what is mathematics in nature essay

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Mathematics in Nature Essay Example

Mathematics surrounds us. Math is everywhere where nature has it. We can see the beauty in nature with the help of math. The patterns, shapes, and designs in nature are God’s beautiful creations. 

In this topic, I learned that nature has also math. Math regulates our universe whereas if we consider our world without it: if we hadn’t learned about basic math operations, as well as the various calculations, neither of the worlds would have turned out the way they do.  It is mathematics that has allowed humanity to discover so much about the universe, nature, among other things. In patterns, shells have natural patterns which are spiral, spider webs illustrate beautiful geometric patterns, etc. In shapes, honeycombs repeating the pattern of hexagons same with the dragonfly's wings with a hexagon pattern that can only be seen in the microscope. The fractals such as ferns and snowflakes which it has the same shape even if it is zoom in or zoom out. In outer space, our galaxy is spiral, “Fibonacci spiral.” I learned that everything we’ve seen in nature by our naked eyes or microscopically has math inside it. The Fibonacci sequence and the golden ratio are the best examples of seeing beauty in nature. Fibonacci sequence is one of the most popular and easy formulas in Math. Each number in the sequence is the sum of the two numbers that forego it. For example, 0,1,1,2,3,5,8,13,21, and so on. This sequence is understandable and easy where everyone will understand it. It can be seen in shells, natural phenomena such as typhoons/hurricanes, waves, sunflowers, spider webs, and many more. The golden ratio is a mathematical relationship where the ratio of two numbers in which the ratio of the sum to a large number is similar to the ratio of the larger number to the smaller. For example, the Fibonacci sequence is 0,1,1,2,3,5,8,13…, 8/5, the large number will be divided into smaller numbers which result in the golden ratio of 1.6000. 

My picture has a fern which is one of the arts of nature. The color of the fern is yellow-green and has a repetitive pattern which makes it a beauty. The role of mathematics in my picture is that it has math, the fractals. Fractal is a pattern that repeats the structures of nature at different scales. The fern is one of the examples of it. The leaves of it have patterns that are beautifully designed. Even if we zoom in and zoom it out, we can see a similar pattern or shale that is seen by our naked eye. Its geometric shape can be seen in every detail. The leaf structure of a fern has different sizes.  From the large in the bottom to the smaller leaf on the top. The front has the same shape from the bottom to the top. It has Fibonacci in it. From top to bottom, the number of the leaf sum the two numbers that precede it which makes it orderly beautiful. Fern leaves seem like a copy or a duplicate but with the same overall shape but different sizes. The leaf is just like the small copy of the fern. In short, the role of mathematics in this picture is to determine its mathematical pattern and beauty hidden in it. To explore the pattern using the math formula specifically the Fibonacci sequence. 

The significance of this picture in my life is that it gives me so much excitement to explore and see more beauty in nature. I realized that nature has math but we unobserved it because we only know that it is beautiful and made by nature, we unnoticed the patterns are hidden in it. I visually perceived that ferns are much appealing so that’s why more people are likely to place them on their houses. This picture gives me a lot of ideas about math especially the Fibonacci sequence. There’s a lot of concepts came into my mind when I captured this photo. I clearly understood how the fern becomes a fractal and how does it relates to math. It also signifies that chasing a dream will start from the bottom and end at the top.

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May 20, 2020

The mystique of mathematics: 5 beautiful math phenomena

by Sherry Landow, University of New South Wales

Mathematics is visible everywhere in nature, even where we are not expecting it. It can help explain the way galaxies spiral, a seashell curves, patterns replicate, and rivers bend.

Even subjective emotions, like what we find beautiful, can have mathematic explanations.

"Maths is not only seen as beautiful—beauty is also mathematical," says Dr. Thomas Britz, a lecturer in UNSW Science's School of Mathematics & Statistics. "The two are intertwined."

Dr. Britz works in combinatorics, a field focused on complex counting and puzzle solving. While combinatorics sits within pure mathematics, Dr. Britz has always been drawn to the philosophical questions about mathematics.

He also finds beauty in the mathematical process.

"From a personal point of view, maths is just really fun to do. I've loved it ever since I was a little kid.

"Sometimes, the beauty and enjoyment of maths is in the concepts, or in the results, or in the explanations. Other times, it's the thought processes that make your mind turn in nice ways, the emotions that you get, or just working in the flow—like getting lost in a good book."

