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Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

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Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#171

Post by trash3 »

maegul wrote: post #169
pa7x1 wrote: post #78

Math used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach…

> but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach a point where a mathematician's in…

This sentiment is humorous, as I'm an optimist apparently. More children will learn more quickly. Applying AI to education should supercharge the smartest.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#173

Post by [deleted] »

__MatrixMan__ wrote: post #157
pa7x1 wrote: post #78

Math used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach…

Another approach to the finite-mathematician-lifespan problem might be to develop new foundations that are closer to the edge. I expect there's a logical universe in which sets are bizarre and hard to construct but objects which would take a modern mathematician years to grok are convenient and simple to work with.

[deleted]

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#174

Post by firecall »

pa7x1 wrote: post #78

Math used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach…

Perhaps math focused hot-housing at a younger age could provide an extension?

(genuine question, as I don't know anything about it)

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#175

Post by ta988 »

x0x0 wrote: post #161
ahzhou wrote: post #143

Earlier quoted context omitted.

While not common, I know of other Chinese diaspora in North America with similar stories. Many graduates from post Cultural Revolution China left the country in 90's and found the language barrier (and accompanying discrimination) too high to overcome. The man delivering your fried rice might have a PhD.

An unfortunate parallel: the best physics professor (unfortunately, just an adjunct) I ever had was a Russian immigrant. He quit teaching to go run a blini restaurant because it paid way more :(

This is so true and still the case. I've seen so many highly skilled immigrants passed over for politics and image reasons... Academia is ruthless but for the wrong reasons.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#176

Post by rnvannatta »

rtpg wrote: post #132
pa7x1 wrote: post #78

Math used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach…

While I get what you're saying, and clearly there is "more stuff", I think we shouldn't discount how progress can make things simpler on this front. Proofs we learn are usually much more refined than the original versions. Notational improvements and more interesting abstractions mean we can cover more ground more quickly. Another angle here, I remember seeing a study where some children were just... taught algebra.…

To add to your comment, quaternions predate rotational matrix operators by a considerable amount (1843 vs not exactly clear, ~1900 with Peano or ~1920 with Weyl), despite quaternions being much more challenging to manipulate. There are definitely simpler ways to view the same things.

There was a cottage industry of exotic hypercomplex numbers that disappeared when linear algebra matured to eclipse them.

In fact, Maxwell's Equations were originally derived with quaternions.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#177

Post by [deleted] »

fnordpiglet wrote: post #53
kenjackson wrote: post #29

Earlier quoted context omitted.

Someone needs to make a movie about his life, or at least a documentary.

Good luck finding a movie about Isaac Newton or Einstein, or literally anyone whose value to the world is more than pretending to be someone else or lying a lot, let alone a very interesting mathematician no one recognizes. (Ok I know there’s a few movies about folks like Turing and Nash, but it’s pretty slim pickings).

[deleted]

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#178

Post by defrost »

fnordpiglet wrote: post #53
kenjackson wrote: post #29

Earlier quoted context omitted.

Someone needs to make a movie about his life, or at least a documentary.

Good luck finding a movie about Isaac Newton or Einstein, or literally anyone whose value to the world is more than pretending to be someone else or lying a lot, let alone a very interesting mathematician no one recognizes. (Ok I know there’s a few movies about folks like Turing and Nash, but it’s pretty slim pickings).

N Is a Number: A Portrait of Paul Erdős is a decent enough documentary about a specific mathematician.

Colors of Math breezes across six contemporary mathematicians.

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#179

Post by pie_flavor »

pa7x1 wrote: post #78

Math used to be a young person game, but it now requires so much knowledge just to get to the frontiers of human knowledge, not to speak of making a dent into uncharted territory, that results are being obtained later and later in life. When mathematicians have had time to accrue sufficient knowledge while still being sharp enough to make the intellectual leap. The sad part is that as the trend continues we may reach…

Scott Alexander has an excellent short story on this subject: https://slatestarcodex.com/2017/11/09/ars-longa-vita-brevis/

Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang

#180

Post by akira2501 »

nullc wrote: post #133
akira2501 wrote: post #126

Earlier quoted context omitted.

If it were just that, it would be trivial to break. It's the fact you generate the key after a modulus operation that makes it difficult to recover.

Nope. The public key is not reduced mod anything in RSA. The large semiprime the user calculates is emitted explicitly as part of the public key and is used as a modulus in RSA operations. Factoring that large integer directly yields the user's private key.

Yep.. should not have done that from memory. I had the private exponent in mind and forgot about the simplicity of the actual "RSA problem."
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