vonLipwig wrote:My impression is that very very few applicants have a publication. I know people who have been accepted to a wide variety of the top schools with no publications.
(This seems to contradict kuz, above. Perhaps undergraduate theses are looked on favourably here, and this would explain the cases I know of)
Certainly most people at other US universities that I know tend not to have publications. So Princeton is a bit of an outlier in that respect, for exactly the reasons that gromov wrote.
gromov wrote:Well, I think admissions styles vary greatly among strong schools. Princeton is a program with an often 4-year track, with no formal course requirements, if I've got that right. As a result, I think they may stress a student's readiness and maturity to jump into research more.
This isn't to say someone without such credentials can't get accepted at Princeton of course. I think very strong letters from reputed faculty, a strong background, and other accomplishments suggesting mathematical talent can also work.
One thing about kuz's experience is that I think he's speaking of those who accepted Princeton's offer, not merely those accepted at Princeton. It is my view that those accepted to Princeton may not always, amidst the applicant pool, all be well suited to its program style, even if they're "strong" enough.
Those who accepted Princeton's offer may be likelier to already be excited about pursuing a certain track, have started along it, and continue in the program this way. I can think of at least one case where this precisely happened.
I think there are plenty of students at Stanford, Chicago, various Ivy Leagues and top US public schools who do not possess a large publication record, and who aren't very sure of what they want to do. Those schools all produce students of exceptional caliber and researchers of exceptional caliber.
General advice: to get into a top program, worry first that your learning, grades, and letters are going to be up to par.
Then add on publications if all is going well, and it could be a bonus to knock you into some of the most hypercompetitive. I think for all but the strongest of the strongest students, it's going to be a bit of luck of the draw, as far as I can tell, to get into schools like MIT, Harvard...
This is spot on. A lot of my fellow classmates are pretty ready to start research. We have to pass a general exam at the end of our first academic year, but then it's research all the way after that; furthermore, there are no requirements to take classes (though most people audit some classes in their first year, and even in their later years if there are interesting advanced classes on offer). So it's a shorter degree (by US standards) that is aimed towards students who are mathematically mature in their ability to do research. Of course this doesn't necessarily mean having already been published.
variationofhedges wrote:Could you give some more concrete description of what the publications are like? (E.g. Journal reputation, length, depth or level of sophistication, relation to student's current research interest, etc.) Could you also comment on the fields of these papers? Thanks in advance.
Not sure I can go into so much detail, as I haven't read half of my fellow students' papers. And bear in mind that at the time of application for Princeton, a lot of these papers may not have even been completed, or were just on the arxiv but hadn't been accepted for publication in a journal as yet (my sole paper at the time fell into the latter category). So I'm guessing the advisory committee either read the papers on the arxiv (if they were up there) or took into account letters of recommendation detailing the applicant's research, rather than looking at the reputation of the journal.
I think a couple of the papers were from REUs and the like, and a couple of others were from senior theses (as mine was). The journal reputation varied; one guy had a (2-part) paper accepted in a top combinatorics journal (and this was a long 2-part paper). Others (from minor REU projects) had short papers accepted in average journals. In all cases, the research involved certainly wasn't mediocre (as many papers are!) but most papers weren't impressively sophisticated.
As far as fields go, I think all of them were related to the respective student's current research interests, but it's first year so too early to tell whether someone's interests might change. Of course there was a broad scope of fields: combinatorics, graph theory, analytic number theory, algebraic number theory.