Here, Dr. Britz shares some of his favorite connections between maths and beauty.

1. Symmetry—but with a touch of surprise

In 2018, Dr. Britz gave a TEDx talk on the Mathematics of Emotion, where he used recent studies on maths and emotions to touch on how maths might help explain emotions, like beauty.

"Our brains reward us when we recognize patterns, whether this is seeing symmetry, organising parts of a whole, or puzzle-solving," he says.

"When we spot something deviating from a pattern—when there's a touch of the unexpected—our brains reward us once again. We feel delight and excitement."

For example, humans perceive symmetrical faces as beautiful. However, a feature that breaks up the symmetry in a small, interesting or surprising way—such as a beauty spot—adds to the beauty.

"This same idea can be seen in music," says Dr. Britz. "Patterned and ordered sounds with a touch of the unexpected can have added personality, charm and depth."

Many mathematical concepts exhibit a similar harmony between pattern and surprise, elegance and chaos, truth and mystery.

"The interwovenness of maths and beauty is itself beautiful to me," says Dr. Britz.

2. Fractals: infinite and ghostly

Fractals are self-referential patterns that repeat themselves, to some degree, on smaller scales. The closer you look, the more repetitions you will see—like the fronds and leaves of a fern.

"These repeating patterns are everywhere in nature," says Dr. Britz. "In snowflakes, river networks, flowers, trees, lightning strikes—even in our blood vessels."

Fractals in nature can often only replicate by several layers, but theoretic fractals can be infinite. Many computer-generated simulations have been created as models of infinite fractals.

"You can keep focusing on a fractal, but you'll never get to the end of it," says Dr. Britz.

"Fractals are infinitely deep. They are also infinitely ghostly.

"You might have a whole page full of fractals, but the total area that you've drawn is still zero, because it's just a bunch of infinite lines."

3. Pi: an unknowable truth

Pi (or 'π') is a number often first learned in high school geometry. In simplest terms, it is a number slightly more than 3.

Pi is mostly used when dealing with circles, such as calculating the circumference of a circle using only its diameter. The rule is that, for any circle, the distance around the edge is roughly 3.14 times the distance across the center of the circle.

But Pi is a lot more than this.

"When you look into other aspects of nature, you will suddenly find Pi everywhere," says Dr. Britz. "Not only is it linked to every circle, but Pi sometimes pops up in formulas that have nothing to do with circles, like in probability and calculus."

Despite being the most famous number (International Pi Day is held annually on 14 March, 3.14 in American dating), there is a lot of mystery around it.

"We know a lot about Pi, but we really don't know anything about Pi," says Dr. Britz.

"There's a beauty about it—a beautiful dichotomy or tension."

Pi is infinite and, by definition, unknowable. No pattern has yet been identified in its decimal points. It's understood that any combination of numbers, like your phone number or birthday, will appear in Pi somewhere (you can search this via an online lookup tool of the first 200 million digits).

We currently know 50 trillion digits of Pi, a record broken earlier this year. But, as we cannot calculate the exact value of Pi, we can never completely calculate the circumference or area of a circle—although we can get close.

"What's going on here?" says Dr. Britz. "What is it about this strange number that somehow ties all the circles of the world together?

"There's some underlying truth to Pi, but we don't understand it. This mystique makes it all the more beautiful."

4. A golden and ancient ratio

The Golden Ratio (or 'ϕ') is perhaps the most popular mathematical theorem for beauty. It's considered the most aesthetically pleasing way to proportion an object.

The ratio can be shortened, roughly, to 1.618. When presented geometrically, the ratio creates the Golden Rectangle or the Golden Spiral.

"Throughout history, the ratio was treated as a benchmark for the ideal form, whether in architecture, artwork, or the human body," says Dr. Britz. "It was called the "Divine Proportion."

"Many famous artworks, including those by Leonardo da Vinci, were based on this ratio."

The Golden Spiral is frequently used today, especially in art, design and photography. The center of the spiral can help artists frame image focal points in aesthetically pleasing ways.

5. A paradox closer to magic

The unknowable nature of maths can make it seem closer to magic.

A famous geometrical theorem called the Banach-Tarski paradox says that if you have a ball in 3-D space and split it into a few specific pieces, there is a way to reassemble the parts so that you create two balls.

"This is already interesting, but it gets even weirder," says Dr. Britz.

