a very effective role in the productivity and...

Life Without Principle

The Relationship Between Mandala and Mathematic Studies

It is an undeniable fact that numbers have an impact on our lives and cover a very large part of our lives. Although many people think that mathematics consists of only symbols and specific rules, in spite of it seems complex when you look into...

Discovering the Effectiveness of College Algebra

Mathematics education at the college level is facing many challenges. These challenges are occurring at a time when most experts believe that students are going to need stronger mathematical skills than ever before in order to compete in the workforce (National Council of Teachers of...

College Students

A Report On The Fibonacci Sequence

“Number rules the universe” ~ Pythagoras Numbers are found everywhere in in all aspects of human life. From the start of the day till the moment we fall asleep, we are surrounded with technology of which lots are made possible by numbers. One example are...

Mathematical Models

The Main Drivers of My Fascination of Mathematics

One of the most striking aspects of mathematics for me is how something so seemingly abstract can have such a major purpose in the inner mechanisms of the universe. For example, which number, when multiplied by itself, is -1? By inspection, you can see that...

Personal Growth and Development
Personal Life

The Use Of Probability Theorem In Everyday Life

Throughout daily life probabilty usage is prevalent throughout all hours of life. Barometers can't anticipate precisely how climates manifest, but utilizing apparatuses and special equipment to decide probability for certain types of weather. By example if there's a certain possibility for drizzle, at that point...

Mathematics Is Not Scary, It’s Beautiful

Mathematics is often times seen as dark and scary. People specially students tried to avoid it. There are students are students tries to take courses that doesn’t have math. Well in fact it is unavoidable since math is seen everywhere and it is not scary....

Beauty Is The Creation Of Mathematics

“You are beautiful no matter what they say words can't bring you down, Oh no, You are beautiful in every single way yes words can't bring you down, Oh no, so don't you bring me down today”, sang by Christina Aguilera. I love this song...

The Beautiful Nature Of Mathematics

Beauty, as its definition given by Miriam Dictionary, is the quality or aggregate of qualities in a person or thing that gives pleasure to the senses or pleasurably exalts in the mind or spirit. In addition, as Cambridge Dictionary, is the quality of being pleasing,...

Golden Mean

Mathematics In Every Aspect Around Us

Mathematics, as complex and absurd it may sound, is literally everywhere. Everywhere in a sense that it is frequently applied in our day-to-day activities, such as cooking (when we make correct measurements of ingredients), planning our daily agenda (how much time we will allocate for...

Mathematics Is Not Just About Numbers, It’s Also About Beauty

It has been said that “Beauty is in the eye of the beholder” for which many may believe is correct, but for some individuals does not accept this quotation. Yes, many may have their differences when it comes to preferences of foods, clothing, gadgets and...

Perfection And Beauty: My Vision Of Mathematics

How we can say Mathematics is perfect? For me Math is perfect because of the many uses or the different uses of mathematics, the benefits of math and the involvement of math in our daily life and how math contributes in our daily life. Mathematics...

The Role Of Mathematics In Creating Beauty

The beauty of mathematics is that it is not a mathematical equation, but rather a concept. I am one of those who believes that mathematics fits not only human life but also in the beauty of nature. It incorporates as part and forms everything in...

Leonardo Da Vinci
Natural Environment

Best topics on Mathematics in Everyday Life

1. Math: The Efficient and Effective Methods to Study Math

2. Math Discovery and Mathematical Patterns in Standard of Living

3. Problem Solving: Use of Math in Our Everyday Life

4. Doubt as a Key to Mathematical Knowledge

5. The Application of Persistence and Perseverance in Mathematics

6. The Essence of Mathematics and Its Significance Towards the Behavior of Nature

7. The Power of Mathematics: Unveiling its Influence on Nature and Phenomena

8. The Meaning of Application of Principles in Real Life

9. The Relationship Between Mandala and Mathematic Studies

10. Discovering the Effectiveness of College Algebra

11. A Report On The Fibonacci Sequence

12. The Main Drivers of My Fascination of Mathematics

13. The Use Of Probability Theorem In Everyday Life

14. Mathematics Is Not Scary, It’s Beautiful

15. Beauty Is The Creation Of Mathematics

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260 Interesting Math Topics for Essays & Research Papers

Mathematics is the science of numbers and shapes. Writing about it can give you a fresh perspective and help to clarify difficult concepts. You can even use mathematical writing as a tool in problem-solving.

