A few unrelated items:
- I’ve been hearing from several people about their plans to travel to China this summer, just realized that they’re all going there for the same reason, to participate in the First International Congress of Basic Science. This is something new and on a grand scale, featuring 240 or so invited speakers, award of a new million dollar – plus prize, together with prizes for “Best paper” over the last five years in 36 different categories. Yau is the main organizer, and the Chinese government is providing the funding. So, if it’s July 16-28 and you are wondering where your colleagues are, quite possibly the answer is Beijing.
- I’m doing my best to try not to think about the implications of recent AI developments for mathematics, but someone who is doing a lot of thinking about this is Michael Harris, who this week at his Silicon Reckoner substack discusses Google’s use of arXiv math papers to train their Minerva language model. Harris raises the interesting question of whether this use of arXiv papers violates the licenses of these papers, standard ones of which include language like
You may not use the material for commercial purposes.
Even if Google is massively violating the arXiv licenses for commercial purposes, it’s unclear whether anything can be done about this, especially given the legal resources Google can afford. In addition, I suspect that when hearing about this a more common response than “this is terrible, I want to sue” would be “this is great, how can I get this thing to write papers for me, or even better, get Google to pay me to help make this possible.”
- Last month Symmetry magazine had an article Whatever happened to the theory of everything? featuring some quotes from me and John Ellis. Ellis explains that the particle physics community has become skeptical of supersymmetry and string theory:
Supersymmetry seemed less and less likely to be right, and superstring theory never materialized into something with testable and concrete predictions.
“The rest of the community is asking, ‘Where’s the beef?’” Ellis says. “There hasn’t been any beef yet. Maybe particle physicists have turned a bit vegetarian and have lost interest in stringy beef.”
- Possibly in response to the problem for string theory that Ellis is pointing to, Witten next week is giving a non-technical theoretical physics colloquium talk at the ICTP on What Every Physicist Should Know About String Theory. Back in 2015 he published something with the same title in Physics Today, which I wrote about here. We’ll see if there are any new arguments on this now very old topic.
Update: The 2023 Shaw prize in mathematics is going to Drinfeld and Yau.
Update: I missed the fact that last there was a Breakthrough Prize ceremony last month. This year they’ve emphasized even more the “Oscars of science” idea by moving the ceremony from Silicon Valley to LA and having it at the Academy Museum of Motion Pictures. The announcement has none of the names of the scientists, just the names of the Hollywood stars that would attend.
Update: I see (from a Strumia tweet) that a Witten 2015 talk with the same title is available here, was given I guess as a public talk at Strings 2015. It’s all about the differences between the 1d single-particle path integral and the 1+1d worldsheet path integral, unclear to me why this is something every physicist needs to know about, or whether this year’s version will be different.
From playing around with language models, it seems to me that they are quite good at assimilating information that is on the internet and applying it to problems, but remarkably bad when faced with problems where they actually have to do something new. If I’m correct about this, the Minerva language model will fall well short of their hopes that it will “help push the frontiers of science and education.”
Philosophy wise, if there’s a basic science field that can make a call to assemble all the others together, that field may well be mathematics. Still, social wise is puzzling that in fact are mathematicians the ones who try to bring different kind of basic scientists together.
The question remains, why named it: ICBS, if they don’t even include the life sciences or chemistry.
PS. Fesenko continues to be a peculiar story (aswell as Caucher B., if for entirely different reasons)
PS2. Seems almost all current russian math luminaries will be speakers
Particle physicists would be well advised to think about what went wrong so they don’t go on repeating their mistakes. A huge amount of brain-time was spent on producing papers that will never serve any useful purpose. Thousands of intelligent people have wasted their life on this. I find it incredibly tragic. Imagine how much farther ahead society could be if they’d put their mind to work on something useful.
The Minerva model was announced almost a year ago (June 30, 2022) on the Google Research blog, making it ancient technology by now. No commercial use has emerged since then, and probably none can at this late date.
Setting that aside, I believe Harris misunderstands the NonCommercial (NC) clause. He says:
“Google is not a charitable organization; all of Google’s purposes are “commercial” unless demonstrated not to be…”
But Creative Commons repudiates this reasoning at https://wiki.creativecommons.org/wiki/NonCommercial_interpretation
“The definition of NonCommercial depends on the primary purpose for which the work is used, not on the category or class of reuser. Specifically, a reuser need not be in education, in government, an individual, or a recognized charity/nonprofit in the relevant jurisdiction in order to use an NC-licensed work.
Under the NC clause, Google and others may use arXiv papers in a manner “not primarily intended for or directed towards commercial advantage or monetary compensation”. Creative Commons further clarifies, “The inclusion of “primarily” in the definition recognizes that no activity is completely disconnected from commercial activity; it is only the primary purpose of the reuse that needs to be considered.”
In short, Google appears to have used the arXiv content for a research publication, which is permitted under the NonCommercial clause. Am I missing something???
LLMs won’t be very good at producing proofs but they are of course not the right tool for that. One possible right tool would be something like a DeepRL proof search which uses LLM for the heuristics, there have been attempts at this like GPT-f but they are not very flashy, producing formal proof is less flashy than human readable proof…
What do you think of the point of view that maths is so important for humanity that we should not leave it to humans alone. If large parts of maths can be automated, we’ll get more powerful mathematical tools. For my own satisfaction, I can solve already solved problems, they are still fun like Olympiad problems.
