Great IdeasNature and science
Mathematics as nature's language
The surprising fact that numbers and shapes describe the physical world.
The question
Why does mathematics describe the physical world so well? Is nature written in numbers and shapes?
How the books answer
Oldest first. Each stop is our own short summary of what the author argued; follow the link to the rung for the whole lesson.
c. 360 BC
Plato, Timaeus and Critias
Plato imagines the world built by a good maker using mathematical patterns: harmonious ratios for the soul of the world and geometric shapes for the elements. Nature is beautiful because it follows mathematical order.
“He was good, and the good can never have any jealousy of anything.”
3rd century BC
Archimedes, On the Equilibrium of Planes, On Floating Bodies, Measurement of a Circle, The Sand-Reckoner, On the Sphere and Cylinder, and others
Archimedes proves the law of the lever and the law of floating bodies as mathematical theorems from a few simple assumptions. Physics, in his hands, looks like geometry. He was among the first to do this.
“Two magnitudes, whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.”
c. AD 150
Claudius Ptolemy, The Almagest
Ptolemy describes the motions of the sun, moon and planets with circles on circles and tables of numbers. Whether his circles were real or only a way to calculate, the mathematics predicted the sky. Astronomy was the first science built on math.
1619
Johannes Kepler, The Harmonies of the World, Book V
Kepler searched for the mathematical harmony of the heavens. In The Harmonies of the World he announces his third law: the square of a planet's year is proportional to the cube of its distance from the sun. He also imagined the planets singing chords as they moved.
1638
Galileo Galilei, Dialogues Concerning the Two New Sciences
Galileo believed the book of nature is written in mathematics. He found that a falling body's distance grows as the square of the time and that a thrown body follows a parabola. Measuring and calculating replaced arguing about natures.
1687
Isaac Newton, Mathematical Principles of Natural Philosophy
Newton's book is titled Mathematical Principles of Natural Philosophy. From his laws of motion and gravity he calculates the orbits of planets, the tides and the shape of the earth. Nature's whole system follows from a few equations.
“The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.”
1902
Henri Poincaré, Science and Hypothesis
Poincaré asks how far mathematics in physics is discovered and how far it is chosen. Some principles, he argues, are useful conventions, not facts. Mathematics gives physics its language, but experiment decides what the language should say.
1916 (English 1920)
Albert Einstein, Relativity: The Special and the General Theory
Einstein uses a geometry of curved space-time, worked out by mathematicians decades earlier for its own sake, to describe gravity. It was a striking case of pure mathematics turning out to fit the world.
1925
Alfred North Whitehead, Science and the Modern World
Whitehead asks why modern science arose in Europe. He suggests it rested on a deep belief that nature is orderly and can be understood, a belief he traces in part to medieval theology. Without that faith in order, he says, scientists' labors would be hopeless.
“Without this belief the incredible labours of scientists would be without hope.”
For young readers
Isn't it amazing that math describes the world? The same numbers that count your toys can tell us when the next eclipse will happen.
Galileo found that a falling ball goes 1 unit in the first second, 3 in the next, then 5, then 7: the odd numbers! Add them up: 1, 4, 9, 16. Those are square numbers. Nature seems to like patterns.
Talk about it
- Where do you see math in nature? (Think of honeycombs, flowers and shells.)
- Why do you think nature follows mathematical rules?
- Kepler imagined the planets making music. Can math and music be connected?
- Can you think of something in nature that math can't describe?
Where else on the site
- Kepler's Third Law
- Free Fall
- Levers and Balance
- Buoyant Force and Archimedes' Principle
- Newton's Law of Gravitation
- Arithmetic Sequences
Every rung tagged with this idea:
- Plato: Timaeus and Critias
- Archimedes: The Works
- Ptolemy: The Almagest
- Copernicus: On the Revolutions
- Kepler: The Harmonies of the World
- Kepler: Epitome of Copernican Astronomy
- Galileo: Two New Sciences
- Huygens: Treatise on Light
- Newton: The Principia
- Whitehead: Science and the Modern World
- Poincaré: Science and Hypothesis
- Whitehead: An Introduction to Mathematics
These pages are our own short synthesis, written for families. They were inspired by Mortimer J. Adler's Syntopicon, the index of great ideas in volumes 1 and 2 of Great Books of the Western World, but the questions, summaries and groupings are ours, not the Syntopicon's. Short excerpts come from public-domain translations, credited where they appear.