“Math 2.0” will need to value mathematical progress more holistically

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• Hacker News
• Pure mathematics, in my view, is not science, not craft - it is art.

  AI, however powerful, is a tool, only as important as the amount it helps mathematicians. Creating mathematics without human understanding is as sound as mass producing copies of Michelangelo David.

  “Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture [...] yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.” - Bertrand Russell, "From The Study of Mathematics" (1902)

  “A mathematician, like a painter or a poet, is a maker of patterns. [...] The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.” - G. H. Hardy, "A Mathematician's Apology" (1940)

  by stared
• Why were we doing math in the first place? We should be happy that math problems were being solved, since presumably they were blockers for other problems in science and the like. But it feels like math was really more about seeking enlightenment, like a form of mental yoga or something. If so, we can just ignore AI proofs and continue on maybe?
  by devolving-dev
• The future of "math" is not just solving, but communicating what was solved, and why that solving is important. "Math" as a discipline is only ever been half created, they abandoned explaining themselves like it was beneath them. Well, now in "Math 1.0 finally whole" they will be explaining what they did to the rest of us. If you can't explain you are not really there.
  by bsenftner
• >the mere knowledge that a solution exists "contaminates" efforts by both humans and AI to find alternate routes to the problem that reveal additional insights

  This really expresses the heartburn you see across all fields, not exclusive to careerism. I certainly have friends in decomp and fan translation spaces that have been demotivated by the current rash of efforts happening there.

  The rush to be "first" has always been over-celebrated, but it would be nice to believe there's a way to get beyond that thinking.

  by AlexAplin
• The same could be said of Software. Instead of giving up on creating novel projects and instead just taking other peoples ideas and porting them to Rust, we could be embracing AI to push software and computers farther.

  Im not sure how that will work, but im convinced the current paradigm of just pushing agents into codebases for not much reason other than you can is going to make building software incredibly boring and push creative people away from the field and stagnate progress.

  My prediction is software gets boring and building hardware projects will be the new frontier for creative engineers looking to push computing further. Which is probably a good thing.

  by lifeisloving

•   The authors of the proof are invited to give many talks, and meet with other experts in the area.  Workshops are set up to discuss the proof, as well as other recent developments.
  
    problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is "solved", and do not understand the AI output well enough to answer questions on the result
  

  The value here seems to be the insights that the author of the proof gained, and the paths they took and maybe more importantly didn't take. Inviting only the human prompter to a talk on the paper is like inviting only the department chair, manager of the actual author.

  The valuable part that Tao is feeling the absence of is the insight, and you can only get that from talking to the swarm of agents that developed the original proof with all of their context.

  So to me it feels like we don't need Math 2.0, but Authorship 2.0. I want to "meet" the context that generated these proofs. I mean luckily these were not generated by faceless systems like a SAT solver, you can actually talk to it, but I'm not sure if we can step beyond our pride and grant the true authors of these proofs that recognition.

  by j-pb
• A very balanced perspective, and the concerns he raises are reasonable. He acknowledges that AI is going to transform mathematics, but simply dumping proofs on the math community and expecting others to do the grunt work of verifying, refining, and expanding on them is hardly a productive way to advance the field.

  There seems to be more interest in hitting some arbitrary benchmark (we proved X unsolved problems) than in genuinely contributing to mathematics. But what else is to be expected? It's become a maniacal race with too much money. Too much effort is being invested in proving that the exponential curve is still holding.

  by shubhamjain
• I'm a lot more skeptical. I'm not a mathematician, but from my use of LLMs a very clear pattern of what they are good and bad at has emerged. They are extremely good at combining large amounts of information, and it seems this is what the current AI results in mathematics are. There are so many subfieleds of math with ties to each other, so many papers and niche results, that no human could ever read, comprehend, connect and organize that information in their brains. Pretty much all of it was created by humans. And there is real value in doing this and creating new results from what we've already discovered.

  But there also is another type of discovery that requires taking a step back and looking at the problem from a different angle. If you are an engineer, how often has an LLM told you (without you explicitly prompting for it): Wait, what you are doing here doesn't really make sense, there exists a much more elegant abstraction that nobody has thought of, let's remove all that code, let's tackle the problem in a different way by thinking from first principles. Pretty much never. But in science a lot of the biggest discoveries have come from this kind of first principle thinking, questioning existing work and approaches and going against what already exists, not combining all existing data which is likely to be just a local optimum.

  by loveparade