Timeline for How does one find out what's happening in contemporary mathematics research?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 20, 2014 at 15:49 | comment | added | Michael | @Joël: I agree, in all the time-sensitive examples the fast improvements were done by specialists. | |
| Jun 20, 2014 at 15:32 | comment | added | Joël | use with profit a new discovery, compared with an older practitioner of the field. This is in part compensated by the help of his PhD advisor, but a PhD students who likes to works alone and is independent-minded (certainly an important quality to do good research in the long run) will have this disadvantage, and the solution is to work on problems which are not very time-sensitive. Fortunately, the are the majority of interesting math questions. | |
| Jun 20, 2014 at 15:30 | comment | added | Joël | connection with the field which comes from years of work in the subject. That's in my opinion the main problem for an outsider doing mathematics: when there is something to do fast, people with a lot of experience in the field will in general be way faster. But this problem does not only concerns outsider who has left mathematics. It also concerns in a fundamental way PhD students. A well-informed PhD student, which goes to many seminars and attends conferences and speaks to many people so that he hears of everything that's happening in his field is still at an enormous disadvantage to... | |
| Jun 20, 2014 at 15:26 | comment | added | Joël | @Michael: Thanks. The first example is too far from my interest to let me really appreciate it, ut the second is very interesting, and I didn't think of it. I actually thought of the third, about Zhang, and still think it illustrate my points. The strengtenings of Zhang's results were done by people who were some of the leading experts in the field. The edge they had over anyone trying the same endeavor did not come from their knowledge of the existence of Zhang's work (which was announced in the free newsletter of the AMS the very week it was put on the Arxiv) but from their intimate... | |
| Jun 20, 2014 at 15:01 | comment | added | Michael | @Joël: Here are some very fast development examples, from 3 different decades: 1. Date-Jimbo-Kashiwara-Miwa approached in 1981 non-linear PDEs with affine algebra representations; subject effectively closed in 1982. 2. Seiberg-Witten invariants appeared in 1994; most striking applications, such as the proof Thom's conjecture, were completed within a year. 3. Strengthenings of Zhang's results by Tao & Co and Maynard came out within months from the Zhang's paper, sometimes even BEFORE the original paper was published... | |
| Jun 20, 2014 at 13:29 | comment | added | Yemon Choi | @Michael I am inclined towards Joël's views on timescale, but would be happy to be corrected with specific examples in mathematics. (Theoretical computer science may be different.) | |
| Jun 20, 2014 at 11:23 | comment | added | Joël | Interesting. Can you give some examples of such "short windows of opportunity for important research"? I can perhaps think of a few examples in my own field, but then the only people who could possibly make use of that "short window of opportunity" are expert themselves, who'll get directly informed by their network (seminars, conferences, papers submitted on arxiv and to journals, friends) of the developments opening the "window of opportunity". And even then, research done through those windows will not be that important. | |
| Jun 20, 2014 at 3:58 | comment | added | Michael | I would have to disagree about timescale: there have been many important developments with relatively short windows of opportunity for important research. Sometimes getting to the subject just one year after it was introduced means you shouldn't bother, the subject is effectively closed. Thus announcements with short high level overview on timescale of a few weeks would be very important to those not in direct contact with the leading specialists. | |
| Jun 20, 2014 at 2:20 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Jun 20, 2014 at 1:57 | history | answered | Joël | CC BY-SA 3.0 |