by TDGperson » Thu Dec 03, 2020 11:24 pm
Is the centuries old problem Fermat's Last Theorem? YesI'm not sure what we're looking for at this point. We've established that the donut-shape is a torus? As it relates to the complex plane, and the elliptic curves that result, or some such?
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I was originally planning to wait until someone mentioned Weierstrass's elliptic functions before calling this solved, as they are crucial in establishing the equivalence between complex elliptic curves and tori. But you've already got the rest of it and I don't think it would be good to keep waiting, so I'll just call it solved
The answer is elliptic curves. Wiles used them to solve Fermat's last theorem. The discrete logarithm problem for elliptic curves over finite fields is a computationally difficult problem that some cryptographic protocols are built from. Using Weierstrass's elliptic functions, every elliptic curve is isomorphic (as both a group and Riemann surface) to a complex torus, thus establishing an equivalence.