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@esamut@mathstodon.xyz

Recent advancements in AI proof generation has reminded me of my experience that mathematics can be thought of as this giant interconnected codebase. Many elementary theorems can be proven without any deep understanding at all, by simply stitching basic facts (properties, definitions, etc.) together. This is how I got somewhat good at my undergraduate functional analysis class: I just saw the design patterns of its "codebase" in my head.

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So what I am getting at here is that we should really stop pretending as if people can predict breakthroughs or estimate the importance/difficulty of problems. The project has been going on for some time, it has plenty of legacy code (not going to disclose what this corresponds to, I don't want to upset some folks) as well as some pretty elegant abstractions and templates (category theory, anyone?). Plenty of maintainers died along the way and their areas have fallen into obscurity. The whole thing is a mess! There was certainly some low-hanging fruit out there, we just didn't have the right tools to examine our codebase and see them. Well, until recently. Similarly to software engineers - mathematicians should evaluate each other based on the overall contribution, and not just per "ticket" (e.g. theorem). Refactoring math, as in simplifying things and making them more readable, is as important if not more important now than ever. This post will be updated, just wanted to share the rough concept first.

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  1. @yoginho@spore.social

    RE: mathstodon.xyz/@tao/1173952677… (a) AI didn't solve any problems. Models were used, by humans, to solve problems humans had clearly defined and prioritized. (b) This "success" is neither surprising nor shocking. LLMs are actually quite hard to get to work on mathematical problems. (c) Verifying and digesting the "results" requires time and effort. Until then, this is not real maths. (d) AI is (and as long as it is algorithm-based remains) 100% incapable of pushing mathematics in new directions.

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  2. @loleg@hachyderm.io

    🧠 Traditional 🧑‍🏫 breakthroughs enriched the field; today, AI solves problems without contextualizing or communicating them, bypassing scholarly activities and undermining the long‑term health of mathematics. @tao proposes a “Math 2.0” vision to shift emphasis toward holistic contributions—exposition, community building, and new directions 👇 mathstodon.xyz/@tao/1173952693…

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  3. @conitzer@sigmoid.social

    A contrary take on these dumps of math results: *if* these models are going to be built and released anyway, then it's better that the results come out like this than that a bunch of random users get the proofs out of the model and all try to claim credit and priority. The challenges for the field of mathematics (and far beyond) are fundamentally due to the rapid improvement of the models, not due to OpenAI's approach to releasing the results. github.com/openai/math/blob/ma…

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