nLab The Unreasonable Effectiveness of Physics in the Mathematical Sciences

In view of the developments in theoretical physics from about the the 1980s, and in reference to Eugene Wigner‘s famous phrase of the The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Atiyah-Dijkgraaf-Hitchin 10 wrote this:

But over the past 30 years $[$ 1980s- 2010s $]$ a new type of interaction has taken place, probably unique, in which physicists, exploring their new and still speculative theories,have stumbled across a whole range of mathematical “discoveries”. These are derived by physical intuition and heuristic arguments, which are beyond the reach, as yet, of mathematical rigour, but which have withstood the tests of time and alternative methods. There is great intellectual excitement in these mutual exchanges.

The impact of these discoveries on mathematics has been profound and widespread. Areas of mathematics such as topology and algebraic geometry, which lie at the heart of pure mathematics and appear very distant from the physics frontier, have been dramatically affected.

The meaning of all this is unclear and one may be tempted to invert Wigner's comment and marvel at “the unreasonable effectiveness of physics in mathematics”.

(Atiyah-Dijkgraaf-Hitchin 10, p. 915 (3 of 14))

The phrase is picked up also in Dijkgraaf 14, Moore 14, p. 10, Tong 17 and elsewhere.

References

• Michael Atiyah, Robbert Dijkgraaf, Nigel Hitchin, Geometry and physics, Phil. Trans. R. Soc. A 368 1914 (2010) 913-926 [doi:10.1098/rsta.2009.0227, pdf]

• Gregory Moore, Physical Mathematics and the Future, talk at Strings 2014 (talk slides, companion text pdf, pdf)

• Robbert Dijkgraaf, The Unreasonable Effectiveness Of Quantum Physics in Modern Mathematics, Perimeter Public Lecture 2014 (web, pdf slides).

• David Tong, The Unreasonable Effectiveness of Physics in Mathematics, LMS Popular Lecture 2017 (webpage, talk recording)

• Natalie Paquette, The Unreasonable Effectiveness of Physics in Mathematics, talk

category: reference