Relationship between mathematics and physics

The relationship between mathematics and physics has been a subject of study of philosophers, mathematicians and physicists since antiquity, and more recently also by historians and educators.

[9][10] Before giving a mathematical proof for the formula for the volume of a sphere, Archimedes used physical reasoning to discover the solution (imagining the balancing of bodies on a scale).

[21] In the 19th century Auguste Comte in his hierarchy of the sciences, placed physics and astronomy as less general and more complex than mathematics, as both depend on it.

The mathematical rigor of this function was in doubt until the mathematician Laurent Schwartz developed on the theory of distributions.

[29] According to David Hume, only statements that deal solely with ideas themselves—such as those encountered in mathematics—can be demonstrated to be true with certainty, while any conclusions pertaining to experiences of the real world can only be achieved via "probable reasoning".

[35] But many definitions and arguments found in the physics literature involve concepts and ideas that are not up to the standards of rigor in mathematics.

The outward face looked at nature and there the predictions of quantum field theory are exceptionally successful.

[51] This led some professional mathematicians who were also interested in mathematics education, such as Felix Klein, Richard Courant, Vladimir Arnold and Morris Kline, to strongly advocate teaching mathematics in a way more closely related to the physical sciences.

A cycloidal pendulum is isochronous, a fact discovered and proved by Christiaan Huygens under certain mathematical assumptions. [ 1 ]
Mathematics was developed by the Ancient Civilizations for intellectual challenge and pleasure. Surprisingly, many of their discoveries later played prominent roles in physical theories, as in the case of the conic sections in celestial mechanics .