this post was submitted on 19 Oct 2026
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This is a pretty easy mistake to make when you don't have firsthand experience, but the problem is that's not a reinvention of what mathematicians do at all, it's only a reinvention of the presentation. Big mathematical advances are almost invariably driven by curiosity, but the university writing your paycheck wants their name attached to yours in publications of breakthrough results. Proofs are just the way a mathematician justifies that they're working on math. No proofs means a risk admin will triple their teaching load and say "you're only getting paid to teach now" with lip service about encouraging them to continue math on their own time.
If you have an oracle that gives a true/false answer to a conjecture, it won't destroy a mathematician's curiosity to ask why, but it will absolutely affect his ability to convince the admin that can't even read the abstract that this pursuit is worth funding. That's the crisis. Math papers are unreadable without years of study training your brain to think that way. A headline of "AI proves big theorem" is likely to win over a public that's grown up disliking math because of its use as an educational gatekeeper, even when it's unrealistic for human mathematicians to verify the AI's claim. There is a very realistic risk of administrators who can't define what a topology is declaring that mathematicians are obsolete.
The final answers to whether conjectures are true/false have never been the fruit of mathematics research. Think about Grothendieck's work towards solving the Weil conjectures - the machinery he developed to solve them is modern algebraic geometry, world-changing stuff that's become the backbone of cryptography among other things. Learning the conjectures are true is a footnote. If everyone had already known they were true in advance though, no one would have paid him to start working on them in the first place.
It would be like someone telling you we can finally stop playing your favorite sport now that the games can be simulated, but you try convincing them otherwise when they've never understood one rule and never put a game on because they'll just be confused and bored.
I pretty much agree with most of your comment. Grothendrieck's work would be theory crafting and the curiosity point is similar to what I was thinking when writing about novel proofs/increasing understanding
Right, but my point is that's still what mathematicians do. That has never changed. Grothendieck was a great mathematician, but the difference is not that other mathematicians don't approach problems with sufficient curiosity. I would go as far as to say Grothendieck's strength was a heavier time commitment very early in his career to just publish less "deep" results, because that time investment allowed him a very deep understanding of the objects he was working with, which is the key to making real insights. Directing mathematicians away from investing time on more boring proofs to only work on fun theory is misguided.
Saying mathematicians don't focus enough on curiosity and novel discoveries is completely at odds with all of my experience in math research. That's the fun part of math! For everyone! It's throwing aside that the amount of time and effort Grothendieck put into producing "ordinary" results beforehand was completely necessary in developing schemes. Dismissing the kind of results Grothendieck had published earlier on as not theory-crafting destroys theory-crafting, because deep insights don't pop out of thin air and thinking outside the box, they come from years of familiarity with the objects you're working with. It's also throwing aside that he himself saw toposes as much deeper than schemes, but those did not catch on to the same degree, and that most mathematicians who have been in it for a few decades have their own body of work like that that could be easily dismissed from the outside as not "theory crafting" because the audience is niche in the same way it is for toposes. There's no "need to reinvent" towards "theory crafting", and saying that there is is misunderstanding the crisis by misunderstanding how math research has worked in reality.
Gotcha. Thanks :)