Some great thinker once said that after a cataclysm books would be what remains to rebuild humanity. Actual books: "Here is one of the world's most important theorems." Also Actual books: "The proof is left to the reader."
-
-
Show this thread
-
Sometimes I think about Évariste Galois, who effectively invented a form of algebra that was decades ahead of its time, all by the young age of 20. He also did this while desperately in love, and subsequently died in a duel because of those feelings. I will never be that smart.
Show this thread -
Seriously though, I cannot stress enough how ahead of its time Galois theory was. It took decades to fully explore its impact. It turned a problem that had been standing for 350 years on its head. It is, today, the topic of advanced graduate courses.
Show this thread -
Galois' proof of the non-solvability by radicals of the general quintic is so brilliant that it almost makes me want to shift to become an algebraist. It's what Erdős may have called a "proof from The Book."
Show this thread -
(I should actually look up if he said that) Galois' proof came chronologically after the results by Abel and Ruffini, so we still call the proof the Abel-Ruffini Theorem today. But their solution was a sledgehammer and Galois' was artful.
Show this thread -
It's interesting that the Abel-Ruffini Theorem implicitly comes up in data science all the time and we don't ever realize it. A consequence of the result is that the eigenvalues of a general matrix of degree 5 or greater cannot be computed non-iteratively.
Show this thread
End of conversation
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.