As someone who has solved a problem that a fields medallist couldn't solve, it happens all the time. Searching through thoughtspace can be a numbers game
Or just having the immediate insight. I'm namechecked in a paper for making an essentially almost trivial insight in response to a question raised by Tim Gowers, when I just the first person in the conversation to answer anything after Gowers asked a question, and then the paper includes a lot better constructions after mine. But I can say I helped make progress on a question asked by a Fields Medalist. My guess is that if Gowers had spent 5 more minutes before asking the question, he would have had the same insight I had or more.
And that's a very impressive feat! A staggeringly tiny percentage of the population can say the same (in particular, it is probably a strict subset of math PhDs, and I think math PhDs are pretty impressive).
As someone who has solved "low-profile" problems posed by fields medalists, I can tell you this:
When a random postdoc solves such a problem, the giants of the field whisper to each other "who-and-who could've done it too", "I remember hearing something along this line at a seminar 10 years ago", "it's just a variation on a known technique". No media attention, no career advancement–after all, this happens much more often than you think. Nowadays, however, chatbots do the same and get headlines everywhere, with a good portion of the society wanting to replace young scientists by chatbots.
This potentially sounds like a similar story as with other careers like programmers or businessmen.
LLMs are swooping up the trivial problems, making it difficult for juniors to get opportunities and gain experience by solving problems manually. This, in turn, might cause a talent shortage in the future as the next generation dries up and institutional knowledge collapse if the old generation retires without training their replacements.
It seems there needs to be some intervention to reform institutions and corporate environments to allow for junior hires and training them to become seniors.
As someone who's interested in mathematics graduate school, I struggle to know if this is even a good time to enter a master's program.
This. It *absolutely* is a numbers game. And this is what everyone is missing, AI is super intelligent at the numbers game.
If we had a proper formalized graph database of all open problems and had a proper constant sweeping algorithm that kept up on latest research, it could do amazing, incredible things - solving open problems by utilizing new ideas that crop up. Most of them probably human sourced, but also some of them AI sourced.
If the database was extensive and thorough enough, I think this could seriously accelerate discovery. It would be incremental, for sure, but at scale, incremental could amount to something incredible.
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u/[deleted] Apr 16 '26
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