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W. S. Anglin wrote

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.

What wildernesses are being explored these days and by whom?

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  • $\begingroup$ Historically, Newton, Euler, Fourier, Heaviside, and Riemann were iconic explorers blazing trails through strange widernesses, but today ... ? $\endgroup$
    – Tom Copeland
    Commented Feb 8, 2020 at 16:12
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    $\begingroup$ I think at present this is far too broad. $\endgroup$
    – Noah Schweber
    Commented Feb 8, 2020 at 17:13

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The landscape of string theory is aptly characterized as a "wilderness" for mathematicians.

"String theory is a piece of 21st-century physics that has fallen by accident into the 20th century and therefore will require 22nd-century mathematics to solve."
Daniele Amati

See also The mathematics of string theory by Robbert Dijkgraaf.

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    $\begingroup$ Who is Daniele Amati? A great deal of 20th century physics was solved with 20th century mathematics.. think of quantum mechanics or general relativity $\endgroup$
    – Bernie
    Commented Feb 8, 2020 at 17:25
  • $\begingroup$ Daniele Amati was referring to string theory, which seems out of reach of presently available mathematical tools. $\endgroup$
    – Carlo Beenakker
    Commented Feb 8, 2020 at 19:24
  • $\begingroup$ What would it mean to "solve" string theory? $\endgroup$
    – Wojowu
    Commented Feb 8, 2020 at 19:47
  • $\begingroup$ @Wojowu --- perhaps in the sense that the anti-de Sitter/conformal field theory correspondence "solves" string theory on a manifold of constant negative curvature. $\endgroup$
    – Carlo Beenakker
    Commented Feb 8, 2020 at 20:09
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    $\begingroup$ Certainly one of the first to spring to mind, with Witten as one of the explorers. $\endgroup$
    – Tom Copeland
    Commented Feb 10, 2020 at 15:25

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