From: https://thenaturalog.wordpress.com/2015/04/01/m-theory-the-most-influential-scientific-idea-of-the-twentieth-century/

“M-theory has also significantly influenced the mathematical community. At most research universities today there are at least one-two pure or applied mathematicians exploring the mathematical frameworks of topics like ST/SST, quantum field theory, quantum electrodynamics, condensed matter physics and high energy physics. In fact, many of the opulent mathematical questions, inspired by theoretical physics, can be attributed to Edward Witten himself. Being the first and only physicist to have been awarded the prestigious Fields Medal by the International Mathematical Union, Witten is irrefutably prolific in both theoretical physics and pure mathematics.

To give an example of how the conceptual principles of M-theory have informed pure mathematics, and visa versa, let’s go back to 1985 when Witten publishes Dimensional Reduction of Superstring Models, an article in which he discusses the compactification of ten-dimensional supergravity on Calabi-Yau manifolds. Calabi-Yau manifolds or spaces (and hyperkähler manifolds) are a special type of construction (studied in algebraic geometry) whose unique properties (particularly relating to the curvature and surface geometry of manifolds) have motivated a conjecture that the extra dimensions of spacetime may take the form of six-dimensional Calabi-Yau manifolds. This postulation has further lead to the idea of mirror symmetry (MS)/mirror manifolds, an elegant symmetry property between manifolds requiring that they are employed as curled up dimensions of string theory. Mirror symmetry was an original discovery made by physicists, but by 1990 mathematicians were discovering effective applications in enumerative geometry, a branch of mathematics concerned with counting the number of solutions to geometric equations. Today MS (which assumes the consistency of M-theory) is a major research topic in pure mathematics, and results of this nature have compelled mathematicians to drastically rethink their traditional views on how/if to distinguish between pure and applied mathematics.”

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