Relationship between mathematics and physics

The relationship between mathematics and physics has been a subject of study of <a href="/facts/Philosopher/Hyvzc54m">philosophers</a>, <a href="/facts/Mathematician/eaFSR8Fx">mathematicians</a> and <a href="/facts/Physicist/cQcgvSIm">physicists</a> since <a href="/facts/Classical_antiquity/JBq8vEX9">antiquity</a>, and more recently also by <a href="/facts/Historian/5DBH5eCb">historians</a> and <a href="/facts/Educator/5zkjcWo8">educators</a>. Generally considered a relationship of great intimacy, <a href="/facts/Mathematics/pxTouaz4">mathematics</a> has been described as "an essential tool for physics" and <a href="/facts/Physics/a7aH2y08">physics</a> has been described as "a rich source of inspiration and insight in mathematics".
Some of the oldest and most discussed themes are about the main differences between the two subjects, their mutual influence, the role of <a href="/facts/Rigour/v23FKfhw">mathematical rigor</a> in physics, and the problem of explaining the effectiveness of mathematics in physics.
In his work <a href="/facts/Physics_(Aristotle)/Mop5uWJB">Physics</a>, one of the topics treated by <a href="/facts/Aristotle/U2bDlBFW">Aristotle</a> is about how the study carried out by mathematicians differs from that carried out by physicists. Considerations about mathematics being the language of <a href="/facts/Nature/YVJharv5">nature</a> can be found in the ideas of the <a href="/facts/Pythagoreans/25BjMN2z">Pythagoreans</a>: the convictions that "Numbers rule the world" and "All is number", and two millennia later were also expressed by <a href="/facts/Galileo_Galilei/98VT2z3v">Galileo Galilei</a>: "The book of nature is written in the language of mathematics".

Relationship between mathematics and physics open-in-new

Relationship between mathematics and physics