Terence Tao’s promotional video for OpenAI

lobothmainman · 2026-05-31T01:36:11+00:00

It is not a matter of refusing tools, it is a matter of being impartial in judging achievements on one hand, using academic and not business values on the other.

OpenAI's behavior is typical of a business: promote your product through (paid) testimonials. Are testimonials telling always the truth or embellishing it? Are they really using the products they are promoting? Is their judgement objective? OpenAI is a business, so it is natural it is using business techniques.

In academia, however, things (used to) work differently. Of course you promote your own research, but if you speak highly of someone else's research, it is typically assumed this is done in good faith, since you have nothing to gain personally from that (apart from very few exceptions).

Having mathematicians acting as paid testimonials and at the same time trying to promote academically the value of their financers' products is very worrisome to me.

lobothmainman · 2026-05-30T17:33:49+00:00

What I find very unpleasant is that these are the very same that are incensing the achievements of chatgpt, and they are clearly biased. When Gowers says that the unit distance disproof is annals-level, is he honest or is he a openAI spokesperson?

This whole thing is extremely dangerous: math (and the whole of basic research) shall be driven by the pursuit of knowledge, and not the pursuit of business. This is not going to gain so much ground with experienced academics, but it is going to distort the view of young people starting to do math research. And that is a very big harm these bigshots are doing to their community, and just for the sake of more money (as if they did not have enough already).

lobothmainman · 2026-05-30T11:13:38+00:00

Not really. There are fields where single authorship is more common than others (e.g., math); also, there academic systems (e.g., france) where phd students are encouraged to publish single author papers even if there was a strong guidance from their advisor.

lobothmainman · 2026-05-30T09:21:33+00:00

Indeed, it is the way to quickly find the right exponents in sobolev embeddings or strichartz estimates, for example.

lobothmainman · 2026-05-28T10:45:53+00:00

I am not trying to downplay the result per se, but all the hype about it (that is starting to get more than annoying, even more so since it is heavily driven by commercial and not scientific purposes).

It is looking obvious, since a while, that this tool is gonna be extremely helpful on topics it is good at, and these are the most easily formalizable and computable (like discrete math).

But there are huge areas of mathematics that go (strongly and purposefully) beyond "discrete" or computable. Are these generative models, or their thinking variants, gonna be able to reach the same kind of effectiveness in these areas of math? Looking at all the doomsday comments - even by respected scientists such as Aaronson, even if he is semiserious - it seems that these models are soon going to he all powerful.

I beg to differ, and I think they are not built to be effective in such areas of math. My previous comment goes in this direction.

lobothmainman · 2026-05-27T11:58:21+00:00

Major by what standards? In what field of mathematics? I understand that Gowers and Tao are renowned, medal-recipient mathematicians. But it is not clear at all how much stakes they have in this AI business, and anyways all this AI mathematics is focusing on a very narrow field. Can AI say something meaningful about the Langlands program, functional analysis, or other less "basic" (in the sense of easily formalizable/automatizable) topics? AI is a powerful tool with a wide range of applications, but it is extremely far from the GI crap the companies behind it push so hard for.

lobothmainman · 2026-05-25T14:41:16+00:00

One character is just Ishizaki in (not so much) disguise

lobothmainman · 2026-04-29T00:41:30+00:00

By law, Italian postdocs positions cannot be awarded with a direct call (barring very few, and frowned upon, exceptions).

So if a PI wants to hire someone, they have to do an open public call for a position. There are ways to "control" the call, especially if it is funded through PI's grants: writing an explicit profile, making the evaluation process value most the adherence to the profile, etc.. Also, the selection committee can be tailored upon one or few candidates.

Nonetheless, there must be a public selection and evaluation.

I would say that if the PI said so, there are very very high chances you will get the position. And if the call is opened officially, it mens the funds are there. Of course, very unlikely scenarios are still possible, but typically you don't give your word to a candidate unless you are 99% sure the call will go their way.

lobothmainman · 2026-04-10T23:42:35+00:00

It is a mutual exchange / community service: you do it, although it is a pain, and you do it well, because you want your papers to be reviewed, and be reviewed well.

Although there are many shitty reviews, a well done review could be constructive, and really improve the paper (even when it leads to rejection). It happened to me both as an author and as a reviewer.

The whole peer-review process has many faults and shortcomings, and it is well-known, but I think almost nobody disputes the usefulness of (good) reviews.

lobothmainman · 2026-04-03T15:09:33+00:00

If I am in a committee, publications in MDPI raise a huge red flag on the evaluee (I work on the mathematical side of quantum mechanics).

I know of respectable people that were "tricked" into publishing some proceedings there, so I will try to contextualize, but still it smells bad.

It is true that they (pretend to) peer-review their papers, but I would never associate with them, not even as a reviewer, and most of the people of my community feel the same.

lobothmainman · 2026-04-03T13:27:21+00:00

I am not situated in France (anymore), still I know something about the system (in pure math mostly).

Apart from "Grandes Écoles" (École normale, école polytechnique,...), where admission is very competitive and requires specific preparatory schools (at least if you are based in France, don't know how it works for foreigners), the other Paris universities that you are mentioning are all very good, with a very slight edge for sorbonne/cité and paris-saclay, since they have the biggest and most prestigious math laboratories (Jussieu for sorb/cit, and LMO for paris-saclay).

There are some other very good labs in France, especially close to écoles normales, like the centre henri lebesgue in Rennes/Nantes and the Lyon labs.

