Is this something a proof assistant could be used to help validate?
Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
181–190 of 439 posts
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#182Earlier quoted context omitted.
Patent clerk (at least back then) is a more skilled job than it sounds, as it's someone that actually reviews the patents rather than just a general office dogsbody, so you have to understand the technology and to some extent the science in those patents. It's not totally unrelated to being a scientist and definitely a less surprising early career job than delivery driver.
A patent clerk now is a technical job as well. It’s a flaw in peoples thinking that “clerk” implies something low rank. If someone tells you they were a “clerk” for a Supreme Court judge don’t be surprised when later in life they have an impressive legal career
Pretty sure all the SC justices clerked in their early careers. I'm not in law but I think it's the expected path
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#183Is Yitang Zhang this century's Ramanujan?
> While he never went to school at UK, this will not be his first time on campus. Following his graduate work at Purdue University, Zhang lived in Lexington for a few years and managed the finances at a local Subway franchise. During that time he would also spend hours in the mathematics library at UK, reading journals on algebraic geometry and number theory. A real-life Good Will Hunting, his backstory is incredible…
This sounds like the Margaret I. King library building AKA the Science & Engineering library. Otherwise, I'm not sure which library they're referring to. Interestingly, there was a subway on campus too. I wonder if it was that one, by chance. Small world.
source: UK is my alma mater.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#184Earlier quoted context omitted.
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, Maxw…
I am somewhat unconvinced that quaternions are more challenging, or at least a worse way to think about the issue :
And speaking of Maxwell's Equation"s" :
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#185Big if true
I was gonna comment this too goddamn
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#186Earlier quoted context omitted.
> While he never went to school at UK, this will not be his first time on campus. Following his graduate work at Purdue University, Zhang lived in Lexington for a few years and managed the finances at a local Subway franchise. During that time he would also spend hours in the mathematics library at UK, reading journals on algebraic geometry and number theory. A real-life Good Will Hunting, his backstory is incredible…
This sounds like the Margaret I. King library building AKA the Science & Engineering library. Otherwise, I'm not sure which library they're referring to. Interestingly, there was a subway on campus too. I wonder if it was that one, by chance. Small world. source: UK is my alma mater.
IIRC, in the 90s there was a Subway in the same complex that housed the Kentucky Arcade, but maybe it was a Blimpie's. Maps show it as a seven minute walk to the King Library. My hope is that I crossed path with this genius at some point in between epic battles of Tekken 3 or NBA Jams. I grew up in Lexington.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#187Earlier quoted context omitted.
The Greek characters in the screenshot are standard for the subject. The letters "chi" and "psi" (in that order) are the preferred letters for denoting Dirichlet characters, and zeros of L-functions are always denoted by "rho."
See, this is what I meant. Not only reading in the paper where X was defined but have this in-depth knowledge of why a certain symbol was used and how it came to be, knowledge that probably not even all full-time mathematicians that studied their entire life have.
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Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#188Earlier quoted context omitted.
I feel like saying this is similar to making progress on P!=NP is not accurate (extreme disclaimer: I have no formal math training). My understanding of P!=NP is that an answer to that has strong implications for the nature of the concept of determinism _of reality_, let alone most cryptography and lots of other stuff too. From my quick scan of the GRH wikipedia article, it doesn't appear that the GRH has the same wi…
I think P != NP is extremely interesting, but I wouldn't say it has strong implications for the nature of the concept of determinism or reality. I think that the idea of a Turing machine / the notion of computability has deep philosophical implications, but even that I wouldn't say has implications for "the nature of reality." If you think that prime numbers are interesting, then I can tell you that GRH is the single…
>has deep philosophical implications, but even that I wouldn't say has implications for "the nature of reality."
what would be an example of "deep philosophical" implication that has no bearing on the "nature of reality"
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#189Earlier 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).
This whole theme is sort incompatible with movies. Most people like to relate to the characters in the plot. The "genius guy" does something we can't understand has very little appeal as a story.
Same thing goes for mathematics that is too "deep". Most people could not care less about prime numbers. Yes, they drive important cryptographic procedures. But we care about cryptography. We care that the message gets to its destination "safely". If its done using prime numbers, imaginary numbers, geometric numbers or fantasy numbers, it does not matter.
Re: Monumental (if correct) advance in number theory posted to ArXiv by Yitang Zhang
#190Earlier quoted context omitted.
> For some 10 years, I had recommended 100 mainland Chinese students to the department and all accepted by the department. I am always indebt to the trust of my judgements by the department. Only very few of them misbehaved, bit the hands which fed them, none of them intended to murder their parents/friends , almost all of them performed well and became well-liked. No murderers, great success!
It's a reference to Brendt Christensen.
I’ve looked it up and wished I had not.
( Interestingly, every summary of the case in media and Wiki stops listing the evidence against him at his secretly taped confession to a girlfriend - confession that included some things absolutely not confirmed. The most convincing evidence to my eyes is the victim’s DNA in the blood found under the carpet and elsewhere there it has survived cleaning efforts. This is not mentioned anywhere except in the court recordings: https://news.wttw.com/sites/default/files/article/file-attac... . Kinda sad what is convincing these days ).