In the sciences, if experiment disagrees with theory, the theory is wrong. In mathematics, theory can not be disproven by experiment.

i’m seeing matrix calculus in a whole new light

for me, the pendulum swung from pure math to applied science a few times before settling on statistics, the best of both worlds

Terry Tao rates the math ability of the current version of ChatGPT as a "mediocre" but not completely incompetent math graduate student. I don't know about you but mediocre for a Fields medalist is 100% good enough for me.

I don't think LLMs are doing what I'm doing when I "think". They can push symbols around but they don't know what any of it *means*. They don't know that these symbols are shadows of a bigger, weirder world that exists beyond the symbols. My words aren't my thoughts. My words

I literally (re)invented this idea this week. I started keeping a file called “scratch.R” and it’s been life changing. It’s a nice place to keep all my half-baked ideas and stuff I’m afraid to delete while at the same time not cluttering up the rest of my code.

A lot of the people arguing "AI is or will soon be conscious" are really arguing "the human mind is just a fancy computer". In other words, it's not an elevation of what AI is, it's a deflation of what humans are, which is fine, but it would be more honest to admit that up front.

Einstein, 1905: > 1st paper: explains photoelectric effect revealing the quantum nature of light > 2nd paper: explains brownian motion proving atoms exist > 3rd paper: special relativity, time dilation, etc > 4th paper: discovers E=mc² leading to atomic energy

Andrew Wiles > decides he can prove Fermat's Last Theorem > slow rolls old projects to seem busy > monk mode. no conferences, minimal teaching > 1.5 years studying up > 2 more years to 1st major breakthrough > does not quit until the final proof, 9 years after starting