Einstein and Maxwell were fortunate to find the mathematics they needed already available. When Newton developed his Theory of Gravitation, the mathematics he needed had not been developed, so he invented Calculus. Likewise when Edward Witten began his work on String Theory and M-Theory he had to do pioneering work on many of the mathematical tools required and is the only physicist to win the top award in Mathematics: the Fields Medal. Here is the official Fields citation of his mathematical achievments:
Stephen Hawking in his book The Grand Design co-authored with Leonard Mlodinow notes that:
M-theory is the most general supersymmetric theory of gravity. For these reasons M-theory is the only candidate for a complete theory of the universe.
Read Natalie Wolchover's articles from Quanta Magazine:
Why Is M-Theory the Leading Candidate
for Theory of Everything?
the Nature of Reality
Ed Witten - Mystery Theory ('Big Ideas' Interview)
Edward Witten: String Theory and the Universe
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