gavagai691

9 ms·

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by gavagai691 4y ago
I didn't know how to make the links clickable. Thanks!
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Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
1303 points by gavagai691 4y ago|417 comments
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In Science, “The Fate of What We Say and Make Is in Later Users’ Hands”(3quarksdaily.com)
2 points by gavagai691 4y ago|0 comments
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Transformative Experience and Pascal’s Wager(3quarksdaily.com)
1 points by gavagai691 5y ago|0 comments
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by gavagai691 5y ago
The people who write these kinds of papers, believe it or not, prefer to spend most of their time playing with numbers compared to watching Netflix. (This is not to say that they don't enjoy spending any time on the latter.)
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by gavagai691 5y ago
Probably nothing is quite so abstruse as abstract mathematics, and few subjects in math are as abstruse as arithmetic geometry (the subject of this paper).
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by gavagai691 5y ago
Unfortunately, I don't think anything matches Quanta for what they do (covering cutting-edge advances in science in an accurate and accessible manner). One of the things that really helps Quanta is that if there is an article about mat
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by gavagai691 5y ago
I guess I feel that there is a big discontinuous jump between "not clearly better than humans" and "clearly better than humans," where the latter is much, much more significant than the former. It seems like going on a h
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by gavagai691 5y ago
Another huge advance in number theory--alongside the subconvexity result posted last month--in a vastly different area of the subject. 2021 was a great year for number theory. (This of course assumes both results are correct!)
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by gavagai691 5y ago
Apologies, I don't quite follow your reasoning.
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by gavagai691 5y ago
I looked into this again and the hotkey situation seems more unclear than I suggested. You could not log into your Battle.net account, so it would have been somewhat time consuming to change all of your settings manually. If I had to guess,
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by gavagai691 5y ago
Two possible reasons. 1. First, though I am not sure of this (i.e. this should be verified), I heard that the team working on AlphaStar initially tried to create a Starcraft AI entirely through "self-play," but this was not succes
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by gavagai691 5y ago
Note that finding "a k-digit prime" is not the same as finding "the kth prime." I don't have any strong feelings either way about whether the former would be possible in polynomial time or not, but I would be pretty
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by gavagai691 5y ago
"Also I think we have shown using a variant of Galois theory that there can not be a closed from solution for the nth prime." I don't think this is correct. For one, it is not clear what "closed form" would mean in
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by gavagai691 5y ago
By that definition, I agree, if you add the qualifier "Nelson solved the subconvexity problem for for automorphic L-functions." I still think it's vague to talk about "the" subconvexity problem without specifying wh
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by gavagai691 5y ago
I don't believe it... it's really him https://www.youtube.com/watch?v=ZHpG135ge7Y !
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by gavagai691 5y ago
Thinking about digit size is sort of fine for simplification / not turning off general audiences with equations, but a bit of a pain to think about if , e.g., the things you're comparing might be smaller than one. What Lindelof s
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by gavagai691 5y ago
It's not entirely fair to call the second point a major slip. I think that it is still sort of inaccurate, but not exactly for the reason I had said above; see the thread following kevinventullo's comment below. In any case, my se
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by gavagai691 5y ago
As a further addendum, there are different "aspects" in which you could want the bound to be subconvex. As a result, even for a given family of L-functions) there is more than one "subconvexity problem." In this case, Ne
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by gavagai691 5y ago
A subconvex bound is any bound that beats the convexity bound of 25%. If you would define "the subconvexity problem" as beating the 25% bound AT ALL (or in other words providing any subconvex bound), then the statement in the subt
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by gavagai691 5y ago
There is actually one interesting connection between RH and integer factorization. This has to do with the idea of "Mobius pseudorandomness." For simplicity, I'll phrase things in terms of not Mobius, but the Liouville functi
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by gavagai691 5y ago
"The Riemann Hypothesis conjectures that there is a way to know the distribution of primes in a higher dimensional imaginary math. That the unintuitive and difficult system that gives us primes in real number space is somehow contained
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by gavagai691 5y ago
(To expand on this a bit: the reason that GRH is so important is because of its ubiquitous applications in mathematics. Maybe you can think of these applications as different food items, whose recipes call for GRH. The problem is that GRH i
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by gavagai691 5y ago
My bets are on another analytic number theorist for the Fields this cycle, namely James Maynard.
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by gavagai691 5y ago
While I had a couple of gripes with the article, I don't get the sense that the article exaggerates the significance of this work. The (Generalized) Riemann Hypothesis implies the (Generalized) Lindelof Hypothesis. The latter is a part
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by gavagai691 5y ago
Two inaccuracies in the article. For purposes of simplicity, the author writes "But the Lindelöf hypothesis says that as the inputs get larger, the size of the output is actually always bounded at 1% as many digits as the input."