Now back from vacation, here’s the latest on revolutionary developments in physics and mathematics:
- On the high energy physics front, the good news is that the LHC is performing remarkably well, with already over 13 inverse fb of luminosity, far above that expected at this time, on track to end up with a lot more than the targeted 25 inverse fb for the year. The bad news however is that new reliable rumors (together with the non-observation of any sign of a “special seminar” at CERN, see here) confirm non-existence of the 750 GeV state that would have killed the Standard Model and revolutionized the field. As far as I know, the plan is still to present these results publicly the first week of August at ICHEP, it looks like this will be on August 5.
For some interesting discussion of the statistical analysis issues that come up when trying to quantify how significant the 2015 evidence is for the supposed 750 GeV state, see the comment section of this blog entry. These subtleties it seems will be made irrelevant by the arrival of new data.
- In mathematics there has also been an unconfirmed claim of something revolutionary, but the problem is that there’s nothing analogous to new data coming in to help decide the issue. This is the claim first made four years ago by Mochizuki to have a proof of the abc conjecture, using new methods he calls “Inter-Universal Teichmuller Theory”. The current situation is an extremely unusual one, with experts still unable to understand and evaluate the purported proof. For the best summary of the situation, see Brian Conrad’s detailed explanation from last December here.
Not much seems to have happened since then, but one very recent development has been the appearance of a new survey of the theory. Unfortunately, my guess is that this is not likely to address the issues raised by Conrad and provide what he and other experts are looking for: precise checkable arguments. Instead the new survey is another attempt by Mochizuki to communicate his general high-level vision, often in very metaphorical terms. The last section of the survey is a remarkable attempt to position his ideas in the landscape of modern mathematics, which includes setting these ideas in opposition to those of the dominant research program (and thus of great value if they work out).
What’s really odd here is the way that usual mechanisms for transmitting understanding have failed. Mochizuki has worked to transmit understanding of his ideas to a small number of others, but the transmission has stopped there, with understanding of the abc proof not moving from them to others. For a while the hope was that Go Yamashita would be the one to move this forward, but he has not produced a promised document, or succeeded in communicating by his talks. More recently, last year Yuichiro Hoshi produced a document that is supposed to explain crucial ideas, but it is in Japanese, so inaccessible to most experts. Why this has not been translated remains very unclear.
Next week in Kyoto there will be another workshop trying to further understanding of the IUT theory. I hope this works out better than the last one. There’s a preparatory document here which to me seems to ignore the fundamental problem of figuring out what has gone wrong so far. In particular, its last point appears to be explicitly aimed at discouraging anyone in the audience from confronting speakers that are not successfully communicating ideas and insisting that they try to do better. It would be more fruitful to encourage this instead.