Edward Witten


Edward Witten is a theoretical physicist at the Institute for Advanced Study.

Witten’s work originates in theoretical quantum field theory and stands out as making numerous and deep connections between that and mathematical geometry and cohomology. In the course of the 1980s Witten became the central and leading figure in string theory.

Insight gained from the study of quantum field theories and specifically those relevant in string theory led Witten to mathematical results deep enough to gain him a Fields medal, see below. Indeed, a whole list of sub-fields in mathematics originate in aspects of Witten’s work in QFT/string theory and carry his name, such as Chern-Simons theory which many people call “Chern-Simons-Witten theory”, Wess-Zumino-Witten theory, the Witten genus, Gromov-Witten theory, Seiberg-Witten theory, Rozansky-Witten invariant, the Witten conjecture. Other parts are still waiting to be absorbed into the mathematical literature such as Horava-Witten theory, Diaconescu-Moore-Witten anomaly etc..

Despite the deeply theoretical and abstract mathematical aspects of his work, Witten has visibly always been motivated by fundamental questions in the phenomenology of the standard model of particle physics and cosmology. (Indeed, some of his work on scattering amplitudes crucially enters into the experimental detection of the Higgs particle, for more on this see at string theory results applied elsewhere. ) He prominently argued that specifically heterotic string theory is a plausible candidate for a fundamental grand unified gauge field theory including quantum gravity.

Since about the turn of the millennium Witten has tended to more esoteric mathematical aspects of string theory, such as its relation to Khovanov homology and geometric Langlands duality which apparently the string theory community at large is following less enthusiastically than it was the case during the excited 1990s.



In Witten 87, very last sentence:

A properly developed theory of elliptic cohomology is likely to shed some light on what string theory really means.

In Nova interview 2003, also American Scientist Astronomy Issue 2002:

Back in the early ’70s, the Italian physicist, Daniele Amati reportedly said that string theory was part of 21st-century physics that fell by chance into the 20th century. I think it was a very wise remark.

Edward Witten in interview with Graham Farmelo, “The Universe Speaks in Numbers”, interview 5, 2019 (quote from 21:15 - 21:46):

I actually believe that string/M-theory is on the right track toward a deeper explanation. But at a very fundamental level it’s not well understood. And I’m not even confident that we have a good concept of what sort of thing is missing or where to find it. The reason I am not is that in hindsight it is clear the view given in the 1980s of what is missing was too narrow. Instead of discovering what we thought was missing, we broadened the picture in the 90s, in unexpected directions.

Fields medal work


  • Michael Atiyah, On the work of Edward Witten, Proceedings of the International Congress of Mathematics, Kyoto 1990 (pdf)

the following “influential papers” are listed as relevant for Edward Witten receiving the Fields Medal in 1990.

First of all

  • Supersymmetry and Morse theory, J. Differential Geom. Volume 17, Number 4 (1982), 661-692. (Euclid)

    This discusses deformations of supersymmetric quantum mechanics on a Riemannian manifold and how its supersymmetric ground states are related to the Morse theory of a deformation function. The way this supersymmetric quantum mechanics appears as the point-particle limit of the type II superstring is explained at the end of

  • Global anomalies in string theory, in W. Bardeen and A. White (eds.) Symposium on Anomalies, Geometry, Topology, pp. 61–99. World Scientific, 1985

which otherwise is on quantum anomalies in string theory, such as the Green-Schwarz anomaly, etc.

Finally Atiyah’s section 2 mentions

  • (with Cumrun Vafa), Eigenvalue inequalities for Fermions in gauge theories, Comm. Math. Phys. 95 (1984) 257 (Euclid)


And various articles on the foundations of topological field theory such as



clearly, this list deserves be further expanded…

category: people

Last revised on November 17, 2020 at 07:40:20. See the history of this page for a list of all contributions to it.