The Pursuit of Beauty: Yitang Zhang solves a pure-math mystery(newyorker.com)
newyorker.com
The Pursuit of Beauty: Yitang Zhang solves a pure-math mystery
http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty
10 comments
It's pretty damning evidence if two of the biggest math breakthroughs needed to occur outside of our best universities.
Arxiv is turning into a great tool to spread academic ideas, and is in some ways replacing the role of traditional journals. However, how do we replace the funding side of the equation? In both of these breakthrough cases, it seems the researchers found a loophole or used their personal savings.
Arxiv is turning into a great tool to spread academic ideas, and is in some ways replacing the role of traditional journals. However, how do we replace the funding side of the equation? In both of these breakthrough cases, it seems the researchers found a loophole or used their personal savings.
I assume by "chinese professor at Harvard tried to steal the credit from Perelman", you mean the defamatory article written by The New Yorker regarding on Shing-Tung Yau. That accusatory article was written by an outsider with no regard to reality. For a correct account from within the mathematical community, see http://doctoryau.com/hamiltonletter.pdf.
While that may be true, there is no denying that Yau is a pretty divisive figure. He seems as interested in building his image in China and making the Chinese nation proud, than he is in doing real math. I can see why this attitude would rub some mathematicians the wrong way.
There is something unethical about Yau. Here is more:
http://en.wikipedia.org/wiki/Manifold_Destiny#Revision_of_th...
http://en.wikipedia.org/wiki/Manifold_Destiny#Revision_of_th...
> Mr X from Princeton solved poincare conjecture
Most likely Prof or Dr instead of Mr ;-)
Most likely Prof or Dr instead of Mr ;-)
Thank you for you comment. Very interesting information just like the article itself.
Hardy's comment about math being a "young man's game" has bothered me since I read his "Course of Pure Mathematics" about 10 years ago.
I'm sure there's at least a bit of truth to the statement that mathematical discovery is, in general, easier for younger minds, but it seems to be an unnecessary and harmful trope to propagate.
Either you still have it, or you don't. Why does the Fields Medal care about age? If a 60 year old proves the Riemann Hypothesis, why is he or she ineligible? This happened notably with Andrew Wiles. He (indirectly) proved Fermat's Last Theorem and was rewarded a "special plaque" instead of the Fields Medal for the crime of waiting until after his 40th trip around the sun to work on it.
There's also the issue of economic pressure. We expect our young minds to solve "real problems" and to want to make a lot of money doing it. Pure mathematicians get to "hide" in academia when times are good and are often on the street when they aren't so good. In the absence of a focus on supporting the arts (including math) through patronage etc it is just hard for young people to get in the field. Older people have more time. Let them create without lowered expectations.
For a deeply beautiful subject with a lot of very smart people, this whole age thing is just scratch-your-head puzzling.
I'm sure there's at least a bit of truth to the statement that mathematical discovery is, in general, easier for younger minds, but it seems to be an unnecessary and harmful trope to propagate.
Either you still have it, or you don't. Why does the Fields Medal care about age? If a 60 year old proves the Riemann Hypothesis, why is he or she ineligible? This happened notably with Andrew Wiles. He (indirectly) proved Fermat's Last Theorem and was rewarded a "special plaque" instead of the Fields Medal for the crime of waiting until after his 40th trip around the sun to work on it.
There's also the issue of economic pressure. We expect our young minds to solve "real problems" and to want to make a lot of money doing it. Pure mathematicians get to "hide" in academia when times are good and are often on the street when they aren't so good. In the absence of a focus on supporting the arts (including math) through patronage etc it is just hard for young people to get in the field. Older people have more time. Let them create without lowered expectations.
For a deeply beautiful subject with a lot of very smart people, this whole age thing is just scratch-your-head puzzling.
Humans are often silly and irrational and like making up arbitrary rules for the games they play. Don't lose too much time scratching your head about these things, or you'll quickly end up bald.
I think the degradation with age as in part bio/physiological might also be in part a matter of adjustment to circumstance. That is to say the really hard problems in mathematics (or physics) one generally doesn't get to work on full-time (since it's very likely that one will work on them for years without producing any results); the most likely path in academia is therefore to do mediocre -to fairly good research that produces results and publications.
When one compromises in to doing work that's less difficult than one can be doing because it's what's necessary career wise, it's not surprising that one's mental alacrity declines.
There are certainly exceptional people that can do one kind of thing for work (or tenure), and at the same time publish significant work in a parallel field - but I think it's rare.
When one compromises in to doing work that's less difficult than one can be doing because it's what's necessary career wise, it's not surprising that one's mental alacrity declines.
There are certainly exceptional people that can do one kind of thing for work (or tenure), and at the same time publish significant work in a parallel field - but I think it's rare.
Once you get enough of an institution built up around you - grad students to bootstrap, grants to write, what have you - there's so much less time to just work on the problems that interest you. I think there's less and less space in Academia for the 'individual contributor.'