In this article, you will find plenty of interesting math topics. Besides, you will learn about branches of mathematics that you can choose from. And if the thought of letters and numbers makes your head swim, try our custom writing service . Our professionals will craft a paper for you in no time!

And now, let’s proceed to math essay topics and tips.

🔝 Top 10 Interesting Math Topics

✅ branches of mathematics, ✨ fun math topics.

🏫 Math Topics for High School
🎓 College Math Topics
🤔 Advanced Math
📚 Math Research
✏️ Math Education
💵 Business Math

🔍 References

Number theory in everyday life.
Logicist definitions of mathematics.
Multivariable vs. vector calculus.
4 conditions of functional analysis.
Random variable in probability theory.
How is math used in cryptography?
The purpose of homological algebra.
Concave vs. convex in geometry.
The philosophical problem of foundations.
Is numerical analysis useful for machine learning?

What exactly is mathematics ? First and foremost, it is very old. Ancient Greeks and Persians were already utilizing mathematical tools. Nowadays, we consider it an interdisciplinary language.

Biologists, linguists, and sociologists alike use math in their work. And not only that, we all deal with it in our daily lives. For instance, it manifests in the measurement of time. We often need it to calculate how much our groceries cost and how much paint we need to buy to cover a wall.

Simply put, mathematics is a universal instrument for problem-solving. We can divide pure math into three branches: geometry, arithmetic, and algebra. Let’s take a closer look:

Geometry By studying geometry, we try to comprehend our physical surroundings. Geometric shapes can be simple, like a triangle. Or, they can form complicated figures, like a rhombicosidodecahedron.
Arithmetic Arithmetic deals with numbers and simple operations: subtraction, addition, division, and multiplication.
Algebra Algebra is used when the exact numbers are unclear. Instead, they are replaced with letters. Businesses often need algebra to predict their sales.

It’s true that most high school students don’t like math. However, that doesn’t mean it can’t be a fun and compelling subject. In the following section, you will find plenty of enthralling mathematical topics for your paper.

If you’re struggling to start working on your essay, we have some fun and cool math topics to offer. They will definitely engage you and make the writing process enjoyable. Besides, fun math topics can show everyone that even math can be entertaining or even a bit silly.

The link between mathematics and art – analyzing the Golden Ratio in Renaissance-era paintings.
An evaluation of Georg Cantor’s set theory.
The best approaches to learning math facts and developing number sense.
Different approaches to probability as explored through analyzing card tricks.
Chess and checkers – the use of mathematics in recreational activities.
The five types of math used in computer science.
Real-life applications of the Pythagorean Theorem .
A study of the different theories of mathematical logic.
The use of game theory in social science.
Mathematical definitions of infinity and how to measure it.
What is the logic behind unsolvable math problems?
An explanation of mean, mode, and median using classroom math grades.
The properties and geometry of a Möbius strip.
Using truth tables to present the logical validity of a propositional expression.
The relationship between Pascal’s Triangle and The Binomial Theorem.
The use of different number types: the history.
The application of differential geometry in modern architecture.
A mathematical approach to the solution of a Rubik’s Cube.
Comparison of predictive and prescriptive statistical analyses.
Explaining the iterations of the Koch snowflake.
The importance of limits in calculus.
Hexagons as the most balanced shape in the universe.
The emergence of patterns in chaos theory.
What were Euclid’s contributions to the field of mathematics?
The difference between universal algebra and abstract algebra.

🏫 Math Essay Topics for High School

When writing a math paper, you want to demonstrate that you understand a concept. It can be helpful if you need to prepare for an exam. Choose a topic from this section and decide what you want to discuss.

Explain what we need Pythagoras’ theorem for.
What is a hyperbola?
Describe the difference between algebra and arithmetic.
When is it unnecessary to use a calculator ?
Find a connection between math and the arts.
How do you solve a linear equation?
Discuss how to determine the probability of rolling two dice.
Is there a link between philosophy and math?
What types of math do you use in your everyday life?
What is the numerical data?
Explain how to use the binomial theorem.
What is the distributive property of multiplication?
Discuss the major concepts in ancient Egyptian mathematics .
Why do so many students dislike math?
Should math be required in school?
How do you do an equivalent transformation?
Why do we need imaginary numbers?
How can you calculate the slope of a curve?
What is the difference between sine, cosine, and tangent?
How do you define the cross product of two vectors?
What do we use differential equations for?
Investigate how to calculate the mean value.
Define linear growth.
Give examples of different number types.
How can you solve a matrix?

