contubernio

I remember in an eight grade game coming back to the huddle and the lineman who played next to me was talking about his sister's homework. He clearly had a concussion and we (the players) sent him to the sideline where the coaches berated him for coming out of the game and sent him back (this was in the 80s).

Already at the JV level I saw multiple concussions in games. Not kos but guys woozy liked they'd been punched. Nobody cared back then (US south).

As a professional mathematician it seems that AI is already at the point where, when well guided, it both does better research and writes better exposition than run if the mill mathematicians.

Well guided is a qualifier that matters.

What is the problem if it is AI written? Properly guided AI writes better than most human expositors.

Many many gaps had been found and patched (by humans) already over the last forty years.

It's not AI that has created those open problems. It has simply shown that some conjecture is false and that leads naturally to problems in a sense already posed.

A very different thing is proposing a framework and in it identifying interesting questions. So far AI has only worked within existing frameworks addressing problems already posed. That may change in the future, but it would be a genuine and qualitative evolution.

He doesn't pay TAs. The university does. They work for the university, not for individual professors. If you have no idea how teaching works in US universities, probably better not to comment on it.

Ways will be found to get it to write propaganda instead.

We research mathematicians are still learning how to use AI in research and how to deal with the output. I drafted eight papers last weekend. This week I advanced on none. AI still gets stuck at the key point on a problem where there isn't already a lot of work done. What falls is where techniques not known to the researcher are available and profitably employed - ai brings them into the fray fast - and someone with experience immediately sees where to go with it - and the dominos fall.

So far AI still doesn't make definitions. It tries but it doesn't really see structure - only patterns on which it can impose (by brute force) known structures.

What's not clear is how the professional infrastructure will survive. Journals seem likely to die. The arxiv is swamped. A human can't assess the volume of the output. Serious conjectures have fallen and serious people have checked them.

We are looking for constructive and productive and socially useful ways forward. One reflection is that a lot of what we have been doing was maybe not so interesting as we thought.

AI would have gotten to the point more quickly.

My first job programming was in a geophysics lab. I had to read fortran 77 codes and write in some slightly more modern variant (I can't remember now which). They were simulating the Earth's mantle and used it because it was fast.

Engineers often forget about thermodynamics. Computer scientists apparently never even study it.

I did best by acting like a real world developer - low-ball everything, everything non-union, ignore community activists at all costs, pay for access, sell for a profit, etc.

Fear-mongering clickbait title signals complete nonsense.

Since I started using AI seriously in my (mathematics) research about 6 weeks ago I've advanced more and been more productive than in years. I'm more motivated and persistent than before because I have at my disposal a tool that helps me get past technical obstacles that previously took up a lot of my time.

Most of the problems that have been solved are problems on which a great deal of progress had already been made. Those who work on well known problems posed by famous people are those who suffer the most from this. Those who do their own thing and pose new problems, on the contrary, benefit from it. Suddenly raw technical power and great memory are not so valuable as a broad perspective, structural insight, and wild ideas. Who can be successful in this new ecosystem is different. Some of the elites are (correctly) more threatened by it than some "mid tier" mathematicians. I see lots of opportunities to overcome obstacles in my research program some of which had confounded me for years.

On the other hand, it puts a premium on resources. AI is not cheap for mathematicians. Folks are fancy universities in rich countries with forward thinking ministries of science will have an advantage over the rest.

What is clearly in immediate crisis is the traditional model of doctoral education. Most of the problems that were "given" to ordinary doctoral students are solvable (quickly) even by something like Claude pro. Mathematicians need to adopt training models more like what is done in experimental and laboratory sciences - collaborative and structured.

Where Tao is wrong is in regards to exposition. AI already writes better lecture notes, problems, and exercises for mid level undergrad math classes than do most of my colleagues. It's exposition is generally well structured and clear and it can adjust level on request quite well. It writes research better than most professional mathematicians too.

Article is not useful because it does not bother to motivate why the scans were requested or why anyone other than a legalistic, formalistic person would consider them administrative documents. The author assumes all this is obvious and it isn't.

Arxiv is the principal forum for publishing mathematics research of quality. Journals serve a purely archival and bureaucratic purpose; almost no value is added by the refereeing process (probably more is lost) and journal publishing neither improves accessibility nor diffusion of results.

This is very cultural. In Spain essentially no one throws dinner parties in the US style. It's rare to invite social acquaintances to one's home. These things are done - but mainly with family. Part of this is cultural and part reflects that homes are too small to fit many people. Most socializing is done outside, at a bar, cafe, restaurant, park, etc.

As a long time user (most professional mathematicians have been) of the now mostly defunct Library Genesis, it is certainly more accurate to describe it as a "sketchy Russian website" than as "a library for sharing books and articles that should be partly public domain because they were paid for by the public". In my country we use it precisely because public universities (paid for by the public) cannot afford to buy math and physics books.

This would be good advice except that students are no better at getting information from AI than they are from getting it from books, botes, or professors. If you know what to ask, AI will give a lot, but if you don't ...

You sound a bit troubled. I was responding to the leading the way part. I'm hardly doing that. I just jumped on the bandwagon. What I do see is a tool that forces me to change behaviors learned over decades and potentially renders useless many of them while facilitating others. That's not all a rosy picture.

As for privilege, don't assume everyone lives and works in the US or gets paid lots of money to be a professor.

Stanford researcher discovers his head and his ass aren't the same thing.

That's not the conclusion. I started using AI after the Jacobian conjecture counterexample and have used a particular problem to learn how to use AI and to explore it's capabilities. I'm not a great mathematician but I'm full faculty with 25+ years of research experience and lots of articles and I just proved in a few weeks something that had resisted my efforts for some years.

The exploration process is much easier now. Ideas are quickly testable and multiple tests can help identify a technical obstruction. The tool requires good guidance and input but as it trains on people like me it will need those less.

At the very least our way of doing things must change. More pessimistic views seem to me defensible.

I'm a professional mathematician. Today I proved what for me is a very solid theorem. It's something I had thought about for a few years. With a few weeks of serious use of AI I've found a proof that I am currently trying to write up, but which appears correct. The change in the workflow is enormous, but so is what one can do if one has clear what to do and how to do it.

As a math professor, I care much more about the key idea, heuristics, and motivation than the proof. With the others in place the proof is clear, something an AI or a student can do.

They should just make them read an old chess book like Lasker that gives low level heuristics

This is the essence of why disciplinary, authoritarian, stick based teaching of humans generally fails. It teaches succeed at any cost.

One sees this in math research. The model reports it has proved X. In fact it has given an erroneous numerical check of Y in a few atypical cases.

What makes math approachable is that the context is so well delimited (semantically) that one can guide the model with adequate correction.

Tha Jacobian conjecture is (was?) notorious for publication of false proofs. There have been many, not all by those who shouldn't have known better.

Perhaps all these fields medalists are just worried that AI mitigates their competitive advantages over a mediocre professional mathematician like me. Their main advantages are a kind of penetrating clear thinking that not all of us have and an ability to work obsessively without tiring or losing focus while retaining with a clear head a great number of facts - AI removed these advantages - as Tao has written it shifts the focus to asking good questions and using available tools to address them - and the traditional elite may not be better than I am at that part - they were just better at the solving the problems part ...

Tao is quite the opposite of what you describe. He's had an ongoing dialogue intellectually with the challenges created by ai for mathematicians for some time (years) now and his viewpoint is quite balanced. He is not alarmist but rather correctly addresses the real problems ai advances create for mathematicians traditional way of working.