At the risk of downvotes, I will state a whole bunch of [Citation Needed] BS, which is, nevertheless, empirically true & in Hardy's favor -
1. Cerebral atrophy affects left brain disproportionately more than the right 2. Math is predominantly a left-brain activity. 3. Ergo, short-term memory & dexterity with numbers generally degrades with age ( supposedly peaking at 25 & declining from then on).
Most math majors I've spoken to ( from prodigies to professors & people in between ) attest to the fact that they were much sharper when they were quite young. It isn't that they become dumber as they age, more like - they pick up a different kind of math to compensate for some of the other math that required them to exercise their symbolic manipulation skills at superior pace, which they have now lost.
1. Cerebral atrophy affects left brain disproportionately more than the right 2. Math is predominantly a left-brain activity. 3. Ergo, short-term memory & dexterity with numbers generally degrades with age ( supposedly peaking at 25 & declining from then on).
Most math majors I've spoken to ( from prodigies to professors & people in between ) attest to the fact that they were much sharper when they were quite young. It isn't that they become dumber as they age, more like - they pick up a different kind of math to compensate for some of the other math that required them to exercise their symbolic manipulation skills at superior pace, which they have now lost.
On the flip side, anyone who's in the social sciences can tell you that self-reporting is a terrible gauge.
I don't want to disagree with such studies (as I agree with them), but at the same time there is a tendency to derive absolutes when looking at such studies. Reality doesn't tend to support absolutes, however. Biological studies like these still fall onto bell curves, and outliers exist on such spectrums.
There's an interesting (and impassioned) critique of this article at
http://www.angrymath.com/2015/02/yitang-zhang-article-in-new...
http://www.angrymath.com/2015/02/yitang-zhang-article-in-new...
Could you perhaps explain what you found interesting? It's an angry screed very revealing of its author's personality, but not particularly insightful about the article.
I was thinking the same, the blogger appears to have a lot of things he's upset about and is taking them out on the article.
This author immediately made me hate him starting with the first paragraph. What was the point of that first paragraph? And I'm OK with adding some color throughout to liven up a story but I felt like this author was just wasting my time to try to show off that he's a writer. What an asshole.
That first paragraph's tl;dr was basically: I'm bad with numbers, I'm an artist, but someone told me about this math guy with an interesting story.
Correct me if I am wrong, but I believe the author made an error. The author wrote:
"A prime from which you can remove numbers and still have a prime is a deletable prime, such as 1987".
However if you remove the 7, then the number is divisible by 2, so the statement: "A prime from which you can remove numbers and still have a prime is a deletable prime" does not apply to 1987.
"A prime from which you can remove numbers and still have a prime is a deletable prime, such as 1987".
However if you remove the 7, then the number is divisible by 2, so the statement: "A prime from which you can remove numbers and still have a prime is a deletable prime" does not apply to 1987.
> However if you remove the 7, then the number is divisible by 2, so the statement: "A prime from which you can remove numbers and still have a prime is a deletable prime" does not apply to 1987.
A deletable prime doesn't require that the deletion order start from the last digit; the deletion order for 1987 is:
1987 -> 197 -> either 19 or 17
A deletable prime doesn't require that the deletion order start from the last digit; the deletion order for 1987 is:
1987 -> 197 -> either 19 or 17
The definition given in the article is an informal shortcut, the complete definition is http://mathworld.wolfram.com/DeletablePrime.html and 1987 is indeed a deletable prime (see http://oeis.org/A080608/b080608.txt for http://oeis.org/A080608).
For anyone behind the paywall, here's a pastebin link. The article was a bit long to break into comments.
http://pastebin.com/Xtm3f64E
http://pastebin.com/Xtm3f64E
Just googling for the article's title leads to a link that works. They don't paywall people coming from Google
OT the cartoons interspersed in the OP are absolutely awful. Nice work if you can get it!
The author does not even understand the difference between arithmetic and mathematics.
What's the difference?
How can it be solved , if it's still considered
a mystery ?
get rid of new yorker = paywall
I too have read my last complimentary article of the month, and am stuck behind the paywall. Could someone paste the article here?
Here's a pastebin link, the article was a bit long to break into comments. I hope that's okay.
http://pastebin.com/Xtm3f64E
http://pastebin.com/Xtm3f64E
Thanks a bunch!
That adjunct job gave him sanity to solve the problem. In the case of Grigori Perelman, these universities (Princeton, Harvard) did not want to give tenure job after his proving Soul Conjecture; this was during his postdoc at Courant NYU.
Of course, these math guys wanna offer a tenure track position, which woulda prevented him from proving Poincare conjecture. He went back to Russia, spent time in isolation for 8 years or so. Proved it. Once he published the paper on arXiv, the shithead professors at Princeton, Columbia want him back, so that they can be co-authors of his paper on poincare conjecture or these universities can appear on the paper a la affliation: you see, these elite universities love to show "Mr X from Princeton solved poincare conjecture".
Another chinese professor at Harvard tried to steal the credit from Perelman for the same conjecture.
It is a big mess out there. Zhang somehow used his adjunct/tutor job to spend time in number theory. Perelman used his postdoc fellowship savings to solve his problem. IN Zhang's case, he got the tenureship after his proof; Perelman gave up math.