"When the two new balls are created, they will both be the same size as the first ball."

Mathematically speaking, this theorem works—it is possible to reassemble the pieces in a way that doubles the balls.

"You can't do this in real life," says Dr. Britz. "But you can do it mathematically.

"That's sort of magic. That is magic."

Fractals, the Banach-Tarski paradox and Pi are just the surface of the mathematical concepts he finds beauty in.

"To experience many beautiful parts of maths, you need a lot of background knowledge," says Dr. Britz. "You need a lot of basic—and often very boring—training. It's a bit like doing a million push ups before playing a sport.

"But it is worth it. I hope that more people get to the fun bit of maths. There is so much more beauty to uncover."

Provided by University of New South Wales

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Nature by numbers: The hidden beauty of mathematics

L iving with a mathematician this year has made me realise the unsung contribution mathematics makes when it comes to providing us with the reasoning to better appreciate the beauty of nature. I’d always thought fractal symmetry, which cropped up in my physical chemistry lectures, was solely a chemical concept. You can probably imagine my surprise when I realised that this characteristic actually stemmed from mathematics. It came as an even greater shock to discover that many natural phenomena are, in fact, fractal to some degree. The Fibonacci sequence, which you may think exists only in the pages of a Dan Brown novel, is also visible in some of nature’s most exquisite structures. So, just how many of us are aware of the way in which mathematics provides us with the reasoning to be able to praise the intrinsic beauty of nature? This is exactly what I hope to achieve in this article; to show you how mathematics, something some of us may have dreaded at school, actually explains a lot of the things we see around us.

Fractal symmetry is when the same pattern is seen at increasingly small scales. In fractal symmetry, you find the same pattern within the pattern, which is why this can also be referred to as self-similarity. The best example to think of is a tree. The trunk of a tree separates into branches which then separate into smaller branches and then twigs, and these get smaller and smaller. In this way, we see a repetition. Another example is the Romanesco broccoli, but my favourite would have to be the Lotus effect. The Lotus leaves have a rough surface with micro- and nano-structures including waxy crystals that contribute to making the surface superhydrophobic. This means that any water droplets on the lotus leaves are strongly repelled and slide off the surface. While doing so, they take up the dust particles from the leaves in order to reduce the surface tension, resulting in the cleaning of the lotus leaves. This is an example of self-cleaning in nature and it is the fractal symmetry of the waxy crystals on the surface of the leaves that provides the enhanced hydrophobicity which makes this possible.

Fractal symmetry is when the same pattern is seen at increasingly small scales. In fractal symmetry, you find the same pattern within the pattern, which is why this can also be referred to as self-similarity

Another type of symmetry I wish to discuss is the so-called wallpaper symmetry. This is the mathematical classification of a two-dimensional repetitive pattern inspired by honeycomb structures. Besides often being seen in architecture and other arts such as textiles, this structure has found great use in the field of chemical catalysis. One of the finest examples of the use of catalysis is in catalytic converters used to turn pollutant gases such as nitrogen oxides and carbon monoxides into nitrogen dioxide and carbon dioxide gases, which are safer alternatives. The support for the precious rhodium or platinum metal catalysts used is cordierite monolith. The metal is dispersed on the honeycomb structure of the support which provides a larger surface area to optimise the flow of gases over the catalyst. This is a fine example of symmetry observed in nature that has now been employed on a large industrial scale and is something used by many of us every day.

Fractal and wallpaper symmetry are the two types I wanted to discuss. However, this article would be incomplete without a nod to the spirals that are too often seen in nature. Some of these spirals arise due to the golden ratio of 1.618[…] which is the most irrational number we can get. Put simply, it is the furthest away we can be from a fraction. In this way, the golden ratio gives the best spiral with no gaps. Hence, flower petals and pinecones are guided by the golden ratio, which is related to the Fibonacci sequence. In the Fibonacci sequence, each number is the sum of the two numbers preceding it. What we find is that if we take the ratio of any two numbers from the Fibonacci sequence, we get values very close to the golden ratio. In nature, the flowers and the shells are not genetically, or in any other way, programmed to abide by the mathematics of the Fibonacci sequence. This is purely a result of evolutionary design. Petals and seeds find that the golden ratio offers the best packing with minimum gaps. I find it absolutely amazing that a series of numbers on a piece of paper can explain why many elements in nature have chosen to adopt this particular configuration.

