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"):
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.
Their Chinese names are Zhāng Wěi (张伟), Yùn Zhīwěi (恽之玮), and Yuán Xīnyì (袁新意); I can’t find one for Zhu Xinwen.
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 don't think this is fault of the journalist, Chinese people in the US use their own transliterated names. The journalist is most certainly just using the name that was given by the Chinese themselves.
> 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.
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.
> 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).
Pinyin with tone marks is a perfectly phonemic orthography (at least as to standard Mandarin). That's a completely unrelated idea. Nobody who doesn't know Chinese will be able to pronounce Chinese names because (1) they don't know how to read them, and (2) the sounds of the language are different.
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.)
The parent commenter for my post was seemingly talking about how English orthography is non-phonemic as an example of why "any language" has the property that you described, so I was just trying to point out that this isn't always the case.
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.)
I did not know that. I always assumed the Romanizations mapped over one-to-one.
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.
The pinyin given by op has a one to one mapping to the pronunciation, and it seems a bit inconsistent that they fully Romanized their names while leaving Ngô Bảo Châu in the Vietnamese alphabet. But even if they did (and I believe this was what op was getting at) afaik there wouldn't be a one to one correspondence between surname pinyin and character. Incidentally, my sense is that their is broad awareness of these problems, at least in academic circles, which have a kind of "your name is your brand" attitude, and its common to see both short and full names in publications.
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.
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.
Do English-language publications change the way authors write their names?
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.
I think the parent commenter's complaint is about this journalistic article (from Quanta), which isn't by any of these mathematicians, just about them.
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
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.
That's definitely a big source of confusion, but in the case of Wei Zhang, he uses the Western name order on his own homepage and for his e-mail address.
"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.
(I'm a number theorist, and this is very close to my research area.) The Gross-Zagier formula (along with work of Kolyvagin) from the 1980s proved the Birch and Swinnerton-Dyer conjecture when "r_an <= 1"; this conjecture is an amazing link between analysis and arithmetic, and also one of the Clay Problems. This number "r_an" is the order of vanishing of a certain "generating function" that counts the number of solution to y^2 = x^3 + Ax + B modulo all prime numbers. For about 30 years now, people have been completely stumped at coming up with even a wishy-washy conjectural half guess* as to what to do when r_an is 2 or larger. In number theory a standard approach is to replace the integers Z = {... -2, -1, 0, 1, 2, ...} with a polynomial ring F_p[X] over finite field, and try to solve analogous problems (this is called working "over a functional field"). The paper that this article is about has come up with exactly what to do in case r_an is 2 or larger in the function field setting. So far they haven't figured out how to do anything over the rational numbers yet. Sometimes solving a problem over function fields provides incredible and valuable insight into how to solve the analogous problem over the rational numbers, and sometimes it doesn't (e.g., the function field analogue of Fermant's Last Theorem and the ABC conjecture are both basically trivial to deal with, whereas the same problem over the rational numbers is ridiculously hard).
When I was at Harvard in the 1970s, I just assumed (algebraic) number theory and algebraic geometry had heavy overlap. I'm surprised that anybody would still argue this is surprising.
You go to school for years and become an expert in a field. Understanding isn't out of the reach of any graduate student in the relevant field I would assume.
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.