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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJun 30th 2013

added to the people-entry Edward Witten a paragraph Fields medal work with a commented list of articles that according to Atiyah won Witten the Fields medal in 1990.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMar 11th 2014

added some actual text to the beginning of the category:people entry Edward Witten. That clearly deserves to be much further improved, but at this moment the entry has the following:

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 theoris 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 cojecture. Other parts of his work currently remain topics in theoretical physics, such as Horava-Witten theory.

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.

• CommentRowNumber3.
• CommentAuthorzskoda
• CommentTimeMar 11th 2014
• (edited Mar 11th 2014)

mathematical geometry and cohomology

Is this phrase intended ?

Wess-Zumino-Witten theory

Wess Zumino model is also sometimes called WZNW (Wess-Zumino-Novikov-Witten) possibly partly due a remarkable (1982?) paper of Novikov.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeOct 10th 2019
• (edited Oct 10th 2019)

Witten in interview with Graham Farmelo, [“The Universe Speaks in Numbers”, interview 5](https://grahamfarmelo.com/the-universe -speaks-in-numbers-interview-5) (2019):

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.

But I didn’t actually check at which time the quote appears in the recording. If anyone has the time stamp mm:ss, let’s add it to the entry.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeOct 11th 2019

A kind soul points out that it’s 21:15.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeOct 12th 2019

So I have completed the quote (going 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.

• CommentRowNumber7.
• CommentAuthorDavid_Corfield
• CommentTimeOct 12th 2019

He continues the interview by giving his backing to the It from Qubit approach.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeNov 17th 2020

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

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeOct 7th 2021

I have added one more quote (here)

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeOct 7th 2021

now expanded the quote as follows (thanks to help from David C. here):

String theory at its finest is, or should be, a new branch of geometry.

I would consider trying to elucidate this proper generalization of geometry as the central problem of physics, certainly the central problem of string theory.

What should have happened, by rights, is that the correct mathematical structures should have been developed in the twenty-first or twenty-second century, and then finally physicists should have invented string theory as a physical theory that is made possible by these structures.

This is back from 1988, recorded in:

• P C W Davis & J Brown (eds.), p. 95-96 in: Superstrings: A theory of everything?, Cambridge University Press 1988, 1991, Canto 1992 (gbooks):