Posted by jlebar 11 hours ago
I’ll also share a Python package I wrote for automated theorem proving that has been super useful in my own research [2].
WHat matters is our understanding of maths, and whether this sort of thing makes us smarter or stupider.
So in the end, it required tooling crafted by humans.
How much more magical do you want this to be?
Tool or not it did something you could never have accomplished.
My logic is that you personally could never have accomplished this feat with all the non LLM tools and content in the world. These kinds of things imply these methods are stepping beyond human ability.
Sure we put walls around it and optimize but the interior of that optimization is not something we understand.
You now have access to a system that for a price could solve something you simply are unable to solve. Not something we programmed it to solve, something that has never been solved before.
Nobody gave it an example of this proof, that's magical.
You can scroll through https://transformer-circuits.pub/ to see the ~extent of our current understanding.
https://news.ycombinator.com/item?id=33176996#33177939
> Now try to make a computer prove that there are no natural numbers a,b,c; so that a^n + b^n = c^n for any n > 2.
> > Shifting the goal posts a bit, aren't we?
I guess the goalposts did change a bit, and in a pretty short time.
Proving that a conjecture is false is very different than what you are proposing. You are proposing an existing proof is simply wrong, that the proof can be checked in Lean, and that no one has bothered to check it yet.
Hopefully this helps mathematicians. It seems very clear to me that it will help software engineers apply formal methods to more of our software.