Comment by JoeH2

Your comments really resonate with me. I have been trying to square the rapid progress in AI's abilities to generate proofs of unsolved math problems with comments that Terence Tao has made regarding whether or not these (incredibly impressive) models are actually contributing to mathematical progress.

From Tao on Mathstodon on April 27, 2026: "We are transitioning in mathematics from an era of proof scarcity to an era of proof abundance, but our mathematical infrastructure and culture has not yet adapted to this. As mentioned previously, there is now a strong (and growing) impedance mismatch between the three core components of mathematical problem solving: proof generation, proof verification, and proof digestion.... Perhaps surprisingly, this massive acceleration in proof generation has not actually produced significant acceleration in mathematical progress itself (with the possible exception of #1196, in which all three stages are largely carried out at this point, and for which some digested assessment of developments will soon be forthcoming)."[0]

And I guess my question is, will it matter if humans grasp these new discoveries? If the models are capable of incorporating these discoveries and using them to recursively self improve to unlock new discoveries without humans in the loop, then I guess we humans never really need to understand. I find it hard to believe that a machine can understand concepts that we never will, but I can't reason why that couldn't be the case. Something that holds trillions of concepts in its mind at once might be capable of generating a proof to something that we simply aren't capable of understanding. And the machine just tells us, "Listen, if you are too stupid to understand the new laws of physics I am giving you, then simply follow these very explicit instructions on blasting hydrogen with this laser at this angle in this exact magnet conformation, then you will get cold fusion."

I am really struggling with this. I think superintelligence implies that there will be things about the world that the models understand that we won't. And I can't quite articulate why that is depressing. Because we should still get some cool new tech and some life saving drugs.

[0] https://mathstodon.xyz/@tao/116477352332170731