🎓 College Math Topics for a Paper

Sometimes you need more than just formulas to explain a complex idea. That’s why knowing how to express yourself is crucial. It is especially true for college-level mathematics. Consider the following ideas for your next research project:

What do we need n-dimensional spaces for?
Explain how card counting works.
Discuss the difference between a discrete and a continuous probability distribution .
How does encryption work?
Describe extremal problems in discrete geometry.
What can make a math problem unsolvable?
Examine the topology of a Möbius strip.

What is K-theory?
Discuss the core problems of computational geometry.
Explain the use of set theory .
What do we need Boolean functions for?
Describe the main topological concepts in modern mathematics.
Investigate the properties of a rotation matrix.
Analyze the practical applications of game theory.
How can you solve a Rubik’s cube mathematically?
Explain the math behind the Koch snowflake.
Describe the paradox of Gabriel’s Horn.
How do fractals form?
Find a way to solve Sudoku using math.
Why is the Riemann hypothesis still unsolved?
Discuss the Millennium Prize Problems.
How can you divide complex numbers?
Analyze the degrees in polynomial functions.
What are the most important concepts in number theory?
Compare the different types of statistical methods.

🤔 Advanced Topics in Math to Write a Paper on

Once you have passed the trials of basic math, you can move on to the advanced section. This area includes topology, combinatorics, logic, and computational mathematics. Check out the list below for enticing topics to write about:

What is an abelian group?
Explain the orbit-stabilizer theorem.
Discuss what makes the Burnside problem influential.
What fundamental properties do holomorphic functions have?
How does Cauchy’s integral theorem lead to Cauchy’s integral formula?
How do the two Picard theorems relate to each other?
When is a trigonometric series called a Fourier series?
Give an example of an algorithm used for machine learning.
Compare the different types of knapsack problems.
What is the minimum overlap problem?
Describe the Bernoulli scheme.
Give a formal definition of the Chinese restaurant process.
Discuss the logistic map in relation to chaos.
What do we need the Feigenbaum constants for?
Define a difference equation.
Explain the uses of the Fibonacci sequence.
What is an oblivious transfer?
Compare the Riemann and the Ruelle zeta functions.
How can you use elementary embeddings in model theory?
Analyze the problem with the wholeness axiom and Kunen’s inconsistency theorem.
How is Lie algebra used in physics ?
Define various cases of algebraic cycles.
Why do we need étale cohomology groups to calculate algebraic curves?
What does non-Euclidean geometry consist of?
How can two lines be ultraparallel?

📚 Math Research Topics for a Paper

Choosing the right topic is crucial for a successful research paper in math. It should be hard enough to be compelling, but not exceeding your level of competence. If possible, stick to your area of knowledge. This way your task will become more manageable. Here are some ideas:

Write about the history of calculus.
Why are unsolved math problems significant?
Find reasons for the gender gap in math students.
What are the toughest mathematical questions asked today?
Examine the notion of operator spaces.
How can we design a train schedule for a whole country?
What makes a number big?

Mathematical writing should be well-structured, precise, and easy readable

How can infinities have various sizes?
What is the best mathematical strategy to win a game of Go?
Analyze natural occurrences of random walks in biology.
Explain what kind of mathematics was used in ancient Persia.
Discuss how the Iwasawa theory relates to modular forms.
What role do prime numbers play in encryption?
How did the study of mathematics evolve?
Investigate the different Tower of Hanoi solutions.
Research Napier’s bones. How can you use them?
What is the best mathematical way to find someone who is lost in a maze?
Examine the Traveling Salesman Problem. Can you find a new strategy?
Describe how barcodes function.
Study some real-life examples of chaos theory. How do you define them mathematically?
Compare the impact of various ground-breaking mathematical equations .
Research the Seven Bridges of Königsberg. Relate the problem to the city of your choice.
Discuss Fisher’s fundamental theorem of natural selection.
How does quantum computing work?
Pick an unsolved math problem and say what makes it so difficult.

✏️ Math Education Research Topics

For many teachers, the hardest part is to keep the students interested. When it comes to math, it can be especially challenging. It’s crucial to make complicated concepts easy to understand. That’s why we need research on math education.

