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bhouston 8 hours ago

I am not a mathematician but are most papers now accompanied by a lean proof?

Is there a central repository of lean proofs shared by mathematicians like an npm repository of JavaScript packages?

Does it all depend on a stupid is-odd package in the end?

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emil-lp 7 hours ago | parent | next [-]

No, almost none (except for in certain fields, such as HoTT) have formalized proofs.

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bhouston 6 hours ago | parent [-]

Why not? It seems like this should sort of be the standard now? Or is it hard to make lean proofs in all fields?

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bbeonx 5 hours ago | parent [-]

i think there are a few reasons.

- lean proofs are hard, and a lot of the time there is so much mathematical machinery that folks are working on that you would need to not only prove your result, but also all of the machinery that your subfield it is built on. it would be infeasible for many authors to do all of this work (this might be a major part of multiple careers, and when there are 5 folks in your entire subfield, the payoff is not really worth it)

- human proofs are readable, and can illustrate concepts better than lean proofs. human proofs give insights into how to think about a type of problem, and this is often the most valuable part of a proof/result.

- lean proofs are often very difficult to read; while they give you a "verified" check mark, they do not necessarily improve the bounds of human understanding if that makes sense.

	▲	bhouston 2 hours ago \| parent [-]
		Thank you for the response.

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danabramov 8 hours ago | parent | prev | next [-]

It's new but there is actually a registry now: https://palomar-registry.org/

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UltraSane 8 hours ago | parent | prev [-]

LLMs have gotten good at creating Lean proofs so the are much more common but not universal. And they depend on https://github.com/leanprover-community/mathlib4