She just doesn’t mention that no WIMPs are also a prediction of superstring theory…

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“In math there is also a tendency to accept weak notions of “solve”, such as qualitative or nonconstructive existence proofs, or proofs of concept that don’t necessarily blossom into a working tool after finding some in-principle solution to a problem.“

In physics we call this working on M-Theory. 😉

]]>Interesting you should mention chiral gauge theories – there is a recent article by D M Grabowska and D B Kaplan

http://arxiv.org/abs/1511.03649

which combines two nice ideas in lattice field theory in a proposal to non-perturbatively regulate chiral gauge theories. ]]>

I’m not advocating that physicists adopt mathematician’s standards of rigorous proof, just that, especially when they can’t make contact with experiment, they devote more attention to making clear what they understand and what they don’t. Sure, leap over steps and see what happens (little known fact: mathematicians do this too), but be aware that you’re doing it and make that clear to others. Would this not make any difference? Maybe. But my experience with string theory has been that the extreme difficulty in figuring out exactly where the subject is, what is understood and what isn’t, has not only made the public hype problem worse, but makes it difficult to make progress (with the progress needed sometimes just achieving clarity on what doesn’t work).

As for QFT, again, I’m not arguing for applying full rigor to what is well understood. An example of what I have in mind is the question of whether the electroweak theory (chiral gauge theory) has a well-defined formulation outside of perturbation theory. Can you even in principle consistently do non-perturbative calculations? This appears to be irrelevant to contact with experiment, and the general assumption is that this is an uninteresting technical issue, but maybe there’s something to be learned there. For people to be motivated to work on it though, there has to be some perception that there is a problem there, and some idea of what would count as progress.

]]>If everything was formulated nice and consistently what then? Streater and Wightman’s axioms had very little effect on the important developments of the 20th century. Do you think that the mental labour involved in proving rigorous theorems about string theory would stop people from hyping it in the popular press?

]]>The main reason is because of spam, but more specifically because after a certain period the ratio of non-spam/spam comments becomes quite small, and the great majority of traffic to the postings is spambots trying to break in. ]]>

I also wanted to comment on the mathbabe thread after it was closed, to prove up-to-date links for people trawling the interwebs for the history of this interesting episode.

[1] Sure it was a generalisation: I had assumed though that old comment threads were closed to prevent spam. The suggestion of starting a new blog to continue the discussion baffles me.

]]>That is not quite accurate. Geometric Langlands is not like some neighboring subjects where there are vast pyramids of conjectures that go far beyond any proven theorems and with no hope for an imminent proof. There is a massive web of both conjectures and theorems, and the weight of the latter is considerable. Lots of the conjectural picture, although still developing, has been proved, and the time span between conjecture and proof has been far shorter for geometric Langlands than classical arithmetic Langlands (because the geometric theory is easier and more structured). The subject is in flux but in a very healthy way where more and more of the expected picture is falling into place, leading to new refinements of that picture, and further cycles of conjecture-proof-application.

]]>I think it should be obvious there’s little point to me responding to Lubos’s ranting, his agenda is just to misinterpret and misrepresent what I have to say. Obviously the few words that fit on a slide can’t convey the actual arguments I’m trying to make (much fuller versions are available of course in many places, for instance my take on the hype problem is http://www.math.columbia.edu/~woit/wordpress/?cat=8, not just the two particular examples in the talk). As I pointed out at the beginning, the intent of the talk was to point to where the actual arguments were, and to be provocative, not make a bunch of carefully worded, fully hedged and defended claims.

There’s no argument in my talk that experiment is dead. Obviously whatever experimental avenues are available should be explored, and I’ve no expertise to advise experimentalists about what they should be doing. The question I was raising was that of, if you’re a theorist interested in certain questions, with no experimental help in sight, what can you do? The Munich conference I was referring to was based on the assumption that a significant part of theoretical activity is now “post-empirical”. A perfectly defensible attitude towards this is that it’s a mistake, that theorists should should stick to thinking about things with some reasonable connection to experiment. A lot of people read my book as making that argument, but that’s not really what I think, and the talk was an attempt to explain why. I do think it is possible to make progress by trying to better understand the internal logic and mathematical structure of a theory, even without help from experiment telling one if one is on the right track. And if you try and do this, there’s a lot you could learn from mathematicians about how to make progress.

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