# Programs Mathematics PhD programs of highest tier

1. May 19, 2010

### deRham

Hi all,

I wanted to request your help in discerning what kinds of things seem to help students get into some of the very selective schools, specifically....Chicago, MIT, Berkeley, Harvard all come to mind... I am not optimistic about Harvard at all, but include it because in my heart of hearts I'm very interested in some of their faculty.

I already know things like a rigorous schedule with good performance, *letters of rec*, figure in. But my question is what might make the final cut into some of these schools [anticipating the answer might vary among them], in your experiences.

2. May 20, 2010

### 98whbf

biggest factor is blind chance

3. May 20, 2010

### Shackleford

Very affluent pedigree helps, too.

4. May 20, 2010

### twofish-quant

One thing about graduate school is that you shouldn't be too obsessed with schools, since the "big name" of a school matters surprisingly little. At the graduate level, there are schools that you've never heard of that are considered super-world class, whereas some of the "big name" schools are considered inferior in certain areas. The real "branding" when it comes to Ph.D. programs is not the school. No one really cares that you went to Harvard. The real "branding" is the dissertation advisor and the committee. The school just keeps the lights on and provides office space.

So the absolutely first thing that you need to do is to do research, and figure out why you want to apply to a specific school, which means being familiar with the academic literature in an area. The fact that you are listing a random set of schools with nothing particular in common suggests to me that you haven't done your homework.

Getting admitted to a particular school usually involves a statement of purpose that specifically indicates that you have a genuine interest and ability to advance the schools research program, which means finding out about the schools research program.

The other thing is that I've found that if you want to interact with a professor its surprisingly easy. Just e-mail them with enough information that makes it obvious that you have the technical competence to talk intelligently about their work.

5. May 20, 2010

### twofish-quant

One other thing that isn't obvious. Attend professional conferences.

6. May 20, 2010

### bignum

Psssss Princeton...

I don't know how Harvard comes to mind when you are doing Science...

7. May 20, 2010

### deRham

Hi all, thanks for the replies.

To twofish-quant and others concerned about this - I know the list looks suspicious like it's just a bunch of prestigious names. But let me assure you that I'm well aware of the standard advices like "your adviser is what counts". Be aware that some of these schools are very broadly strong in math. It so happens there are very specific people at them whom I would like to work with. That does involve getting in as a side thing. I can tell you I probably would not survive at a program which is prestigious but without people I'm interested in working with, so let's hopefully leave this line of discussion. Suffice it to say my interests are a little subtle, which is why I don't just have a simple list like "Princeton and Harvard" for number theory, or "NYU, UCLA, ......" for analysis.

So to be clear, I hope to get advice on what one might do to actually make it into some of these programs, since they happen to be very selective.

Your advice about conferences is well-taken, twofish-quant. What would you say is the primary goal at these - to introduce oneself and stay in touch with professors whose work relates to one's interests, for instance? More advice on this would be appreciated.

Also, it's math, not science, bignum :) and both those schools are great at math, and in fact at some similar fields.

8. May 21, 2010

### mrb

As someone who recently applied to some strong programs, got massacred, and will now be attending a school of a "lower tier" than where I hoped I'd be... Let me just say: it's ridiculously competitive. I was told by someone who would know that Harvard and Princeton pretty much only take students from prestigious schools where the profs have directs connections to the profs there (Yale, Chicago, etc) (with the occasional exception for the student who REALLY stands out). MIT and Berkeley are supposedly not QUITE as picky.

In any case, despite what twofish-quant has to say (and I'm talking about mathematics here), it really seems that almost all tenure track jobs at halfway decent schools are filled by people who got their PhDs at prestigious math departments, and the large majority of graduate students at prestigious departments did their undergrad at very good schools, usually with a well known math dept.

I wish I could tell you more; it's surprisingly hard to find out specifics on what exactly the departments want to see.

9. May 21, 2010

### bignum

More the reason Princeton > Harvard. Their Math program is superb if not the best.

Personally I think you should only go to Harvard if you are into Business or Law or I guess any Humanities.

10. May 21, 2010

### mrb

??? Is this a joke I'm not getting? Harvard's math dept is extremely strong, right up there with Princeton.

11. May 21, 2010

### zpconn

Harvard has one of the most renowned mathematics departments on the entire planet. It is easily on the same level as Princeton. Please in the future do at least a bit of research before commenting on which schools are good in which subjects. :D

I'm just an undergraduate myself, but from what I've been able to gather to get into Harvard, Princeton, etc. for mathematics you need to be one of the most outstanding students in the world. This would typically mean having a nearly flawless record from a top school in your country, countless graduate courses, a significant research accomplishment (if in the US, probably entailing at least two or three REUs, preferably only the most prestigious ones), extremely positive letters of recommendation from distinguished faculty, and then something else to distinguish you--maybe you did well in the Putnam, maybe you studied abroad for a year (Budapest, Moscow, etc.), maybe you taught a course as an undergraduate, etc.

The competition for these schools is truly international.

Last edited: May 21, 2010
12. May 21, 2010

Staff Emeritus

Perspective is important, and I think a poster's perspective is an important criterion to think about.

13. May 21, 2010

### eof

I'm a math grad student and I can tell you that the best mathematicians are at the best schools. Period. It's not like in physics where you have a few distinguished faculty members at some schools you've never heard of. Math is very competitive and elitist (much more so than physics, biology, chemistry and some other fields) and admissions are at the same level than theoretical physics.

