It's not that the horizon is expanding because of this. It's more like a forest getting clear-cut.
Going back to chess, I think the situation is similar where you can’t expect an amateur player to get better by trying to play like a strong engine. I think even professional chess players mainly use engines to prepare or memorize variations that are counterintuitive for their opponent. In other words, getting into situations that look wild, but that part of one player’s preparation.
I’m not sure how it is in math, but in chess, it seems like top players can play just like engines when they are in “normal” positions, so that is where I get a bit confused as to where the direction of insight is coming from because it’s been my view that AI is able to make leaps that we would never think of taking and I’m not sure that anyone could actually learn how to do that on their own unless they were willing to keep failing over and over.
There is a parallel with autonomous vehicles in real life. On northbound 1 in SF going through GG Park, the left turn lane onto Crossover Drive is always backed up. Waymos often do a very late merge into that turn lane in order to jump the queue and save time. With 360 degree sensing they can do this safely in real time but it feels too risky for most humans to attempt.
For 3000 years mathematics has only been a "tabletop science". Even big programs like the classification of finite simple groups have been comprised of small teams chipping away at different (publishable) parts of an overall program.
This latest Navier-Stokes advance cost something like $22m in tokens, already well beyond what a mathematician's research grant can fund. As the easy open problems get mined, the cost of frontier progress will continue to climb. Some part of mathematics as a field will need to transition from tabletop science to big science: Coordinated top-down programs addressing high-priority objectives.
TBD is what the role of individual mathematicians will look like in a "big science" paradigm, but we could look to experimental high energy physics for ideas. For all practical purposes, AI converts math from a theoretical field into an experimental/observational one.
The situation is not that different from John Henry competing against the machine. The question is really: Do people deserve to be allowed to continue doing what they have always done, when doing it is no longer necessary to advance the greater good?
At some point in my suggestion the machine will ask better questions than you, and that will be pointless as well, and you keep doing what you like doing, or you move on to something new. But if you keep tying your value to outcome and recognition instead of process you are going to have some incredibly depressing years ahead, and every time will just be as hard to stomach because of your ego.
It sounds like it could be a pretty horrible world for the majority of people, especially if the AI overlords are only concerned about themselves (be it a small number of people who control the AIs, or the AIs themselves becoming independent entities that prioritize their own lives).
Not sure what the point of this argument is. Do we have mathematics for the sake of mathematicians good mental health and career or to solve and discover novel problems? Why should we care if mathematicians can understand proofs if they are correct?
If this is V0.5 of AGI/ASI then by V1 the only system that will be understanding any of this is the AI itself. If AI creates a new field of mathematics month 1, then solutions to new problems in month 2, then another field of mathematics on top of that at month 3 there's no human who will ever keep up with that.
Or the alternative is a flattening of abilities, the AI cannot proceed further than the collective intelligence of humans and in that case this is correct. We'd be in a future where nobody wants to work in a field with an AI dominating it and when AI hits the limit of no useful training data input we'd have this giant gap of nobody know wtf it's done for years and nobody willing to figure it out and advance it.
Ooo here's a dytopian story: - AI gets better at everything humans do - humans stop trying - AI cannot improve anymore than its input data + human support - AI slowly degrades itself (model collapse) for decades, it slowly hallucinates little by little until its hallucinating entire scientific fields losing quality over time - there's a mass population of people in the future who never learned to do anything and now have to relearn and figure out the equivalent of 100k years of AI work in order to prevent its slow degredation while all the systems they've come to rely on start failing around them. The AI has solved every problem but every real solution is saturated with 1000 false ones. - humanity starts from scratch?
I love the idea of an archive of every solution to every problem existing but it's impossible to figure out the correct one. Infinite library like!
It just so happens that even bizarrely esoteric math can later turn out to have some extremely useful and economically valuable applications. And even more useful to have mathematicians available who already understand that specific math.
The random engineer looking at a funny problem 10 years later now has the literal author of the math to talk to about it and implement it.
I have never even spoken to a world class mathematician and now I can have them design with me?
How is this not better in almost everyway?
If said human is kicked to the street with thousands of other homeless people that can't get jobs because AI then robots replaced them, then those fast math problems sound like a pretty bad trade off.
Now, if there's some future where AI leads to abundance and we can all live off UBI, well, probably a worthwhile trade.
The biggest issue I see is the more controversial people leading the AI race at the moment are not the kind of people I'd hand kids safety scissors much less the future of the human race.