Compare traditional methods of teaching math with unconventional ones.
How can you improve mathematical education in the U.S.?
Describe ways of encouraging girls to pursue careers in STEM fields.
Should computer programming be taught in high school?
Define the goals of mathematics education .
Research how to make math more accessible to students with learning disabilities .
At what age should children begin to practice simple equations?
Investigate the effectiveness of gamification in algebra classes.
What do students gain from taking part in mathematics competitions?
What are the benefits of moving away from standardized testing ?
Describe the causes of “ math anxiety .” How can you overcome it?
Explain the social and political relevance of mathematics education.
Define the most significant issues in public school math teaching.
What is the best way to get children interested in geometry?
How can students hone their mathematical thinking outside the classroom?
Discuss the benefits of using technology in math class.
In what way does culture influence your mathematical education?
Explore the history of teaching algebra.
Compare math education in various countries.

How does dyscalculia affect a student’s daily life?
Into which school subjects can math be integrated?
Has a mathematics degree increased in value over the last few years?
What are the disadvantages of the Common Core Standards?
What are the advantages of following an integrated curriculum in math?
Discuss the benefits of Mathcamp.

🧮 Algebra Topics for a Paper

The elegance of algebra stems from its simplicity. It gives us the ability to express complex problems in short equations. The world was changed forever when Einstein wrote down the simple formula E=mc². Now, if your algebra seminar requires you to write a paper, look no further! Here are some brilliant prompts:

Give an example of an induction proof.
What are F-algebras used for?
What are number problems?
Show the importance of abstract algebraic thinking .
Investigate the peculiarities of Fermat’s last theorem.
What are the essentials of Boolean algebra?
Explore the relationship between algebra and geometry.
Compare the differences between commutative and noncommutative algebra.
Why is Brun’s constant relevant?
How do you factor quadratics?
Explain Descartes’ Rule of Signs.
What is the quadratic formula?
Compare the four types of sequences and define them.
Explain how partial fractions work.
What are logarithms used for?
Describe the Gaussian elimination.
What does Cramer’s rule state?
Explore the difference between eigenvectors and eigenvalues.
Analyze the Gram-Schmidt process in two dimensions.
Explain what is meant by “range” and “domain” in algebra.
What can you do with determinants?
Learn about the origin of the distance formula.
Find the best way to solve math word problems.
Compare the relationships between different systems of equations.
Explore how the Rubik’s cube relates to group theory.

📏 Geometry Topics for a Research Paper

Shapes and space are the two staples of geometry. Since its appearance in ancient times, it has evolved into a major field of study. Geometry’s most recent addition, topology, explores what happens to an object if you stretch, shrink, and fold it. Things can get pretty crazy from here! The following list contains 25 interesting geometry topics:

What are the Archimedean solids?
Find real-life uses for a rhombicosidodecahedron.
What is studied in projective geometry?
Compare the most common types of transformations.
Explain how acute square triangulation works.
Discuss the Borromean ring configuration.
Investigate the solutions to Buffon’s needle problem.
What is unique about right triangles?

The role of study of non-Euclidean geometry

Describe the notion of Dirac manifolds.
Compare the various relationships between lines.
What is the Klein bottle?
How does geometry translate into other disciplines, such as chemistry and physics?
Explore Riemannian manifolds in Euclidean space.
How can you prove the angle bisector theorem?
Do a research on M.C. Escher’s use of geometry.
Find applications for the golden ratio .
Describe the importance of circles.
Investigate what the ancient Greeks knew about geometry.
What does congruency mean?
Study the uses of Euler’s formula.
How do CT scans relate to geometry?
Why do we need n-dimensional vectors?
How can you solve Heesch’s problem?
What are hypercubes?
Analyze the use of geometry in Picasso’s paintings.

➗ Calculus Topics to Write a Paper on

You can describe calculus as a more complicated algebra. It’s a study of change over time that provides useful insights into everyday problems. Applied calculus is required in a variety of fields such as sociology, engineering, or business. Consult this list of compelling topics on a calculus paper:

What are the differences between trigonometry, algebra, and calculus?
Explain the concept of limits.
Describe the standard formulas needed for derivatives.
How can you find critical points in a graph?
Evaluate the application of L’Hôpital’s rule.
How do you define the area between curves?
What is the foundation of calculus?

Calculus was developed by Isaac Newton and Gottfried Leibnitz.

