I am also not a mathematician, but I think this is an assumption that people are making. It could be that by reading the solutions/proofs of these AI-generated results, those methods could still be discovered, ie. the AI could be discovering new novel methods implicitly. It's not exactly the same thing, but when the Navier Stokes blow-up "solution" came out, there was a lot of hoopla around it being stolen and not novel, but then once the dust settled, we had this:
> But closer examination reveals that OpenAI’s proof builds its unnatural force in a totally distinct way. The proof’s similarities to Buckmaster and Alpöge’s progress are superficial...
So I think more time needs to pass before a call can be made.
An interesting thought experiment is this: if we were to go back in time 150 years and tell our ancestors that Newton is just an approximation and give them a 5,000 page book about Special and General Relativity, QM and QFT, would we be robbing them? Initially the whole thing would be incomprehensible, but eventually they would chew through it and make sense of it. I don't really know the answer (and perhaps the analogy is not great since we're quite attached to our physics heroes from the last 150 years).
> It could be that by reading the solutions/proofs of these AI-generated results, those methods could still be discovered, ie. the AI could be discovering new novel methods implicitly.
This is just what is happening. Techniques discovered by AI have already been used to solve other problems, or to extend the AI-discovered solutions.
there is a difference between "knowing" and "knowing about". "knowing" is having it deeply ingrained into one's intuition by working at a solution over years, often without progress in the immediate sense, and often without success in the absolute sense either.
Other than the person who developed the solution, everyone else will have to be "knowing about" it by studying written texts and lectures produced by someone else's mind.
Exactly. Every mathematician is "robbed" from knowing 1-2 things that they would specifically work on, for any given topic, 99.99% of mathematicians are not robbed, and for any given mathematician, for 99.99% of topics they are not robbed of anything. That's my feeling..
Maybe post-LLMs mathematicians will work on problems/topics that even ChatGPT can't solve? Like, P=NP remains unsolved, we can work on that. Sure, it's possible that it will get solved tomorrow by an AI or somebody else, but that possibility was always there.. Or, to be more practical, one of the claimed OpenAI results is that integer multiplication is sub n×log(n), so assuming it stands, now there's a new question: "What is the actual lower bound for integer multiplication?"
I have no proof, but I believe (i) LLM progress will converge at some point, (ii) that point will not be so far off from human intelligence, since they're trained on human intelligence, so.. not all problems will be solved/solvable by LLMs. But they'll be fast(er), like calculators are faster than us.
Yes because except for ones own work, the mathematician is at the mercy of learning from papers and videos any other work whether made by man or by machine, so I do not understand this argument at all.
I think it's disappointing [1] for a group of people (however smart they are, whatever titles and fame they have) to think they are the gatekeepers of mathematics, the core of human knowledge. In this respect "mathematics is what mathematicians do" is no longer true, perhaps it was never a useful thing to say. Mathematics is (downstream) consumed in some shape or form by every human on Earth, and no elite, appointed group gets to decide how new mathematics is created. I feel this is a reaction to the sting of the reality check for these people, who are gifted with amazing genetics, and can think faster and deeper than other humans, that their gifts are relative to humans, and machines can still outdo them.. but this is already true for so many other areas, from physical strength to playing chess. Also, I feel this reaction is just non-sensical, it reminds me of when commercial software company CEOs [2] said open source is communism in the early 2000s, because they felt open source is threating their business model.
Lastly, deep down I don't really get what mathematicians are so upset about. All open problems, once solved, are not solved by 99.9999% of mathematicians, because it's solved by one or a handful of others, and the others just learn of the solution/proof. Mathematicians can now still organize conferences about these proofs, discuss them, digest them, think of new avenues of research, etc. They don't even have to invite OpenAI, in 6 months whatever model is available on chatgpt.com will be this smart anyway, and they can use it in the workshops for explanations, etc.
[1] I was going to write "I'm a bit disappointed by the response of the math community..", but then I remembered, whatever T. Tao writes is not the position of the math community, it's his position. Then I was going to write "I'm a bit disappointed by the response of T. Tao..", but then I remembered, I don't know Tao personally, so why am I disappointed?
Well said! Unfortunately this sentiment seems to be in the minority.
Many of these reactions are much too hasty, making long term claims for something that has only recently happened and is fast evolving.
On top of that, assuming that there are 350,000 math PhDs, that’s 0.0036% of the current population (1 out of 28,000). There have only been 68 Fields Medalists which is 1 out of 122 million people. So, most of us wouldn’t be solving these problems, but now we all can benefit from them.
The study of mathematics is certainly to change, just like it did with previous advancements in mathematics itself and technology.
I don't have insider information, but: if one of the AI companies really wants their models to become really good at this and publicly available datasets are scarce, they can probably just buy anonymized X-ray/MRI scans paired with the human doctor's diagnosis, and train on them. I don't know what the legal story is around this, but AI companies have near infinite money, so I'm sure they can buy their way around regulations (eg. by buying them from a less regulated country).
My understanding is that medical images are part of a patients record (so they must be available for the patient or other docs at the request of the patient) but whoever has collected the images does have some form of ownership. I’m not a lawyer and I have a cursory understanding of this. I believe it would be possible for an AI company to lease or get access to the data through a transaction but I suspect that it hasn’t happened (or happened publicly) due to fear of backlash.