This article would be incomplete without a nod to the spirals that are too often seen in nature. Some of these spirals arise due to the golden ratio of 1.618[…] which is the most irrational number we can get

In addition to mathematics, you could not have avoided noticing the not-so-subtle mention of chemistry in this article. As I researched more into maths, I could easily find myself making connections with chemistry and much of the material I have studied to date. Thinking back to one of the conversations I’ve had with my flatmates in the kitchen, it’s clear that mathematics provides the key to untie the knots in many fields both within and outside STEM. As a chemist, I certainly see how fundamental a role mathematics plays. In this article, I hope I have enabled you to at least begin to appreciate just how much a bunch of numbers can explain to us about the universe.

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Mathematics in Nature

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Mathematics

Mathematics in Nature: Modeling Patterns in the Natural World

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From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks. Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.

Awards and Recognition

• John Adam, Winner of the 2007 recipient of the Virginia Outstanding Faculty Award, State Council of Higher Education for Virginia
• Winner of the 2003 for Professional/Scholarly Award in Mathematics and Statistics, Association of American Publishers
• One of Choice's Outstanding Academic Titles for 2004

" Mathematics in Nature is an excellent resource for bringing a greater variety of patterns into the mathematical study of nature, as well as for teaching students to think about describing natural phenomena mathematically. . . . [T]he breadth of patterns studied is phenomenal."—Will Wilson, American Scientist

"John Adam has combined his interest in the great outdoors and applied mathematics to compile one surprising example after another of how mathematics can be used to explain natural phenomena. And what examples! . . . [He] has done a great deal of reading and exposition, indulging his passions to create this compilation of mathematical models of natural phenomena, and the sheer number of examples he manages to cram into this book is testament to his efforts. There are other texts on the market which explore the connection between mathematics and nature . . . but none this wide-ranging."—Steven Morics, MAA Online

"Adam has laced his mathematical models with popular descriptions of the phenomena selected. . . . Mathematics in Nature can accordingly be read for pleasure and instruction by the select laity who are not afraid of reading between the lines of equations."—Philip J. Davis, SIAM News

"John Adam's quest is a very simple one: that is, to invite one to look around and observe the wonders of nature, both natural and biological; to ponder them; and to try to explain them at various levels with, for the most part, quite elementary mathematical concepts and techniques."—Brian D. Sleeman, Notices of the American Mathematical Association

"Reading this book progressively creates a course in mathematical modeling built around familiar, tangible, human-scale examples, with a trajectory that takes readers from dimensional estimates through geometrical modeling, linear and nonlinear dynamics, to pattern formation."— Choice

"John Adam's Mathematics in Nature illustrates how, in a friendly and lucid manner, mathematicians think about nature. Adam lets us see how mathematics is not only an ally, but is perhaps the very language that nature uses to express the beautiful. . . . This is a book that will challenge while it intrigues and excites."—Stanley David Gedzelman, Weatherwise

"Although Mathematics in Nature has not been written as a textbook, availability of such a manual shall help instructors who choose this delightful book for teaching a course in applied mathematics or mathematical modeling."—Yuri V. Rogovchenko, Zentralblatt Math

"Spanning a range of mathematical levels, this book can be used as an undergraduate textbook, a source of high school math enrichment, or can be read for pleasure by folks with an appreciation of nature but without advanced mathematical background."— Southeastern Naturalist

"Have you wondered how rainbows or sand dunes form? Does it puzzle you why drying mud forms polygonally shaped cracks? Can you explain the patterns on a butterfly's wings or how birds fly? In this delightful book, John Adam invites us to question and to share his enthusiasm for developing mathematical models to explore a wide range of everyday natural phenomena. Mathematics in Nature can be used as a text on mathematical modeling or as a book to dip into and encourage us to observe and wonder at the beauty of nature. It has the potential of becoming a classic."—Brian Sleeman, University of Leeds

"This is a book that I will want to keep close to hand so that I will not be stumped by all those seemingly simple yet subtle questions about nature: Why can fleas jump so high? Why is visibility better in rain than in fog? Why does a river meander? How high can trees grow? But it is much more than a compendium of useful facts and explanations. It is the clearest guide I have seen to the art of conceptualizing, simplifying, and modeling natural phenomena—no less than an exegesis on how good quantitative science is done."—Phillip Ball, Consultant Editor, Nature

