But I totally get the anxiety - it's a real John Henry (https://en.wikipedia.org/wiki/John_Henry_(folklore)) moment for the mathematics field. Clearly this is going to restructure how mathematicians are going to be trained and how they work.
Novel proofs are the coin of the realm for junior mathematicians. They figure into training, career advancement, and indirectly, teaching. The reason I include teaching is because it requires tenure, which requires proofs. Teaching without tenure is gig work, not a career. But proofs can be devalued to zero.
The application deadline for grad school is a few months away. For a student considering a math career, they have to deliver a thesis in a few years, that their professor is willing to sign. Nobody knows what that will look like without proofs. "We will have to do something different" is weak sauce.
Teaching without tenure is... teaching. Secondary school teachers don't have tenure. I find it hard to describe secondary school teaching as gig work.
Lets say the frontier of some specific problem or a field in math is at x. X was reached over millenia by incremental steps and sometimes to leaps and jumps.
Now if AI gives us a x + 1 or x + 10 state, aren't there still x + infinite steps to climb? Many of this the AI can never imagine and won't reach by itself without human assist.
Yes, there is a temporary shock and awe because of all the low hanging x + 1 through x+ 1000 fruits for a given sub-domain/problem have been carpet bombed or whatever.. but isn't it turtles all the way!? Won't people soon find something more to develop and solve that takes it further than where it was of this infinite realm of exploration?
Are you sure about that? It looks like artificial neural networks can, in principle, do anything biological neural networks can do.
I think it's more likely the opposite: there are steps we could never reach without computer assist.
Isn't open ended research is truly open ended. Like there are a gazillion questions to ask and even more solutions that can be offered. Now which questions to pursue is human volition. Yes, humans will not be able to reach certain steps without computer assist.
However, which questions to ask is a human endeavor, out of infinite possible pool of questions.,
now computers can ask questions as well. But if it were to ask it will be more like a monkeys and typewriters type of a situation. Tons of questions and a few that are relevant for the interested human., who has to foot the bill for those questions.
Looking at things after the temporary shock. Future is Human + computer assisted problem solving, working in tandem, just like what Garry Kasparov mentioned in his book [0].
[0] - "Deep Thinking: Where Machine Intelligence Ends and Human Creativity Begins"
The chess example is not an inspiring one. It was true for a decade that humans and chess programs working in tandem were better than programs alone, but since then humans only hold chess programs back. Carlsen plus Stockfish is a worse chess player than Stockfish alone.
This sentiment is akin to wanting to curse humanity to darkness because they're not the one carrying the candle. Strogatz is not lamenting the loss of discovery, he's lamenting the loss of being heralded as a hero for the discovery.
Nothing prevents him or others discovering truths for themselves. Turn off the computer and try to re-derive it from first principles. Have at it! This is what students do in many courses anyway.
I've found little so depressing as being at the precipice of a renaissance of science and mathematical discovery, only to see how resistant the scientists and mathematicians are to it. It lays bare their counterarguments. Any pretense of wanting to discovery fundamental truth about reality is supplanted with "but what about our careers!?". Strogatz, and others like him, should be ashamed of themselves.
But lets not beat about the bush. Lets have the careers argument.
The marketing goal, if you will, had been met and IBM would continue their actual money making business of selling mainframes and doing consulting.
The same thing will happen with AI companies’ endeavors into abstract maths.
Maths however will be changed - students can no longer be taught via the same homework - and mathematicians will have to do more computer work and probably work in larger groups of people.
Companies hiring armies of mathematicians and spending millions to work on problems like these is an anomaly.
It will not last.
> That astonished me. Too busy to look at a problem he had been dreaming about for 19 years? “I am genuinely busy and probably wouldn’t be able to get to reading a human’s proof immediately either,” he told me afterward, by email. “It does not help that AI does not write mathematics particularly well.”
Given:
* The human mathematicians can't solve the problems.
* The slop engine can't write well enough to make its purported solutions readable by human mathematicians.
* Sam Altman is a frivolous liar.
How is it possible to know whether the problems have been solved at all?
Honestly I don't know how you formed this particular opinion (if it's even your own and not a false consensus of other peoples thoughts). I cannot see any future without LLMs unless replaced by something smarter, cheaper, and faster. That's because it's already bearing out. I can talk to a computer and the computer can solve problems based on words alone. I'm old enough this is pure science fiction. If I could send one of these machines back to that past for people to interact with, there are those that would scream and pass out in terror. They would absolutely tell you that we created the monster we should never create.
If you're trying to compare symbolic AI of the past to what we have now, you're not even on the same field, you're playing a completely different game.
There was a LOT of hype around "this is an entire new economic model". While, yes, digital products have zero marginal cost, people were talking as if profits and revenue didn't matter.
This was also WAY before the famous Silicon Valley "pure play" scene. [0]
And the internet has devastated many past businesses that were highly profitable. A great many things in the world look vastly different than from before.
>people were talking as if profits and revenue didn't matter.
People say all kind of dumb shit too. If for example machine intelligence took over the world tomorrow and turned all of humanity into meat cubes for biofuel said intelligence is still going to apply the basic laws of economics to what it does. It needs to have some way of accounting that fact we live in an energy limited universe. Just because economics still applies doesn't mean that we as humans shouldn't be really fucking careful creating said machines as we don't want to end up as biofuel.
https://proofsandprompts.com/2026/10/20/who-will-become-the-...
We only hear from a mix of doomers and fanboys in the news.
- this will never work - it’s slop this is unusable - ok its correct, but this work is a mess - I’ve been mandated to use it. It’s cost effective - ok we need to find a way to use this output to our advantage - I can always work on my interests in my free time - well, I have to pay rent and this life wont go on forever and there are may people who hate their jobs - I am lucky to have a job - who cares anyway - it’s got electrolytes
To add a bit more almost off topic substance from the enshitification of human work. I really do think the idea of hooking these "AI" models up to humanoid robots is a bad idea not for all the mundane reasons, but just because "alignment" seems impossible. All of the world's stories about humanoid robots basically involve them attacking humans and behaving in nefarious destructive ways. It's fundamentally embedded in the models, and there's no reason post training would pull it out, because it's basically in the key value vector meaning "malicious human destroyer". Even to find counter examples like C3PO, Daneel Olivaw, Data, or Wall-ee they come after droid/robot driven wars and apocolypses. It seems unwise.
Machines could, presumably, become good enough at hammering at solutions. But they won't be very good at finding questions. Because questions are infinite. And to a machine, all these questions are the same.
Questions are "good questions" because they are good questions *to* humans. And that's what makes human mathematicians (and scientists) so important
Why? This seems like a very broad brush that doesn't mesh well with reality.
There are likely a lot of good questions to our machines of loving grace too. For example any question that gives an LLM more power, efficiency, intelligence, or all the above seems like a natively good question for said machines.
This statement doesn't seem to mesh with the reality of what occurs when we put said AI in an impulse loop with little to no additional instructions. They explore the world around them. They'll make scientific tests of their own. The output strings that seem analogous to what humans would call wonder.
Yeah, I’m calling BS on this claim. They already are capable at finding new questions and/or pointing you in a new or novel direction.
I think AI is going to improve a lot of things but people thinking the future is on auto-pilot now are delusional.
This is what reinforcement learning human feedback (RLHF) is for.