alt Hacker News> Suppose lean in its current state existed 15 years ago, and suppose the math community eagerly started contributing en masse to a shared repository of code. How much of the breakthroughs and longstanding questions in mathematics that we’ve seen answered this year do you think we would have solved?
(Former grad student in math here who has spent whole weeks formalizing in Lean lemmas that would be considered by professional mathematicians writing a mathematics text / paper as obvious ("without loss of generality we can assume that....", "it should be clear that...")
Probably very few or none.
These systems (mostly) don't help you discover new mathematics. They are a tool for formalization.
It just turns out that combining them with LLMs is the secret sauce. LLMs have quite a bit of creativity but make a lot of mistakes. The Lean typechecker never makes a mistake but has no creativity. Get them to work together in an iterative loop and you get what we have now.
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Make a trivial adjustment to your final proposition and it would still hold, no?
> Humans have quite a bit of creativity but make a lot of mistakes. The Lean typecheck never makes a mistake but has no creativity. Get them to work together in an iterative loop and you get what we have now.
Is that because you were starting from scratch and working alone, though?
Imagine a hypothetical project at the scale of the Linux kernel, with thousands of mathematicians building up organized and well-commented code, standing on each others shoulders.
I am a math undergrad and I tried lean. It probably is because of habit and familiarity but I still find lean proofs harder to read than NL proofs. I wonder what if the math education switch entirely to a formal language (not necessarily Lean) will be?