For example I know that some companies like Tempus had access to imaging that corresponded to tumors which had been biopsies for sequencing and they were developing models in house.
Recently I was at the doctor for a very minor sports injury ("tennis leg"). The doctor — who was in his 50s — was explaining the degrees of the injury to me, and quoted ChatGPT as the source, along the lines of "ChatGPT usually says you have to rest for.." I thought it's quite funny, but after thinking about it, it's really no surprise that doctors also use AIs to look things up / clean up their diagnosis.
I would not call him a crank, he's just an "independent physicist". He is a very successful and wealthy businessman thanks to Mathematica, with $100Ms of wealth presumably, and he choses to do physics in his own way, pursuing subjects that he finds interesting, in ways he finds interesting. And he writes about his work and himself in grandiose ways, usually comparing himself to Newton and Einstein.
Nothing major has come out of his research, other then one of his co-workers proving that one of the simple CAs is Turing complete.
Most academic physicists ignore him, but that's fine. Personally, I think we need more people like Wolfram who are doing totally independent research, with their own funds. Statistically, something unexpectedly good could come out of it!
> And he writes about his work and himself in grandiose ways, usually comparing himself to Newton and Einstein ... Nothing major has come out of his research
Wolfram is definitely not a crank. Cranks do not understand scientific methods and also have a minimal understanding of whatever field they're trying to be active in. Like trying to push physics theories while demonstrably failing to understand high school level calculus. Cranks are also conspiracy theorists who inevitably believe knowledge like theirs is being suppressed.
Wolfram does display a similar ego to cranks. He tends to place his cellular automata at the same tier of importance as general relativity or wave-particle duality. But unlike cranks, he doesn't say that Einstein, Feynman and other greats are wrong, he doesn't "prove" his theories by math-looking babble that is definitely not math. He loves cellular automata and so much of what he writes is more like philosophy of science than science. He will model certain processes as an automaton and then he jumps from that to every natural process being a cellular automaton.
Eccentric, definitely, and most of his physics research isn't accepted but he's several orders above the level of crank.
The word ‘crank’ is a dismissive insult. Wolfram is definitely eccentric, probably hard to work with, but also undoubtedly smart. What good does it do to dismiss him? He’s doing nothing wrong spending his own money the way he wants to. And who knows something will come out of this. Similar to GP I’d like to see more of this.
A crank is a real pattern of behavior where a person tries to prove things they don't have enough knowledge and intelligence to even understand correctly.
Maybe I'm an oddball, but I've always thought this: if a cool company wants to hire me but isn't sure, give me a 3-6 month fixed contract and LFG. There's zero doubt in my mind it would work out. And if not, so what, I'll be okay.
Today I'm 45 with family and have a fancy VP title, but I would have no problem to do this for an interesting role at a cool company.
> Claude Shannon called him "the smartest person I've ever met", a common opinion.
> Von Neumann founded the field of game theory as a mathematical discipline.
> .. leading him to a large number of military consultancies and consequently his involvement in the Manhattan Project.
> In 1950, von Neumann became a consultant to the Weapons Systems Evaluation Group..
> In 1955, von Neumann became a commissioner of the Atomic Energy Commission (AEC), which at the time was the highest official position available to scientists in the government.
> In his final years before his death from cancer, von Neumann headed the United States government's top-secret ICBM committee..
Towards the end of his life as cancer metastasised in his brain he would ask his visitors to give him sums to do to reassure himself that he was still there. Towards the end he wasn't and couldn't. One of the saddest things.
Models have become a commodity, hardware not so much; why would Nvidia care? It's the models who are competing primarily, not hardware manufacturers.
Also, models are software, so easy to switch out. AI hardware otoh has a approx. 3-5 year useful life, I don't see how this affects hardware already running, or getting built.
HW manufacturers work on the software side to make sure that the popular models run well with their systems. From drivers to patches submitted to vLLM etc.
I have an NVIDIA Spark machine, and NVIDIA has a whole team building software, docker images, etc. to make these things relatively easy to use for LLM research etc and running local models because it just makes sense to pull people in like that to keep the market captured using their HW by keeping the software up to date.
Even more so for AMD who is behind on the software side by years and failed to do the above in the early days and lost out for it.
The DeepSeek 3 series models were quite popular, and quite capable. The new ones will likely be as well. Many people will want to host and run them. By making them run initially better on Huawei hardware than on NVIDIA it will encourage API hosting providers to buy Huawei hardware, and to get things like vLLM and llama.cpp working better on them.
> But closer examination reveals that OpenAI’s proof builds its unnatural force in a totally distinct way. The proof’s similarities to Buckmaster and Alpöge’s progress are superficial...
https://www.scientificamerican.com/article/openais-blockbust...
So I think more time needs to pass before a call can be made.
An interesting thought experiment is this: if we were to go back in time 150 years and tell our ancestors that Newton is just an approximation and give them a 5,000 page book about Special and General Relativity, QM and QFT, would we be robbing them? Initially the whole thing would be incomprehensible, but eventually they would chew through it and make sense of it. I don't really know the answer (and perhaps the analogy is not great since we're quite attached to our physics heroes from the last 150 years).