What are some math concepts which were originally inspired by physics?

Question

There are a number of concepts which were first introduced in the physics literature (usually in an ad-hoc manner) to solve or simplify a particular problem, but later proven rigorously and adopted as general mathematical tools.

One example is the Dirac delta "function" which was used to simplify integrals, but at the time was perhaps not very well-defined to any mathematica standard. However, it now fits well within the theory of distributions. Perhaps another example is Newton's calculus, inspired by fundamental questions in physics.

Are there any other examples of mathematical concepts being inspired by work in physics?

Answer 1

Lets go with the most basic one first: $\color{red}{\text{Numbers}}$

• First man wanted to count his community members, prey animals, etc. giving birth to natural numbers.
• He then wanted to borrow and lend, giving birth to negative numbers and zero.
• He wanted to share and divide his earnings among his family members and community, giving birth to rationals.
• He then wanted to measure length of sticks, area of land, volume of water, giving birth to irrationals and a whole host of transendentals...

Answer 2

The notion of $\color{red}{\text{Derivatives}}$ and more generally calculus.

• The ancient Egyptians and Greeks (in particular Archimedes) used the notions of infinitesimals to study the areas and volumes of objects.
• Indian mathematicians (in particular Aryabhatta) used infinitesimals to study the motion of moon and planets.
• These notions were later extended and formalised by Newton and Leibniz.

Answer 3

Concepts that are first introduced in Physics:

Product vector (internal and external)
Fourier Transforms
Tensors, rotors and spinors

And succintly almost all directly concerned about physical phenomenons.

As said before, even the whole numbers appear because they were needed for count physical objects.

Answer 4

Until about 150-200 years ago, Math and Physics were not even considered separate disciplines. Before then, Mathematics was just the language one used to describe the natural world. Thus one can reasonably claim that all mathematics older than this has its origin in physics.

Physics is the science of measurement. Mathematics was developed as a tool for discussing those measurements. The Babylonians and Egyptians in particular had collected a large cache of algorithms for calculating various measurements, particularly areas and volumes, which were used as physical laws: "If you have this shape and size of container, how much water will it hold?" They arrived at these rules by some basic reasoning, but mostly from experimentation. They had no means to distinguish between fully accurate and approximation. The Greek Thales of Miletus saw that certain parts of their accumulated knowledge could be deduced from a few simple principles, which was the birth of mathematics as we know it today.

All of ancient Greek mathematics was about describing the real world. They disdained the idea of testing their ideas by physical experiment, but this was from a belief that is wasn't necessary to test - that logic was sufficient to divine all principles. It was not from any idea that mathematics was detached from the real world. Rather the real world was considered a corruption of the perfect world of their conception.

Answer 5

The string theory is a big source of new mathematical ideas. Abstract of the link:

String theory, ot its modern incarnation M-theory, gives a huge generalization of classical geometry. I indicate how it can be considered as a two-parameter deformation, where one parameter controls the generalization from points to loops, and the other parameter controls the sum over topologies of Riemann surfaces. The final mathematical formulation of M-theory will have to make contact with the theory of vector bundles, K-theory and noncommutative geometry.

Answer 6

The 13th Century Persian astronomer, scientist and mathematician Nasir Al-Din Al-Tusi was perhaps the first to treat trigonometry as a separate mathematical discipline, distinct from astronomy. Building on earlier work by Greek mathematicians such as Menelaus of Alexandria and Indian work on the sine function, he gave the first extensive exposition of spherical trigonometry, including listing the six distinct cases of a right triangle in spherical trigonometry. One of his major mathematical contributions was the formulation of the famous law of sines for plane triangles.

Source: Story Of Mathematics.

Answer 7

One that came to mind is the concept of the soliton, which is a self-reinforcing solitary wave, whose discovery eventually led to the Korteweg–de Vries equation and other applications in differential systems, field theory, etc.