What makes the whole ‘do not use for commercial purposes’ is that the papers are indexed by Google so that they show up in searches. Arguably this is a commercial purpose, but do people really want Arxiv to be unsearchable? If so it’s hard to see how you can be for one commercial indexing scheme and not for another.
With my perhaps-too-cynical hat on, I wonder if Witten will win the Fundamental Science Lifetime Award.
David Roberts,
I think Witten would be a reasonable choice for such a prize. But this makes clear the lack of any good reason for proliferating such prizes, since giving Witten another prize would change nothing about anything. 20 years ago as far as I can remember there were no large monetary prizes in Mathematics. Now we have the Shaw prize, the Abel, the Breakthrough Prize and this prize, all at or above a million dollars. What good do any of these do, what is the point of coming up with new rewards for those already most recognized and heavily rewarded by the field? Is yet more of a star system what mathematics really needs?
David Roberts:
Hasn’t Witten made enough contributions to pure mathematics to deserve the Fundamental Science Lifetime Award? The only argument against giving it to him is that if you do, all the string theorists will say that he won it for string theory.
Didn’t see a mission statement anywhere, apologies if I missed something obvious: Is the “Basic Science” meeting to be focused on those three areas moving forward, or does the International Congress plan on having a theme each year such that other areas of “basic science” are discussed? More of a semantic quibble, but I might have called it something else depending on the answer.
LMMI,
The only general information I see about the conference is here
https://www.icbs.cn/en/web/index/18009_1464241__
Over 300 speakers, awards to be presented by Chinese leaders. It says this will be an annual event, unclear if in other years “Basic Science” will mean a different choice of fields, but that seems possible.
The prize needs Witten (or some other very famous scientist) much more than he needs the prize.
anon,
Very true, and not just in this case…
@Peter Shor
I really wonder how one judges the relative merit of nominees when the field is presumably all of (?pure) mathematics, (?fundamental) physics, and theoretical computer science.
Just looking at the attendees and the organisers, it feels like a string theorist will get the prize, and I presume they will follow the time-honoured tradition of giving the inaugural prize to the biggest name.
On a different note, of the judges for the best paper prizes, there are, for the mathematics topics (if I managed to count them properly; also I checked all the people I didn’t know): 89 men, 4 women, 17 anonymous.
For physics there are 17 judges, one is a woman (and none anonymous).
I haven’t the patience to check the majority of the 47 judges in computer science that I don’t recognise the names of.
On a slightly less serious note: of the four judges for “Mathematical logic, Foundations and Category Theory”, none of the them are category theorists, one is a set theorist, one works on independence results, and two are recursion theorists. Not sure how they are going to judge the quality of an influential category theory paper 🙂
Regarding the Breakthrough prize, it appears this ceremony honors the last 3 years of winners, and see this page: https://breakthroughprize.org/News for the Sept 22 2022 announcement of the 2023 winners. So old news….?
Peter: sad news about Jim Hartle https://www.physics.ucsb.edu/news/announcement/2132
I am surprised you have not mentioned it given that he is one of the pioneers of quantum gravity
@Oisin McGuinness: As a Breakthrough Prize winner who attended the ceremony, let me correct you; The Breakthrough Prize Ceremony did not honor all 3 years of winners; some of them will be honored at next year’s ceremony.
Eric Lehman,
you write:
“The Minerva model was announced almost a year ago…making it ancient technology by now.”
So any genuine idea or insight over a year or so old becomes worthless then?
You also write:
“No commercial use has emerged since then, and probably none can at this late date.”
Not so. The likelihood is that tools to help mathematicians based on this kind of AI will begin to emerge in the next two to three years.
Actually, the Minerva approach is a good one in some people’s opinion, including mine, and the idea is not going to die away.
Using training data that includes TeX markup rather than stripping it out is a good idea for the reasons that the authors give. And having your model also spit out TeX markup is also arguably a good idea because, as long as the output is subsequently rendered by something like KaTeX, it remains human readable.
Unreadable proofs are the bane of formal reasoning systems built on type theories and always have been. I am hoping that approaches such as this will move the field to consider systems with more legible output.
I have repeated the Minerva examples in the arXiv paper by using the current version of the free ChatGPT (based on GPT3.5). The results are better than those reported in the arXiv paper (correct except in one case). Here is a link for the full chat https://chat.openai.com/share/da97cc49-db06-4355-937b-c51ccc2a42f0 Enjoy!
Why on earth would you train a model on arXiv papers and then ask it to solve high school calculus questions?
Peter: Witten’s talk is now online at https://www.youtube.com/watch?v=s9qC7DtB7tY
I predit that the inaugural physics prize will go to C.N. Yang, who is 101 and lives in Tsinghua (5 out of the 7 chairs are at Tsinghua, with Yau sitting on all three committees.)
Peter, something OT: Check out https://pirsa.org/23060016 which is a panel debate related to a recent conference in PI.
and in particular the question asked to Rob Myers (related to string theory) about at 28 minutes. he also said that we have seen evidence for teleportation across an Einstein Rosen bridge.
Hilarious that Fesenko was plastered all over the ICBS homepage at first, only to be dropped in favor of Fukaya and Kontsevich.
My spy in Beijing says that he expects only “students and prize winners” to attend this thing.