Completing the formal proof of higher-dimensional sphere packing

Jeremy Avigad has discussed this in a short preprint [1]:

Gauss’s success was built on almost two years of creative work, scaffolding, and planning by the human participants, and it would have been unfair to them, mostly early-career researchers, to advertise this as solely a success for AI. A bigger concern was that the company would proclaim the project “done.” The formalization, on its own, is close to worthless, since the correctness of Viazovska’s result was never in doubt.

It looks like the formalization process of this result is a very interesting case of human-AI cooperation. I am very positive about the same kind of cooperation in software engineering, given that proofs = programs. Lots of boring stuff can be automated, making formal methods cheap enough to become widely used.

I said this here two or three years ago and I received some interesting feedback, but in more mainstream venues people thought this was nuts. With a quirky homebrewn setup, including a fine-tuned LLM for Isabelle/Dafny, I have been able to reduce my formalization time by a factor of 5-6.

Some minimal formalisms are needed anyway even in case you are not interested in high quality assurance to make sure agents synthesize mostly correct code. IMHO, purely neural agents are much less useful than advertised without some symbolic guardrails.

[1] https://www.andrew.cmu.edu/user/avigad/Papers/mathematicians...

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