Yesterday, 01:18 PM
The opening is an in-depth, technical analysis of a geometry proof by AlphaGeometry, the summary begins at 18:16.
Alex admits that he's not a Computer Scientist and props to him for acknowledging his limitations on this subject (rare nowadays, people tend to assume that, because they can use a computer, they intuitively understand CS which is just not true.) Fortunately for Alex, CS backs up the opinions and intuitions he expresses here.
It would be possible to make AlphaGeometry produce more human-like geometric proofs. When we work out new proofs or new knowledge of any kind, our notes look a lot like the "chicken-scratch" mess that AlphaGeometry produces. But then we do a second, editorial revision, to clean up our notes and present a reasoned argument from beginning to end. AlphaGeometry also does this, but it's just not very human-like in its presentation. So, you could use fine-tuning -- RLHF, DPO, human-preference ranking, etc. -- to make AlphaGeometry produce geometric proofs that are more in the style that humans prefer to read and write them. In other words, Alex's criticism on this point, while completely valid, is currently solved with existing methods, it would just be a matter of implementing it.
But on the wider implications of AlphaGeometry to mathematical proof-search, generally, this is where Computer Science comes back into the equation. Yes, there are problems that cannot be solved, even by AI. It doesn't matter how "incepted" your AI is, it doesn't matter whether it trains itself, rewrites its own code, self-improves itself, etc. It doesn't matter how much energy the AI has access to, nor what frequencies the AI operates at. The entire observable universe can be devoted to the use of an all-consuming, black-hole-scale AI operating at trillions of times the gigahertz frequencies of modern CPUs, and it still won't be able to solve the monster problems that are among the hardest problems in Computer Science. This is not speculation, it is not merely "empirical", this is provable.
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