A math quartet's breakthrough bridges number theory and geometry
quantamagazine.org
quantamagazine.org
What these guys are doing is definitely awesome. (A bit removed from my specialty, so I can't answer detailed questions about it unfortunately.)
But let me add that there are already a LOT of bridges between number theory and algebraic geometry. To get a sense of the scope, google "Arithmetic geometry" or "Diophantine geometry" and you will find much, including (large) books on these topics.
Meanwhile, here is a classical one. How do you find all integer solutions to the equation a^2 + b^2 = c^2?
First of all, it is fairly easy to see that this is the same problem as finding points on the circle x^2 + y^2 = 1 where both x and y are rational numbers. Now, to find these use "stereographic projection". See here (scroll down to "stereographic approach"):
https://en.wikipedia.org/wiki/Pythagorean_triple
The bottom line is that there is a picture you can draw which graphically gives you an easy solution to this number theory problem -- and once you draw the right picture, it is easy to use it to write down the algebraic solution as well.
These four mathematicians are continuing a long and wonderful tradition of finding applications of geometry to other areas of mathematics.
I wish English-language publications would treat Chinese names better. Without the Chinese characters, you can’t tell what their name actually is, and without accent marks on the transliteration, you can’t tell how to pronounce it.
Granted, it doesn’t matter to most English-speaking readers, but it should matter, because those are their names. It’s no wonder so many Chinese feel the need to adopt an extra name when moving to the West.
I can't believe I'm saying this, but: it seems like the sort of thing an awareness campaign could solve, no? a) It can't just be me. b) There's no good argument against it. Not for a formal publication.
https://en.wiktionary.org/wiki/ch%C4%81o#Mandarin
https://en.wiktionary.org/wiki/zh%C4%81o#Mandarin
The places that I've seen names printed in native scripts are Donald Knuth's books (look at the TAOCP bibliography, with native script names all over the place), and, very recently, the Rakudo Perl 6 release notes.
https://perl6advent.wordpress.com/
I thought Knuth regarded it more as a matter of respect than of academic career benefit or scholarliness, but it has all of those virtues, although at least the Cyrillic and Hebrew ones have fairly low transliteration ambiguity.
Tell it to Chebyshev, Chebychev, Chebysheff, Chebyshov, Tchebychev, Tchebycheff, Tschebyschev, Tschebyschef, and Tschebyscheff.
Or maybe that should be "tousché"!
I wonder if this is somehow related to Bibliography and Bibliographical software, indexes and references. If you have started your career with certain name in BibTeX without accent marks, changing it later may screw up references.
Although I sympathize with this concern, it looks like two of these mathematicians write their own names (solely) in Romanization without tone markings in their own academic publications, for example
http://arxiv.org/abs/1512.02683
linked from the article.
So it's not necessarily something that other people are unilaterally doing to them. (Although Prof. Yun has put his Chinese name at the top of his homepage, but seemingly not in any of his papers.) Maybe other people are pressuring academics with non-Latin names indirectly not to use their names in native scripts in their publications because of editorial policies in journals that would discourage or forbid it, or, as you suggested, because of journals' software tools that would have compatibility problems.
E.g. Wei Zhang in the story should be Zhang Wei - his surname is Zhang.
I won't be surprised if he goes by Wei Zhang because that's how his name appears on official documents.
https://www.math.columbia.edu/~wzhang/
(Yes, it's possible that someone else originally chose this order for him.)
朱歆文.
You certainly can in the case of 张 zhāng, and you'd be more than justified in assuming a Mr. Yuan was surnamed 袁 yuán.
On the other hand, no one who isn't already familiar with Chinese will be able to pronounce Chinese names even if tone marks are provided. Accurate pronunciation is not a goal of foreign name representation, because it's impossible.
And of course, an English-speaking audience wouldn't even be able to recognize the same name twice in two publications if it was given in characters.
The only people who can benefit at all from more detailed name information are people who are interested in the foreign language in question. Those people are very rare; magazines tend to be written for their readers. Chinese sources say 薛定谔 rather than Schrödinger, and 奥巴马 rather than Obama, because that's what their audience is able to read.
That goes for most any language. Take a simple and common names like 'Abbott" ... pronounced more like abbit.
https://en.wikipedia.org/wiki/Phonemic_orthography#Compariso...
> Languages with highly phonemic orthographies often lack or rarely use a word corresponding to the English verb "to spell" because the act of spelling out words is rarely needed (careful pronunciation of a word is generally sufficient to convey its spelling).
Spanish also has a perfectly representative orthography, but you should see what's happened to Spanish place names in the US.
(I originally wrote that Spanish also had a "perfectly phonemic orthography". That's not true; some sounds may be represented in more than one written form. But the written form of a Spanish word gives sufficient information to pronounce it.)
I guess the odds are extremely low that people who don't speak a language will get much benefit from access to names (etc.) in its writing system or from the fact that an orthography is regular enough that they could learn it quickly. And I didn't mean to contradict you directly on your original point, but I think I would disagree on a narrow point. Learning a language, speaking a language, and so on, are not binary propositions, and providing information like native spellings can help current and prospective language learners, as well as people who are just curious about a language. I don't speak Italian, Japanese, Bulgarian, or Chinese, but I've spent some time studying their writing systems and could sometimes gain information from non-transliterated written information in those languages. (But it's true that most people don't exhibit much curiosity about languages they don't speak, nor propensity to learn more about them or their writing systems, so it's not clear that these possibilities are a strong argument for an editorial policy of presenting native scripts.)
"Another noteworthy feature of our work is that we need not restrict ourselves to the leading coefficient in the Taylor expansion of the L-functions: our formula is about the r-th Taylor coefficient of the L-function regardless whether r is the central vanishing order or not. This leads us to speculate that, contrary to the usual belief, central derivatives of arbitrary order of motivic L-functions (for instance, those associated to elliptic curves) should bear some geometric meaning in the number field case."
A one-line Clay Prize motivation: Geometric interpretations of higher order derivatives of L-functions could potentially be leveraged (or more likely, illuminate a path) to make progress on conjectures about order of vanishing of L-functions, e.g. Birch Swinnerton-Dyer.
The amount of background research required to even try to understand this is immense
It's just nuts. How does one begin to put the pieces together