alt Hacker NewsWe all know Terry Tao, do you know Peter Scholz?
Fields medalist and as Tao listed as one of the most important mathematicians of our age.
Scholz is known to find „precisely the correct and cleanest way to incorporate all the previously done work and find an elegant formulation for that — and then, because he found really the correct framework, go way beyond the known results“
In a way that man is the complement of an AI, he generates understanding rather than just proofs.
Maybe he is the right template for the mathematicians of the future.
https://www.quantamagazine.org/peter-scholze-and-the-future-...
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I did not; thank you.
One bit stands out to me: to better understand, Scholz will work the problem backwards. Sometimes that strategy is just so spot on.
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To my eternal shame, philosophy (like this OC) makes my head hurt. Pretzels my brain, ouroboros like (aka "head up my own butt").
Caveats covered, here's my cave man cold take on two aspects of this topic.
#1 As we're all trying to paraphrase here: answers are great; understanding is even better. I like the word "legibility" (h/t James Scott). The current models are not very legible.
Which directly leads to:
#2 Understanding enables predictions.
If LLMs are stochastic parrots, then pi.dev (GPT + reasoning + ralph loop) is a drunken sailors walk (thru a solution space). A kind of messy heuristic for optimization. With some kind of gate for declaring "done!" Pretty useful.
However, I don't expect Pi.dev to make predictions. That'd require something else. Maybe that something is being worked on; am noob, so I wouldn't know. (I'm still unclear about whatever Jeff Hawkins is doing, in practical terms.)
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Wrapping up: Automated prediction would be cool. That's very different from finding solutions to problems. And the current cohort of AI can't even explain why, much less make predictions.
Assuming predictions requires understanding. Maybe there are other strategies to generate predictions. Like a meta drunken sailor's walk, with drunken sailors all the way down.
(Someone please correct me as needed. TIA.)
[Aside: That article has an ad for their podcast They Joy of ₍₎. Perfect. I have no idea if it lives up to its promise.]
Even Peter Scholz is not always sure of correctness of extremely complicated mathematical statements and welcomes computer assistance in verification of his results.
See the Liquid tensor experiment:
https://xenaproject.wordpress.com/2020/12/05/liquid-tensor-e...
https://www.ma.imperial.ac.uk/~buzzard/xena/pdfs/liquid_tens...
" I spent much of 2019 obsessed with the proof of this theorem, almost getting crazy over it. In the end, we were able to get an argument pinned down on paper, but I think nobody else has dared to look at the details of this, and so I still have some small lingering doubts. "
In a sense, mathematics is not very different from software engineering.
More precisely: Curry–Howard correspondence
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...