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Terrence number theory11/19/2023 I'm tired of showing how dumb I am for now, but you get me. I do know this one, but I actually wouldn't have figured it out if he hadn't pointed out this is induction. > Preserved by successor -> suffices to test base case and/or limiting cases > Multiplicative structure (in analytic number theory) -> suffices to check prime powers "Dense subclass" is exactly how I'm feeling right now. > Invariance under limits -> suffices to check a dense subclass > Invariance under tensor products -> suffices to check one-dimensional/irreducible caseĪha! Tensors! Like TensorFlow! I know one-dimensional too! This is the closest I've gotten to having a smart thought. > Invariance under linear combinations / convex combinations / algebraic operations -> suffices to check basis elements / extreme elements / generatorsĬombinations has something to do with choosing things? Generators. Good thing the spherical harmonic behaviour sufficies, I do not know I would test the cubic dissonant one. > Rotation invariance -> suffices to test the case of spherical harmonic behavior in angular variable (separation of variables). If this didn't have "functions" in it I would think it's biology. > Dilation invariance -> suffices to test homogeneous functions. A plane wave sounds like part of a DnD spell. > Translation invariance -> suffices to test individual plane waves (i.e., to inspect the Fourier multiplier symbol).įourier transform has something to do with frequencies. Maybe reflection means flipping a function? Or when it goes above or below an axis? > Reflection symmetry -> suffices to test odd and even functions separately. Tao is obviously a genius, but to me he's an alien.įor fun then, let's see just how far I am: Maybe Adderall could help me care, like it did for Erdos. I'm just so overwhelmingly glad I don't have to care about any of it. But honestly why does anyone care enough about the twin prime conjecture to go through this pain, and what possible practical application could there be compared to algebra (cryptography) and geometry/topology (physics).Īnd I am saying this as someone who took some graduate-level mathematics. There are other areas of math (geometry, etc.) which seem a lot more fun. That being said, Tao works on twin primes I don't really care about the means because I don't care about the end. I am just so glad I wasn't stupid enough to lock myself into a 6-10 year PhD/postdoc process, and I don't have to care about any of these tricks or existence proofs about technical constructions that will always exist only in theory. As I read through this, I just feel this great sense of relief that I switched from math into CS.
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