When you are using the "AI" framing, does the way you talk about "AI" carry water for the Sam Altmans of the world? That is, are you helping to paint a picture of their tech as inevitable, all powerful, and/or anything other than commercial products?

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Right, so maybe a better way to frame the question of the thread is, what are good ways to teach people how to meaningfully contribute w/o setting themselves up as smarter / better / faster / superior?

But if the student has already solved the problem, they may not know how to meaningfully contribute without "giving the answer away" other than by attempting to teach their peers, so they need alternatives in that situ.

Very different than taking on teacher/leader role just b/c they feel like it.

I wouldn't reinforce the false idea he is better, ofc!

But there is different advice to give to a student who has solved a problem b4 other students (which could happen to the same student on some problems & not others).

In either case there are social/collaborative skills to be advised on but...

I agree they can learn! But I still think I'd give different advice to a student who was in this position because they are in fact solving problems faster than others vs a student who is still working through the material at roughly the same pace as others but acting like this for other reasons.

Ok, but is he? Like, if he is solving the problems in his head before other students even pick up a pen, I think my advice would be very different than if he was actually struggling with the problems exactly as much as other students and just taking a leadership role and ending up condescending.

I think you can get it from the Pieri rule:

S²V⊗V*≅S²V⊗Λ^{n-1}V⊗D^{-1} where D is the 1-dim determinant rep.
Let W=S^{(3,1,1,...,1,0)}V (Schur functor)
Pieri now gives S²V⊗Λ^{d-1}V≅(D⊗V)⊕W
Tensoring with D^{-1} gives V⊕(D^{-1}W), so the cokernel of your map is always the GL_d irrep D^{-1}W

Wait, I recognize that but can't place it. What is it?

Does that also let you use lightning against the snakes at your thesis defense?

Whoa whoa whoa wait a second. Do you do stand up comedy?? Like fr?

Do you have the option to either
A) write on paper w a doc camera overhead that sends it to the screens?
B) write on a digital tablet that displays on the screens?

Indeed five months later a Frucht Theorem for finite quantum groups (using quantum graphs) was established:

arxiv.org/abs/2503.111....

If you are a vector in a vector space at 7pm, STAY IN THE VECTOR SPACE