Comment by Spacecosmonaut
2 hours ago
Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field.
Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI generates and verifies proofs without humans in the loop. Where the mathematics may be beyond human comprehension.
In that future, does it matter that early career mathematicians are inhibited by these developments? Perhaps not. Programming faces the same issue. As AI crawls up the competence ladder, does it matter that fewer people have opportunities to develop the skillset of a senior engineer? Perhaps not.
Chess has set rules and is a closed world with a set objective. In maths, you make up the rules. For every clearly defined problem that everybody cares about and is not yet proven, there's someone who first who recognised the importance of that given problem and managed to define it clearly enough for it to be recognised as such.
There's also the separate, less glamorous issue that people don't want to talk about, which is proof reliability. [0] If you have systems to help you formalise the problems and leave an algorithm or AI or whatever solve it in a verifiable way, that's a win for both the mathematicians and the rest of the world.
The deeper question is whether AI can replace the human role in deciding what mathematics should be done and what concepts matter. If that's automated, then yeah, we're screwed.
[0] https://lamport.azurewebsites.net/tla/proof-statistics.html
> However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now).
Isn't chess more popular than ever? Ai dominating the game didnt seen to matter
Chess is a game where we play and observe for the sheer joy of mastery. Mathematics has some of that “done for its own sake” aspect but not as cleanly. There’s always the chance that some applied mathematics might help something in science or engineering. Whether we care more about process vs outcome is now more important than ever before.
Sure, but if we continue that analogy it does mean that there will be no human contributions to frontier mathematics.
(This doesn't disprove your point because it seems like it should be trivial to make but interestingly)
I don't think there's any computer system which autonomously come up with new directions in openings. As far as I know; a GM looks at stockfish's evaluation of the top x moves and analyzes one that hasn't been played a lot etc.
> imagine a future where even talented mathematicians are nothing but noise
That would be AGI. My conjecture is that LLMs alone are not enough for that future. They are incredible, but AGI needs other breakthroughs.
In that sense, I think math is very different from chess or Go. Chess and Go are complete-information games with fixed rules and a fixed board. Math is open-ended.
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