" Mathematics in Nature leads the calculus-literate reader on a vigorous tour of nature's visible patterns—from the radiator-sailed dinosaur Dimetrodon to fracturing of dried mud and ceramic glazes, from the dispersion of rainbows and iridescence of beetles to the pearling of spider silk. Eschewing phenomena that are too small to see or too large to grasp, Adam shows how elementary college mathematics, rigorously applied, can give precise expression to everyday natural phenomena. His extraordinary range of examples and meticulous explanations document mathematics' wonderful capacity to describe and explain nature's patterns."—Lynn Arthur Steen, St. Olaf College

"This work is outstanding! The color photographs are beautiful. The writing style is splendid."—Robert B. Banks, author of Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics

"This is a unique, even great book. It is in the spirit of a number of books on topics like symmetry and chaos that look at mathematics in the context of visually striking natural and other phenomena but is more broadly based. The author leads with the phenomena and follows with the math, making the book accessible to a wider audience while still appealing to math students and faculty."—Frank Wattenberg

"This is one of the best contemporary texts on the subject, appealing to a very broad audience that will definitely love this excellent book."—Yuri V. Rogovchenko, Zentralblatt Math (European Mathematical Society)

John A. Adam’s website

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Mathematics in Nature

Modeling patterns in the natural world.

• John A. Adam
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• Language: English
• Publisher: Princeton University Press
• Copyright year: 2003
• Edition: Course Book
• Audience: Professional and scholarly;College/higher education;
• Main content: 392
• Other: 24 color illus. 84 line illus. 9 tables.
• Keywords: Quantity ; Theorem ; Wavelength ; Surface area ; Mathematics ; Calculation ; Convection ; Approximation ; Geometry ; Amplitude ; Refraction ; Equation ; Proportionality (mathematics) ; Instability ; Diameter ; Gravity wave ; Dimensional analysis ; Square root ; Reynolds number ; Lee wave ; Temperature ; Drop (liquid) ; Line segment ; Surface tension ; Curvature ; Differential equation ; Partial differential equation ; Fermi problem ; Length scale ; Density ; Earth ; Angular diameter ; Differentiable function ; Gravity ; Mathematical model ; Dimension ; Buckling ; Natural number ; Dune ; Wavenumber ; Refractive index ; Gravitational acceleration ; Kinetic energy ; Dispersion relation ; Mathematician ; Variable (mathematics) ; Boundary value problem ; Soap bubble ; Fibonacci number ; Circumference ; Initial condition ; Scattering ; Solitary wave ; Prediction ; Three-dimensional space (mathematics) ; Viscosity ; Trigonometry ; Diagram (category theory) ; Molecule ; Wave equation ; Wing loading ; Summation ; Wave ; Dimensionless quantity ; Theory ; Air mass ; Golden angle ; Vibration ; Pattern formation ; Natural frequency ; Estimation ; Cloud ; Without loss of generality ; Iridescence ; Ray (optics) ; Diffusion equation ; Iteration ; Kootenay Lake ; Notation ; Wind shear ; Arc length ; Eye (cyclone) ; Aerosol ; Ordinary differential equation ; Applied mathematics ; Surface wave ; Rayleigh scattering ; Oscillation ; Mathematical analysis ; Sine wave ; Mathematical physics ; Probability ; Temperature gradient ; Snell's law ; Wave power ; Radius of curvature ; Vertical direction ; Differential calculus ; Golden rectangle ; Two-dimensional space
• Published: October 2, 2011
• ISBN: 9781400841011

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Mathematical understanding of nature: essays on amazing physical phenomena and their understanding by mathematicians.

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V. I. Arnold

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

• Table of Contents

This is a collection of 39 essays from the distinguished mathematician Vladimir Arnold. He was a man of very strong opinions. One of these is especially pertinent for this collection:

Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.

The book’s editor notes that from the age of eleven Arnold was a member of the “Children’s Learned Society”, which had been organized by A. A. Lyapunov and run at his home. The curriculum included mathematics and physics with a bit of chemistry and biology. The current book seems to have been motivated by these early experiences.

The essays are short — none longer than about six pages — and address topics mostly in mathematics and physics. The levels of sophistication and difficulty vary widely. Some topics would be accessible to high school students with a little bit of algebra and geometry; others might challenge even specialists. In the first category is an essay on the eccentricity of the orbit of Mars. It is implicitly a lesson on intelligent estimation. In the second category is a piece about adiabatic invariants.