Most modern mathematical problems are sufficiently abstract that their proofs or disproofs have no direct application. There's no problem you can fix or invention you can build based solely on OpenAI's construction, because analytic solutions to the Navier-Stokes equations are not used for practical purposes in fluid dynamics. The problems and their proofs are only interesting to the degree that they help us better understand how the math works.
IIUC the Navier-Stokes proof is understandable by human beings, but if it weren't it would be no more useful than a proof that 3 dimensional florg-complete entry seams have no durdle-nodes.
Unless your argument is that mathematicians are effectively useless?
I am assuming that's not your point though.
It's always been a bit bizarre that this isn't the case. Mathematicians are almost always working on problems that there is no good reason to expect to have utility in the real world... problems they selected because of their elegance or whatever... yet there is a strong historical trend of their work having huge importance after the fact. Sometimes in fields that weren't even invented yet at the time of the work.
There's something to be said for the idea that disrupting a system that is working well for no apparent reason is a bad idea.
If AI can perfectly replicate their work but faster and better then what?
SWE have nobody crying for them as they've been massively disrupted.
1. Proving theorems - what AI can apparently replicate faster and better.
2. Creating definitions and new theorems from those definitions to prove, selecting which of the possible statements to work on. I.e. developing the "language" of mathematics. So far there is no evidence that LLM can do this at all well. And there's some reason to think that mathematicians won't be as good at this if they aren't also doing the first part.
The value to society only comes when they do both "well", and it's 2 which is really the black magic where we don't understand why they've been so useful to us.
So I totally agree if AI also cannot do the second part better than a person.
Honestly though, I wouldn't want to take that bet. I never thought that the first thing AI would become super human AGI like is math.
You ask me 10years ago and I'd think the opposite. I think we all would have said we'd have super human HR employees before a super human mathematician.
But here we are.
During the process of optimising and understanding the programmer might learn something new or have some kind of "aha" moment of insight that might lead them down a new path of study where fantastic new technologies and capabilities can be realised
Fast forward to 2026
Most web pages take several seconds to load
Applications crash often for no apparent reason
A vast majority of programmers have no idea what their applications are actually really even doing anymore, so they stack bloat on top of bloat and if something breaks, well I guess that's someone elses problem cos I have no idea what's going on anymore
There's something to be said about levels of abstraction being useful, but abstracting away understanding of the task itself is not the path to generating useful knowledge or applications for humanity
We might be gaining the "what" but we are losing the "why" and the "how" and these are generally fundamentally more important
The answer is 42 but what is the question?
The gatekeeping in math academia is extremely unfair, or should I say objectively fair but personally unfair. I won’t cry crocodile tears.
Because there's lots and lots of money in that and there's not in funding pure math. It sounds like your problem is with the people holding the purse strings.
(I suppose it's possible that in some distant AI future there might be no value in people understanding theoretical math, but I'm pretty skeptical of that; to me it seems like the same error as thinking nobody needs to understand multiplication because you can ask the computer to solve any multiplication problem.)
People usually use these tools in math and science to find an answer. Then often they will work it back using more sane or human pathways. So it's shareable or even beautiful.
Knowing the answer has value. But, often in math the best thing was how someone got there.
If you take that away and turn math into a less fulfilling pursuit where you mostly try to make sense of the output of an LLM, and it's "Astra's theorem #18398" and not "John Doe's last theorem", I'd wager that far fewer people will have any interest in the field.
This is really not unique to math, by the way. AI is undermining a lot of creative work. Why blog when you have much better odds of making it to the top of HN with autogenerated blog-slop? Why write books when many nonfiction categories on Amazon are now dominated by AI? The list goes on.
There's plenty of people on HN who think it's nothing new, ignoring the huge change in scale. And those who think this is good because there's no inherent value to human creativity if we can get the same content faster and for less. I disagree.
This is an absurd thing to say. Hacker news is not the only place that knows about the most famous mathematician in the world. Glancing at Google Trends he seems to be roughly as famous as Linus Torvalds. Not exactly a household name but by no means obscure.
Ask 1000 different individuals if Terrence Tao rings a bell. If 5% or less can answer you who Tao is, it is safe to say that Tao is obscure.
I'd be very surprised if you can find over 50 individuals, out of the 1000, who can tell you who Terrence Tao is. Even big names like Euler or Gauss would surprise me.
Stop 100 people on the street in NYC or Berlin or Tokyo and I bet none of them will be able to name any living mathematician. A few of them might know Linus, though.
[0]: https://trends.google.com/explore?geo=US&q=%2Fm%2F047mjr%2C%...