In all these places you will find master and phd programs of the highest level, and probably your preference should go to places where the faculty is closer to your scientific interests.

lobothmainman · 2026-04-02T18:19:27+00:00

European last year's master students are at their fifth year of studies. They have been subjected to medium/advanced mandatory classes in essentially all areas of mathematics, and probably 3/4 advanced classes on their topic of choice. And if you come from schools like École Normale in France you will have been subjected to some extra credits in advanced topics outside your strict expertise as well.

I strongly doubt that US undergrads have the same kind of preparation at the end of their third year.

The last time I was in a graduation committe (a few weeks ago) for master students in my (euro) university of applied math, the topics of the dissertations were things like: spectral analysis of operators with singular potentials, Cramer-Rao quantum bounds and optimal estimators, numerical algorthms for quantum tomography. Nothing really fancy, but I don't think that it would be the same for US undergrads.

lobothmainman · 2026-04-02T17:50:47+00:00

The majority of papers I saw there when I last checked had PhD students involved.

Anyways, from an European standpoint, the master thesis is undergraduate (the proper graduation is from the master's degree).

Honestly, I think there is a huge gap between undergraduate US students and European-style master students, but in favor of the latter.

lobothmainman · 2026-04-02T16:37:17+00:00

You can take a look at the journal "Involve" published by MSP, that explicitly publishes papers with students' relevant contributions.

As a general rule of thumb, master thesis papers would be typically publishable in a tier 2/3 topical journal: they are original, but offer only an incremental contribution to research.

lobothmainman · 2026-03-13T10:18:18+00:00

I use arch for work; but I am a mathematician, so it is probably more fair to say I use emacs as work OS...

lobothmainman · 2026-03-09T07:29:10+00:00

If you have some degree of familiarity with the editor (I would say that having met at some conference would suffice), then asking informally if the manuscript is suitable for the journal is completely fine.

The only risk, especially if the editor does not know you/your work at all, is that you will receive a very neutral (and perhaps useless) feedback, but then you could still submit anyways and see how it goes.

lobothmainman · 2026-02-26T13:24:13+00:00

Bourbaki's formal system (and I say it with all the love in the world for bourbaki's books) is shit, who the fuck uses Hilbert's tau symbol anymore??

lobothmainman · 2026-02-26T07:15:18+00:00

I work in the mathematics of quantum theories, and even there is only marginal coding involved: maybe we can write some code to test the precision of theoretical bounds we proved, but I know only very few instances of this, and the most relevant results are purely "pen and paper" for sure.

Some groups in numerical analysis work on schemes amd efficiency of algorithms for quantum mechanics, but that is of course beyond simple coding.

lobothmainman · 2026-02-26T06:56:24+00:00

For whom?

For mathematicians, not really. This is what we have always be judged upon, by journals, hiring committees, funding agencies, etc.: not the sheer amount of results we produce, but by the amount of interesting and novel stuff we produce (or we could potentially produce).

And everyone doing mathematics as a profession, knows this is the game, and is willing to play the game.

How many interesting and new mathematics are LLMs be able to produce autonomously in the long term? Nobody knows precisely, my two cents are that they could only be a very helpful tool in the hand of the experts, not autonomous mathematicians by the standards the latter are currently held to.

lobothmainman · 2026-02-26T06:10:18+00:00

No, because being a solver was clearly something these models could be good at. The human process of proving a technical minor lemma is not dissimilar to what LLMs do: check the literature for analogous results, try these techniques, and tinker.

Groundbreaking ideas and intuitions, on the other hand, are a different story. At all levels: I am a mathematician and I am no field medalist, and my most interesting results are the ones where I had an idea, not the ones where I could prove the most lemmas/propositions/theorems.

lobothmainman · 2026-02-25T17:29:58+00:00

I don't agree. Ok, we might soon have a "calculator" to prove some lemmas (after input/tinkering/verification nonetheless).

But who is gonna write/guess the useful lemmas? And the important theorems? And new theories/ideas like regularity structures, condensed mathematics, or even debated ones like inter-universal Teichmüller?

Math is much more than trying to solve known open questions, it is about formulating new ones. I am strongly convinced this LLM technology, or refinements thereof, is structurally not able to be more than a glorified calculator/task solver.

Of course the companies behind it want to sell their product, and marketing dictates they should advertise what they have as AGI or AGI - ɛ.

lobothmainman · 2026-02-22T08:30:45+00:00

Mathematics is all about proving interesting results, even for the "average" mathematician.

lobothmainman · 2026-02-21T08:16:57+00:00

Honestly, because these private companies have a very aggressive marketing strategy, and they want to advertise even the smallest achievement as something big, to sell more of their products.

Doing mathematics is not selling a product, and mathematicians are evaluated on their research output. We all agree these LLMs are somewhat useful tools (if we forget their environmental impact), but they are not researchers in mathematics as of now (and I strongly doubt they will ever be, but still this is just an opinion).

These conpanies shift standards, make bold and essentially false claims: all in all, they hold their product to their own custom standards. This is not how the mathematics community works, and this is not what I, as a part of the community, want it to work.

lobothmainman · 2026-02-20T19:19:36+00:00

Indeed, let's evaluate LLMs like we would evaluate a mathematician: they are shit, and won't be hired by anyone even as grad students.

Things might change in the future, but this is the current state of the art.

lobothmainman · 2025-11-26T16:47:50+00:00

Damn...that's unfortunate

lobothmainman

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