Jean-Pierre Serre's 100th birthday editionprevious:>>16991839
>>17054862I tried to read his book Linear Representations of Finite Groups but it was very difficult because of all the errors
>>17054917The dude is a better mathematician than textbook writer
>NOOOOOOO YOU WERE ONLY SUPPOSED TO GROW SMARTER AND THEN PLATEAU AT A LEVEL JUST BELOW ME.
There was a panel about AI in math>Michael Harris>Peter Scholze>Jacob Tsimerman>Geordie WilliamsonModerated by some DeepMind guyhttps://www.youtube.com/watch?v=H7_d_sgui6o
>>17055513lol, at 10 minutes Scholze says he has never typed anything into an LLM and doesn't use a smartphont. at 11 minutes Michael Harris says LLMs are theft and should be illegal.
>>17055556I mean he's not completely wrong about LLMs. All the top AI companies have ignored every intellectual property and copyright law in existence and then left it to the lawyers to deal with the consequences, if any.
>>17055513This was good. It's charming in a way how aloof Scholze is. Tsimerman is the most clear minded of the group.
>>17055556>Scholze says he has never typed anything into an LLM he's a liar
>>17054862I'd ask this in a physics gen if we had one but alas this board is too full of opinionated schizos to sustain one so I apologize for sloppiness.Consider L^2 or a sufficiently well behaved subspace thereof. The Fourier transform can be expressed as a linear, unitary operator in this space:[eqn]\psi(x) = \hat{\mathcal{F}} \phi(x) = \int_{-\infty}^{\infty} \frac{\exp(-ikx)}{\sqrt{2\pi}}\phi(k) dk[/eqn][math]\hat{\mathcal{F}}^4 = 1 [/math] makes its powers isomorphic to the cyclic group [math]C_4[/math], and it rotates the operators x and p=-id/dx as a 90° rotation. Now the question: obviously (taking the rotation property of (x,p) as the defining feature) a group of operators isomorphic to SO(2) can be identified. What is its infinitesimal generator? Another way of phrasing the same question is, what is the phase space angular momentum operator A such that [math]\hat{\mathcal{F}} = e^{-i\frac{\pi}{2}\hat{A}}[/math]? A sloppy guess would be x id/dp - p id/dx = x^2 + d/dx^2 which would be the quantum HO for omega = hbar = m = 1 (which is a Hermitian operator that commutes with the fourier transform) but I didn't do it properly yet.
>>17055761there's sign errors in there I didn't fix but you get the general idea.
>>17055761>>17055762Nailed it, see Wikipedia, eigenfunctions of F
should I apply to university to learn maths or can I self-learn with chatbots?
>>17056462university, not even a question. You should be around people with the same basic interests and ideally a vast breath of different experiences in your most formative years. Even if a chatbot could replace curriculum (lmfao) it cannot help you grow as a person or intellectually challenge you.
>>17056462the fact that a chatbot will occasionally sperg out and get something completely incorrect with utmost confidence should be enough to tell you it's not a good idea to study material you don't know under one