How does multivariate calculus work?
Discuss the use of Stokes’ theorem.
What does Leibniz’s integral rule state?
What is the Itô stochastic integral?
Explore the influence of nonstandard analysis on probability theory.
Research the origins of calculus.
Who was Maria Gaetana Agnesi?
Define a continuous function.
What is the fundamental theorem of calculus?
How do you calculate the Taylor series of a function?
Discuss the ways to resolve Runge’s phenomenon.
Explain the extreme value theorem.
What do we need predicate calculus for?
What are linear approximations?
When does an integral become improper?
Describe the Ratio and Root Tests.
How does the method of rings work?
Where do we apply calculus in real-life situations?

💵 Business Math Topics to Write About

You don’t have to own a company to appreciate business math. Its topics range from credits and loans to insurance, taxes, and investment. Even if you’re not a mathematician, you can use it to handle your finances. Sounds interesting? Then have a look at the following list:

What are the essential skills needed for business math?
How do you calculate interest rates?
Compare business and consumer math.
What is a discount factor?
How do you know that an investment is reasonable?
When does it make sense to pay a loan with another loan?
Find useful financing techniques that everyone can use.
How does critical path analysis work?
Explain how loans work.
Which areas of work utilize operations research?
How do businesses use statistics?
What is the economic lot scheduling problem?
Compare the uses of different chart types.
What causes a stock market crash?
How can you calculate the net present value?
Explore the history of revenue management.
When do you use multi-period models?
Explain the consequences of depreciation.
Are annuities a good investment?
Would the U.S. financially benefit from discontinuing the penny?
What caused the United States housing crash in 2008?
How do you calculate sales tax?
Describe the notions of markups and markdowns.
Investigate the math behind debt amortization.
What is the difference between a loan and a mortgage?

With all these ideas, you are perfectly equipped for your next math paper. Good luck!

What Is Calculus?: Southern State Community College
What Is Mathematics?: Tennessee Tech University
What Is Geometry?: University of Waterloo
What Is Algebra?: BBC
Ten Simple Rules for Mathematical Writing: Ohio State University
Practical Algebra Lessons: Purplemath
Topics in Geometry: Massachusetts Institute of Technology
The Geometry Junkyard: All Topics: Donald Bren School of Information and Computer Sciences
Calculus I: Lamar University
Business Math for Financial Management: The Balance Small Business
What Is Mathematics: Life Science
What Is Mathematics Education?: University of California, Berkeley
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I need a writer on algebra. I am a PhD student.Can i be helped by anybody/expert?

Please I want to do my MPhil research on algebra if you can help me

shall your university help me on research in mathematics ?

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14 May 2024

Why mathematics is set to be revolutionized by AI

Thomas Fink 0

Thomas Fink is the director of the London Institute for Mathematical Sciences, UK.

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You have full access to this article via your institution.

Giving birth to a conjecture — a proposition that is suspected to be true, but needs definitive proof — can feel to a mathematician like a moment of divine inspiration. Mathematical conjectures are not merely educated guesses. Formulating them requires a combination of genius, intuition and experience. Even a mathematician can struggle to explain their own discovery process. Yet, counter-intuitively, I think that this is the realm in which machine intelligence will initially be most transformative.

In 2017, researchers at the London Institute for Mathematical Sciences, of which I am director, began applying machine learning to mathematical data as a hobby. During the COVID-19 pandemic, they discovered that simple artificial intelligence (AI) classifiers can predict an elliptic curve’s rank 1 — a measure of its complexity. Elliptic curves are fundamental to number theory, and understanding their underlying statistics is a crucial step towards solving one of the seven Millennium Problems, which are selected by the Clay Mathematics Institute in Providence, Rhode Island, and carry a prize of US$1 million each. Few expected AI to make a dent in this high-stakes arena.

AI now beats humans at basic tasks — new benchmarks are needed, says major report

AI has made inroads in other areas, too. A few years ago, a computer program called the Ramanujan Machine produced new formulae for fundamental constants 2 , such as π and e . It did so by exhaustively searching through families of continued fractions — a fraction whose denominator is a number plus a fraction whose denominator is also a number plus a fraction and so on. Some of these conjectures have since been proved, whereas others remain open problems.

Another example pertains to knot theory, a branch of topology in which a hypothetical piece of string is tangled up before the ends are glued together. Researchers at Google DeepMind, based in London, trained a neural network on data for many different knots and discovered an unexpected relationship between their algebraic and geometric structures 3 .

How has AI made a difference in areas of mathematics in which human creativity was thought to be essential?

