Now back from vacation, and as far as I can tell, not much happened while I was away. Here are a few things I’ve seen that may be of interest:
- Mochizuki has posted a long progress report on “activities devoted to the verification of IUTeich.” New Scientist has an article about this here, which quotes Minhyong Kim making comments I think most experts would agree with:
Some mathematicians say Mochizuki must do more to explain his work, like simplifying his notes or lecturing abroad. “I sympathise with his sense of frustration but I also sympathise with other people who don’t understand why he’s not doing things in a more standard way,” says Kim. It isn’t really sustainable for Mochizuki to teach people one-on-one, he adds, and any journal would probably require independent reviewers who have not studied under Mochizuki to verify the proof.
If you are a professional mathematician, you know all too well that the verification of a proof is a shared responsability of the author and the mathematical community. We all received a referee report once complaining that a certain proof was ‘unclear’ or even ‘opaque’?
The usual response to this is to rewrite the proof, make it crystal-clear, and resubmit it.
Few people would suggest the referee to spend a couple of years reading up on all their previous papers, and at the same time, complain to the editor that the referee is unqualified to deliver a verdict before (s)he has done so.
Mochizuki is one of these people.
His latest Progress Report reads more like a sectarian newsletter.
There’s no shortage of extremely clever people working in arithmetic geometry. Mochizuki should reach out to them and provide explanations in a language they are used to.
Mochizuki’s progress report strikes me as quite an odd document, especially in its insistence that experts need:
to deactivate the thought patterns that they have installed in their brains and taken for granted for so many years and then to start afresh, that is to say, to revert to a mindset that relies only on primitive logical reasoning, in the style of a student or a novice to a subject.
He at times seems to be arguing that his ideas are nearly disconnected from the rest of known mathematics, and the only way to understand why the abc conjecture is true. This is highly implausible, since the great beauty and strength of mathematics is the way in which deep ideas are interconnected, with many paths from one place to another. If he wants to convince people that he really has what he claims, the best way to do it would be to follow the conventional route: write himself a document giving an exposition of a proof of abc, in as clear and simple terms as possible.
Unfortunately, that doesn’t seem to be what he has planned, with his efforts devoted to getting others to start from the beginning and master his long series of papers. If this works, at some point there will be others able to write up a proof of abc using his ideas, and when that happens, experts may have something they can work with. This looks now like a story that is going to go on for a long time…
- The last couple weeks in Jerusalem there was a Winter School on General Relativity. It included a final session (video here) largely devoted to defending string theory as the one true path to quantum gravity. This included a panel discussion where Carlo Rovelli held his own in a battle of the LQG/string wars, with him ganged up on by Gross and Arkani-Hamed. Mostly I don’t think there were any new arguments, just a rehash of the tediously familiar. Gross did give an enthusiastic call for all students to read the Dawid book discussed here.
For yet another promotional effort about strings, one that seems like it could have been written exactly the same way twenty years ago, see here.
- One new argument from the Rovelli side was to point out that “Nature talks”, and what it has said at the LHC so far is that SUSY is not there, blowing a big hole in the expectations of the superstring theory community. The Economist has a piece about how the upcoming LHC run at 13 TeV will be:
the last throw of the dice for the theory, at least in its conventional form.
As often the case though, the article misrepresents the strength of arguments for SUSY:
But, though the Standard Model works, it depends on many arbitrary mathematical assumptions. The conundrum is why these assumptions have the values they do. But the need for a lot of those assumptions would disappear if the known particles had heavier partner particles: their supersymmetric twins.
This is pretty much complete nonsense, since the problem with SUSY has always been that it doesn’t actually explain why the SM model parameters take the values that they do, and this has always been the best reason to be skeptical about it.
On the other hand, the Economist and Rovelli do get the basic story right: Nature talks, and if what it says in LHC Run 2 is that the theoretical physics community has been barking up the wrong tree for the last forty years, it will be interesting to see if theorists are still willing to listen.