The Relation between Mathematics and Physics
Pure mathematics and theoretical physics are becoming ever more closely connected. On the pure mathematics side we are interested in questions related to operator algebras, K-theory, geometry, analysis and topology; on the physics side we are interested in quantum field theory and statistical mechanics.
The relation between Mathematics and Physics has produced important results: these have had a deep influence on each other in recent years.
The way used by physicists to explore the nature and to observe the universe and the way used by mathematicians to do a powerful cognitive process developed over thousands of years is often the same: sometimes it does, sometimes it doesn’t.
Paul Erdos said: “A mathematician is a device for turning coffee into theorems“. These words contain a portion of truth.
For example: a topologist cannot distinguish a coffee mug from a doughnut! The doughnut and the coffee mug therefore have the same topology:
For a physicist, a doughnut-shaped chamber is used in fusion research in which a plasma is heated and confined by magnetic fields.
Richard Feynman wrote: “In theoretical physics we discover that all our laws can be written in mathematical form; and that this has a certain simplicity and beauty about it. So, ultimately, in order to understand nature it may be necessary to have a deeper understanding of mathematical relationships.”
Laws of Nature should have a mathematical form, because Nature is written in mathematical language.
In 1981, Feynman claimed that a scientist can see more beauty in a flower than an artist:
“To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.”