I know a guy who is doing finance at Chicago (ranked #1). There's nothing special about him and there's absolutely no chance he would have got accepted to a similar program in math given his credentials. Regarding top math schools, I know that MIT, Berkeley, Stanford are slightly easier to get accepted to than Harvard and Princeton. For Harvard and Princeton you usually need to have done your undergrad at a top 5 college with an almost perfect record. The two North American exceptions at Princeton that I know of who didn't go to any of these schools for undergrad got a perfect score on the IMO and did some other incredible things...

At my top 20 school there's actually not a single professor who doesn't have an Ivy League Ph.D. This also seems to be the norm at every good school.

EDIT: Someone also mentioned analysis being NYU, UCLA... For analysis the place to go is Princeton. That's where the Chicago school moved.

14. May 21, 2010

### Animastryfe

Do you mean literally only Ivy League schools? So no Stanford, MIT, Berkeley, etc?

15. May 21, 2010

### deRham

Guys, I know how good Harvard is at math, I guess you may be posting clarifications for the
integrity of the forum.

"Do you mean literally only Ivy League schools? So no Stanford, MIT, Berkeley, etc?"

I bet that's not true. Honestly, the Ivy Leagues are terrific, but among them, only PhDs from Harvard and Princeton are the real ones I think are faculty with high frequency at top math schools.

"Someone also mentioned analysis being NYU, UCLA... For analysis the place to go is Princeton. That's where the Chicago school moved."

I realize I didn't include every terrific analysis school, which is why the "..." were necessary.

16. May 21, 2010

### Shackleford

I'm just happy to eventually hopefully graduate from an upper-level tier two university with physics major/math minor. :/

17. May 21, 2010

### eof

All professors except one are from Harvard or Princeton. I would say that it's just a coincidence that there is no one from Stanford, MIT, Berkeley or Chicago.

18. May 21, 2010

### BR40201

This is utter nonsense. There are plenty of phenomenal mathematicians at less prestigious schools, and "best" is often simply a matter of taste. How does one compare, for example, a leading algebraic geometer with a leading model theorist?

The "common knowledge" that there is a "highest tier" of math schools is largely based on such asinine indicators as the U.S. News rankings, the methodology of which simply involves requesting selected faculty members to rank various departments on a scale of 1 to 5 and then averaging the scores received from the self-selected sample (about 30% of those selected) that respond. If you look at the scores posted on the U.S. website, you will notice that a score difference of "0.1" can have a significant affect on ranking.

In practice, the credence given to these rankings mean that higher ranked schools generally receive applications from students with stronger undergraduate records, which explains how these reputations are maintained. Of course, undergraduate record is not a perfect indicator of success as a research mathematician (in particular, international students are often passed over in favor of American students from better known schools). I (like, I am sure, many others here) know plenty of mathematicians that received their PhDs from lesser known schools but have a very impressive research record and, conversely, plenty that went to Harvard/Princeton/Berkeley (etc.) and have achieved comparatively little.

As for the original poster's question, I think the "blind luck" comment is fairly pertinent (assuming they have a strong record and good GREs, and have not proved a significant result or attended Harvard/Caltech/MIT as an undergraduate). That said, letters of recommendation are probably the most important part of the application, so be sure to choose your referees carefully. Out of interest, what are your "subtle" research interests?

19. May 21, 2010

### deRham

"This is utter nonsense. There are plenty of phenomenal mathematicians at less prestigious schools, and "best" is often simply a matter of taste. How does one compare, for example, a leading algebraic geometer with a leading model theorist?"

I think it is somewhat nonsensical, not fully. Remember there may be great algebraic geometers, model theorists, string theorists, K-theorists, etc all at the same school. But yes, only the ignorant live by US News, and to know the real deal, one must actually know the work of faculty deeply...certainly there are mathematicians of the greatest caliber outside the schools US News graces most favorably.

"(in particular, international students are often passed over in favor of American students from better known schools"

So true.

Last edited: May 21, 2010
20. May 21, 2010

### deRham

Oh didn't see the remark about interests - well, that could get drawn out, because I'm still deciding, but what I meant was it wasn't a simple matter of answering "topology" or "logic"! If you would like to chat about our interests, feel free to introduce yourself and send me a message individually though.

21. May 21, 2010

### zpconn

I don't think anybody in this thread who said Harvard was one of the best schools for math did so because of anything U.S. News published.

Edit:

For clarity, I agree with nearly everything that BR40201 wrote. I just think BR40201 is overemphasizing the role of U.S. News in this. I knew of the reputation of Harvard/Princeton/etc. before knowing that U.S. News even ranked math grad schools.

Last edited: May 21, 2010
22. May 21, 2010

### BR40201

I think there is no doubt that Harvard has an outstanding math department, and I agree that many prospective grad students will be aware of Harvard without being familiar with any rankings. However, there is a difference between viewing Harvard as "one of the best schools" (similarly to how one might speak vaguely of "top ten" schools) and placing it firmly within an absolute "highest tier" of three to seven schools. In particular, I am concerned by the recent tendency to identify a group of "top n schools" (where $$5\leq{n}\leq{7}$$), invariably consisting of Berkeley, Princeton, Harvard, MIT and Stanford, together with some subset of Chicago and Caltech. This list is largely derived from the U.S. News rankings, and very misleading. The difference between the schools on this list and those slightly lower in the rankings, such as UCLA and Cornell, is largely research tastes, rather than quality of the research being produced, or (even more so) quality of graduate education offered. There is also a fashion component to the rankings (currently, algebraic geometry, algebraic number theory and Langland's program/representation theory in general seem to be favored), which should be taken into account.