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> It’s not a ridiculous bar for “once in a lifetime” “dazzling” discoveries. As a mathematician, there are plenty of my discoveries in my field that are once i

by JadeNB 4y ago

> It’s not a ridiculous bar for “once in a lifetime” “dazzling” discoveries. As a mathematician, there are plenty of my discoveries in my field that are once in a lifetime and dazzling (to specialists) that would be meaningless to the average mathematics undergraduate student, much less changing textbooks.

unsupp0rted 4y ago
Is there an example in mathematics of a once in a lifetime dazzling discovery that doesn’t change anything?
- JadeNB 4y ago
  (Sorry for the long delay in responding—I was “posting too fast”.) > Is there an example in mathematics of a once in a lifetime dazzling discovery that doesn’t change anything? That doesn't change anything? No, probably not. But that doesn't change undergraduate textbooks? I'd imagine it's harder to find a once-in-a-lifetime, dazzling mathematical discovery that does change them. (RSA encryption, maybe, although that was famously at least twice in a lifetime, RSA being re-discoverers of classified work.) I think of Fermat's last theorem (https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem#Wiles's_general_proof https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem#Wiles'... ) and the bounded-gaps results on primes (https://en.wikipedia.org/wiki/Prime_gap#Upper_bounds https://en.wikipedia.org/wiki/Prime_gap#Upper_bounds ), both of which will surely be mentioned in new editions of good textbooks, but neither of which is likely to change the actual mathematical content of those textbooks. And these are just the ‘popular’ ones! For a long list of others, one can look at Fields-Medal work. In my own area, there is the recent proof of the fundamental lemma (https://en.wikipedia.org/wiki/Fundamental_lemma_(Langlands_program) https://en.wikipedia.org/wiki/Fundamental_lemma_(Langlands_p... ), which is unlikely to be suitable even to be stated in any but the most advanced textbooks.

by JadeNB 4y ago

unsupp0rted 4y ago

Is there an example in mathematics of a once in a lifetime dazzling discovery that doesn’t change anything?

JadeNB 4y ago
(Sorry for the long delay in responding—I was “posting too fast”.) > Is there an example in mathematics of a once in a lifetime dazzling discovery that doesn’t change anything? That doesn't change anything? No, probably not. But that doesn't change undergraduate textbooks? I'd imagine it's harder to find a once-in-a-lifetime, dazzling mathematical discovery that does change them. (RSA encryption, maybe, although that was famously at least twice in a lifetime, RSA being re-discoverers of classified work.) I think of Fermat's last theorem (https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem#Wiles's_general_proof https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem#Wiles'... ) and the bounded-gaps results on primes (https://en.wikipedia.org/wiki/Prime_gap#Upper_bounds https://en.wikipedia.org/wiki/Prime_gap#Upper_bounds ), both of which will surely be mentioned in new editions of good textbooks, but neither of which is likely to change the actual mathematical content of those textbooks. And these are just the ‘popular’ ones! For a long list of others, one can look at Fields-Medal work. In my own area, there is the recent proof of the fundamental lemma (https://en.wikipedia.org/wiki/Fundamental_lemma_(Langlands_program) https://en.wikipedia.org/wiki/Fundamental_lemma_(Langlands_p... ), which is unlikely to be suitable even to be stated in any but the most advanced textbooks.