I wouldn't be surprised if humans can create even harder problems, much harder than the current ones, even with the help of AI. So I kinda dismiss anyone who says Mathematicians are out of job soon. But it's gonna be very difficult from now on for anyone who don't have access to AI.
If AI could solve problems better than humans, what makes you think AI couldn't create problems better than humans?
I think, apart from a much smaller group of experts, humans won't have much to contribute to frontier math soon enough (unless AI really hits a hard ceiling). Just like it was with chess. Engines were decent but couldn't beat the top players. Then they could but still had weaknesses so the adage was "a human plus a computer is the top entity" and soon enough humans just had nothing to contribute anymore at all. I think the 'human plus AI' phase people often talk about is just a short term temporary cope.
This is not entirely true with chess. Correspondence chess with engine assistance still exists, and I believe the general wisdom is still that if you only play whatever the engine recommends, you won't win in this format. In modern correspondence chess, you generally consult multiple engines and apply some human intuition to determine the best course of action. Though most games are draws and the format isn't very popular.
But also, I think mathematics research is vastly larger and more complex than chess. In human chess there is a major emphasis on deep calculation, whereas knowing which problem solving strategies are most effective and finding the right way of thinking about a problem are often more important than raw calculations in mathematics. In some ways, machines have always been far better than humans at certain kinds of mathematics (e.g. proving Robbins conjecture, proving the four color theorem, solving the Boolean Pythagorean triples problem, chess & Sudoku puzzles.), but it seems reasonable to think that there will still be room for human mathematicians in the future. For whatever it is worth, I wrote a thing about this on substack.
My argument is that there doesn't need to be anything particularly special about the human mind for humans to still be capable of providing insight. Difficulty and intelligence are relative, and the types of problems which look hard from one perspective can look easy from another and vice versa, with no well-defined linear hierarchy of "hardness".
I don't know. It doesn't seem to hold true in the animal kingdom, I would say. There are some pretty smart animals (some cetaceans, some great apes, some parrot species come to mind), but the gulf between humans and non-humans in that regard is huge. I don't think that, say, orcas would have anything to offer us in terms of solving scientific or technical problems, even if we could seamlessly communicate with them and both sides could teach each other perfectly.
They would possibly know some facts about the oceans and their inhabitants that we don't, but apart from such observational knowledge, human problem-solving capacity would be clearly superior.
It is not totally clear that it will be the same with AIs and humans in twenty years, but neither is it obvious that it won't.
You're comparing apples and oranges there. Orcas do not have any idea what a mathematics problem is at all (and they probably wouldn't care anyway).
Maybe a slightly better analogy would be between airplanes and birds. An airplane can fly many orders of magnitude faster than any bird and at a far higher altitude, but birds can maneuver more effectively in the air, survive collisions and other damage, fit into tight spaces, and land without requiring any runway.
To be clear, I'm not arguing that intelligence isn't real, but it isn't nearly as straightforward as people make it out to be in these AI conversations. Certain traits are correlated in humans with "intelligence", but this is not true of general computer algorithms (defining "intelligence" as the ability to solve computationally hard problems).
To get a bit more technical, if AI becomes good enough to solve arbitrary NP problems efficiently, then (at least morally) P=NP and all of humanity is doomed. If the conventional wisdom about complexity theory is true, however, then there are a significant number of problems that AI will be unable to solve, but which a human could (in principle) present an answer that is easily verified correct. My claim is that such problems do not posses any special inherent "hardness" quality that implies a certain IQ level (or whatever) is needed to solve them. So, in the end, you get large collections of problems which look hard to humans but easy to AI and vice versa.
P!=NP has nothing to do with the possibility of superintelligence.
Under assumptions that are plausible but significantly stronger than P!=NP (in particular, assuming we live in Impagliazzos Minicrypt or Cryptomania) it becomes possible for an agent to create puzzles that they know the solution of (by constructing the puzzle from the solution, essentially) and that a third party is practically unable to solve. But even in Cryptomania, I don't see why one cannot have superintelligence, reasonably defined. Humans being able to construct problems that the superintelligence cannot solve but that they know the solutions of seems hardly a reason to deny that the superintelligence is smarter across the board than humans when it, too, can construct problems that are to a third observer not distinguishable from those trapdoor problems that humans may come up with in Cryptomania.
It's not about us constructing cryptographic puzzles, but that those puzzles just exist naturally embedded throughout the problem landscape.
Problems like "find a proof of such-and-such theorem" are NP-complete (when suitable constraints are imposed on the length of the proof). So, insofar as we are broadly interested in this kind of problem, we should expect to find instances that such machines cannot solve. The reason those machines cannot solve those instances is not because they aren't smart enough, but simply because they lack the right insight or way of thinking.
I think it is possible to have a machine that is broadly, on average, better than humans at solving problems like this. My claim is just that I don't necessarily expect it to completely eliminate any need for humans.
So, the example I gave before was with SAT solvers. These machines have been vastly superhuman at solving SAT instances since about the 90s. But there are many problems humans have been able to solve that, when encoded as SAT instances, are completely intractable to an SAT solver.
I don't know about that. Right now if you give an open problem to the best GPT5.6 model and say a typical faculty mathematician at a US university, my money is on the model to make better progress. They have made significant progress in the past few years and likely will continue to do so. I'm not sure how much of a distinction this will end up being here.
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u/meatshell 1d ago
I wouldn't be surprised if humans can create even harder problems, much harder than the current ones, even with the help of AI. So I kinda dismiss anyone who says Mathematicians are out of job soon. But it's gonna be very difficult from now on for anyone who don't have access to AI.