First, there are no coincidences in maths. In real-world experiments, false negatives and false positives abound. But in maths, a single counterexample leaves a conjecture dead in the water. For example, the Pólya conjecture states that most integers below any given integer have an odd number of prime factors. But in 1960, it was found that the conjecture does not hold for the number 906,180,359. In one fell swoop, the conjecture was falsified.

Second, mathematical data — on which AI can be trained — are cheap. Primes, knots and many other types of mathematical object are abundant. The On-Line Encyclopedia of Integer Sequences (OEIS) contains almost 375,000 sequences — from the familiar Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, ...) to the formidable Busy Beaver sequence (0, 1, 4, 6, 13, …), which grows faster than any computable function. Scientists are already using machine-learning tools to search the OEIS database to find unanticipated relationships.

DeepMind AI outdoes human mathematicians on unsolved problem

AI can help us to spot patterns and form conjectures. But not all conjectures are created equal. They also need to advance our understanding of mathematics. In his 1940 essay A Mathematician’s Apology , G. H. Hardy explains that a good theorem “should be one which is a constituent in many mathematical constructs, which is used in the proof of theorems of many different kinds”. In other words, the best theorems increase the likelihood of discovering new theorems. Conjectures that help us to reach new mathematical frontiers are better than those that yield fewer insights. But distinguishing between them requires an intuition for how the field itself will evolve. This grasp of the broader context will remain out of AI’s reach for a long time — so the technology will struggle to spot important conjectures.

But despite the caveats, there are many upsides to wider adoption of AI tools in the maths community. AI can provide a decisive edge and open up new avenues for research.

Mainstream mathematics journals should also publish more conjectures. Some of the most significant problems in maths — such as Fermat’s Last Theorem, the Riemann hypothesis, Hilbert’s 23 problems and Ramanujan’s many identities — and countless less-famous conjectures have shaped the course of the field. Conjectures speed up research by pointing us in the right direction. Journal articles about conjectures, backed up by data or heuristic arguments, will accelerate discovery.

Last year, researchers at Google DeepMind predicted 2.2 million new crystal structures 4 . But it remains to be seen how many of these potential new materials are stable, can be synthesized and have practical applications. For now, this is largely a task for human researchers, who have a grasp of the broad context of materials science.

Similarly, the imagination and intuition of mathematicians will be required to make sense of the output of AI tools. Thus, AI will act only as a catalyst of human ingenuity, rather than a substitute for it.

Nature 629 , 505 (2024)

doi: https://doi.org/10.1038/d41586-024-01413-w

He, Y.-H., Lee, K.-H., Oliver, T. & Pozdnyakov, A. Preprint at arXiv https://doi.org/10.48550/arXiv.2204.10140 (2024).

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For everyone whose relationship with mathematics is distant or broken, Jo Boaler , a professor at Stanford Graduate School of Education (GSE), has ideas for repairing it. She particularly wants young people to feel comfortable with numbers from the start — to approach the subject with playfulness and curiosity, not anxiety or dread.

“Most people have only ever experienced what I call narrow mathematics — a set of procedures they need to follow, at speed,” Boaler says. “Mathematics should be flexible, conceptual, a place where we play with ideas and make connections. If we open it up and invite more creativity, more diverse thinking, we can completely transform the experience.”

“Mathematics should be flexible, conceptual, a place where we play with ideas and make connections," says Professor Jo Boaler. (Photo: Robert Houser Photography)

Boaler, the Nomellini and Olivier Professor of Education at the GSE, is the co-founder and faculty director of Youcubed , a Stanford research center that provides resources for math learning that has reached more than 230 million students in over 140 countries. In 2013 Boaler, a former high school math teacher, produced “How to Learn Math,” the first massive open online course (MOOC) on mathematics education. She leads workshops and leadership summits for teachers and administrators, and her online courses have been taken by over a million users.

In her new book, Math-ish: Finding Creativity, Diversity, and Meaning in Mathematics , Boaler argues for a broad, inclusive approach to math education, offering strategies and activities for learners at any age. We spoke with her about why creativity is an important part of mathematics, the impact of representing numbers visually and physically, and how what she calls “ishing” a math problem can help students make better sense of the answer.

What do you mean by “math-ish” thinking?

It’s a way of thinking about numbers in the real world, which are usually imprecise estimates. If someone asks how old you are, how warm it is outside, how long it takes to drive to the airport – these are generally answered with what I call “ish” numbers, and that’s very different from the way we use and learn numbers in school.