Arnold’s introduction includes the comment: “Examples teach no less than rules, and errors, more than correct but abstruse proofs.” It is a wonderful teaching point that is amplified by at least a few unintentional errors in the text. One, noted by the editor, is about the forward motion of a bicycle. (If you attach a string to lower pedal of a bicycle at rest and pull straight back, does the bicycle move forwards or backwards?) Another occurs in an essay about the rainbow, and rather oddly attributes the blueness of the sky to a Moiré effect.

This is a wonderful book for browsing, for anyone drawn to physical applications of mathematics or to Arnold himself and the breadth of his interests. To sample some of his wizardly work, look at the essay on the maximum deviation of a light beam through a water drop and the following essay on the rainbow.

Bill Satzer ( [email protected] ) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

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Copyright © 1989, 1990 by American Association for the Advancement of Science

Why the Book of Nature is Written in the Language of Mathematics

• First Online: 04 February 2024

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• Dustin Lazarovici 28  

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 215))

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The essay traces the following idea from the presocratic philosopher Heraclitus, to the Pythagoreans, to Newton’s Principia : Laws of nature are laws of proportion for matter in motion. Proportions are expressed by numbers or, as the essay proposes, even identical to real numbers. It is argued that this view is still relevant to modern physics and helps us understand why physical laws are mathematical.

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Unless stated otherwise, Presocratic fragments are quoted in the translation by Burnet ( 1920 ).

On these questions, see, e.g., Kurtz ( 1971 ); Jones ( 1972 ); Schadewaldt ( 1978 ); Kirk et al. ( 1983 ).

The Pythagorean influence on Plato is undeniable (the Platonic character Timaeus is commonly identified as a Pythagorean). Placing Heraclitus in the same lineage is more contentious. Plato criticizes Heraclitus on the basis that if everything were in flux, truth and knowledge would not be possible ( Cratylus 402a ff.). Heraclitus calls Pythagoras an “imposter” (fr. B129 DK), someone who has studied many things but lacks understanding (B40 DK). Heraclitus was not an easy fellow. Nonetheless, a reconciliation of these great thinkers is not only possible but plausible, and I set forth the connections as they seem correct to me.

árritos , which translates more literally to ineffable or inexpressible ; also alogon .

Although Newton had developed a more abstract differential calculus in his Method of Fluxions (completed 1671, but not published until 1736), it was not used in the Principia (first published 1687).

Ideally, it needs what Dürr, Goldstein, and Zanghì ( 1992 ) named primitive ontology (see Lazarovici and Reichert ( 2022 ) for a recent discussion) or what John Bell ( 2004 , Chap. 7) called local beables .

I will also not discuss the ontological status of other mathematical objects. Both a selective realism and full-blown Platonism are consistent with the view I propose in regard to numbers.

What is physics and to what end does one study it? Christmas lecture at the University of Munich. Translation by D.L.

J.S. Bell, Speakable and Unspeakable in Quantum Mechanics , 2nd edn. (Cambridge University Press, 2004)

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S. Drake (ed.), Discoveries and Opinions of Galileo (Knopf Doubleday, New York, 1957)

D. Dürr, Was heißt und zu welchem Ende studiert man Physik? Weihnachtsvorlesung WS 07/08 (2007), http://www.mathematik.uni-muenchen.de/~duerr/WeihnachtsvorlWS0708.pdf

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Acknowledgements

I owe most of the insights explored in this essay to Detlef Dürr, who owed just as much to his friend Reinhard Lang. I thank Yoav Beirach and Enrico Piergiacomi for very helpful comments and Stephen Lyle for his excellent copy editing.

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Sheldon Goldstein

Fachbereich Mathematik, Eberhard Karls University of Tübingen, Tübingen, Baden-Württemberg, Germany

Roderich Tumulka

Dipartimento di Fisica, Università di Genova, Genova, Italy

Nino Zanghì

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Lazarovici, D. (2024). Why the Book of Nature is Written in the Language of Mathematics. In: Bassi, A., Goldstein, S., Tumulka, R., Zanghì, N. (eds) Physics and the Nature of Reality. Fundamental Theories of Physics, vol 215. Springer, Cham. https://doi.org/10.1007/978-3-031-45434-9_26

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