In the book I share an example of a multiple-choice question from a nationwide exam where students are asked to estimate the sum of two fractions: 12/13 + 7/8. They’re given four choices for the closest answer: 1, 2, 19, or 21. Each of the fractions in the question is very close to 1, so the answer would be 2 — but the most common answer 13-year-olds gave was 19. The second most common was 21.

I’m not surprised, because when students learn fractions, they often don’t learn to think conceptually or to consider the relationship between the numerator or denominator. They learn rules about creating common denominators and adding or subtracting the numerators, without making sense of the fraction as a whole. But stepping back and judging whether a calculation is reasonable might be the most valuable mathematical skill a person can develop.

But don’t you also risk sending the message that mathematical precision isn’t important?

I’m not saying precision isn’t important. What I’m suggesting is that we ask students to estimate before they calculate, so when they come up with a precise answer, they’ll have a real sense for whether it makes sense. This also helps students learn how to move between big-picture and focused thinking, which are two different but equally important modes of reasoning.

Some people ask me, “Isn’t ‘ishing’ just estimating?” It is, but when we ask students to estimate, they often groan, thinking it’s yet another mathematical method. But when we ask them to “ish” a number, they're more willing to offer their thinking.

Ishing helps students develop a sense for numbers and shapes. It can help soften the sharp edges in mathematics, making it easier for kids to jump in and engage. It can buffer students against the dangers of perfectionism, which we know can be a damaging mind-set. I think we all need a little more ish in our lives.

You also argue that mathematics should be taught in more visual ways. What do you mean by that?

For most people, mathematics is an almost entirely symbolic, numerical experience. Any visuals are usually sterile images in a textbook, showing bisecting angles, or circles divided into slices. But the way we function in life is by developing models of things in our minds. Take a stapler: Knowing what it looks like, what it feels and sounds like, how to interact with it, how it changes things — all of that contributes to our understanding of how it works.

There’s an activity we do with middle-school students where we show them an image of a 4 x 4 x 4 cm cube made up of smaller 1 cm cubes, like a Rubik’s Cube. The larger cube is dipped into a can of blue paint, and we ask the students, if they could take apart the little cubes, how many sides would be painted blue? Sometimes we give the students sugar cubes and have them physically build a larger 4 x 4 x 4 cube. This is an activity that leads into algebraic thinking.

Some years back we were interviewing students a year after they’d done that activity in our summer camp and asked what had stayed with them. One student said, ‘I’m in geometry class now, and I still remember that sugar cube, what it looked like and felt like.’ His class had been asked to estimate the volume of their shoes, and he said he’d imagined his shoes filled with 1 cm sugar cubes in order to solve that question. He had built a mental model of a cube.

When we learn about cubes, most of us don’t get to see and manipulate them. When we learn about square roots, we don’t take squares and look at their diagonals. We just manipulate numbers.

I wonder if people consider the physical representations more appropriate for younger kids.

That’s the thing — elementary school teachers are amazing at giving kids those experiences, but it dies out in middle school, and by high school it’s all symbolic. There’s a myth that there’s a hierarchy of sophistication where you start out with visual and physical representations and then build up to the symbolic. But so much of high-level mathematical work now is visual. Here in Silicon Valley, if you look at Tesla engineers, they're drawing, they're sketching, they're building models, and nobody says that's elementary mathematics.

Visualization of different ways to calculate 38 times 5

Click to enlarge: A depiction of various ways to calculate 38 x 5, numerically and visually. (Image: Courtesy of Jo Boaler)

There’s an example in the book where you’ve asked students how they would calculate 38 x 5 in their heads, and they come up with several different ways of arriving at the same answer. The creativity is fascinating, but wouldn’t it be easier to teach students one standard method?

That narrow, rigid version of mathematics where there’s only one right approach is what most students experience, and it’s a big part of why people have such math trauma. It keeps them from realizing the full range and power of mathematics. When you only have students blindly memorizing math facts, they’re not developing number sense. They don’t learn how to use numbers flexibly in different situations. It also makes students who think differently believe there’s something wrong with them.

When we open mathematics to acknowledge the different ways a concept or problem can be viewed, we also open the subject to many more students. Mathematical diversity, to me, is a concept that includes both the value of diversity in people and the diverse ways we can see and learn mathematics. When we bring those forms of diversity together, it’s powerful. If we want to value different ways of thinking and problem-solving in the world, we need to embrace mathematical diversity.

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