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Harvard mathematics Ph.D

  1. Dec 6, 2009 #1
    Does Harvard expect people with straight A's in every subject in academic (including history, English, etc.) and perfect 2400 on SAT for getting into Ph.D program in mathematics in Harvard, or they expect just average scores on other academic subjects and SAT, but perfect 800 on mathematics on SAT and good grades in mathematics?
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  3. Dec 6, 2009 #2

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    Nobody cares what you got on your SATs in high school when applying for a PhD program.
  4. Dec 6, 2009 #3


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    PhD programs care about the GRE.

    In this case, probably the GRE and the GRE Math
  5. Dec 6, 2009 #4
    jhooper - worry about getting through bachelors and masters first. Nothing from high school will ever matter again. Honestly, not much in bachelors will matter as long as you do great on Masters.

    Be warned... not everyone can get a phd in mathematics. It's not something you will really be able to figure out whether or not you can do until after you've at least gotten your bachelors. Phd requires the ability to really come up with something new and original in the field, and in math, that's a whole different ball game

    the only reason i say this is to broaden your horizens and see whatelse is out there that you like. I got my bachelors in math and discovered i love programming and now going CS for masters. So keep your mind open for other science

    Study for the GRE and get into a good grad school once you've gotten your bachelors!
  6. Dec 6, 2009 #5
    Also while Ph.D.'s schools care about test scores and grades, they care a lot more about undergraduate research, letters of recommendations, and what courses you take. One thing that surprises people is that "how smart you are" is only a secondary consideration for graduate school admissions in physics and math. It matters, but it's not the main consideration, since intelligence is useful for getting a Ph.D., but it's not the most important thing.

    The primary worry for a graduate school is that they will admit someone that burns out during the program. The reason that the look at people with research and hard classes, is that if you've done research and hard classes, it makes it less likely that you'll burn out.

    One other thing about graduate schools is that the criterion for admission is very, very different between different schools.
  7. Dec 6, 2009 #6
    There is a site out there where people post all sorts of information about test scores, gpa, research, where they applied and where they got accepted. Actually its all for physics but I imagine its mostly the same for maths.

    Having read through pretty much all of these posts, it seems like getting into a top 10 school entails,
    - luck
    - extremely high subject test score
    - not a terrible gpa (like, less than a 3.5 or so)

    Other definite trends seem to be
    - attended a top 10 school in undergrad
    - first author on some sort of paper (I still don't get how an undergrad could bring new knowledge to the forefront of physics but w/e - maybe publishing a paper is about something else).

    This is the harsh reality. Jumping through hoops for 4-5 years to get a high GPA matter less to these people than your ability to solve freshman physics problems at a rate of 2 minutes/answer.

    The general GRE probably won't be that important and you'll probably smoke the math portion anyways since its pretty much at the high school level. But make sure you review a bit so you can get accustom to their tricks.
    Last edited: Dec 6, 2009
  8. Dec 6, 2009 #7
    The trouble with these sites is that they can be pretty misleading. There is a lot of self-selection involved, and things can be very, very different between different fields. Graduate school admissions in physics/astronomy is *very* different than MBA's.

    One other thing is as far as physics goes is the rankings are pretty much hokum. I have no idea what the top 10 physics Ph.D.'s programs are, and I seriously doubt that it matters very much in the grand scheme of things.

    That doesn't matter very much either. Also in situations were answering physics questions quickly *does* matter, then it's just a matter of drill and practice.
  9. Dec 6, 2009 #8
    I don't think that the US have the same definition of paper as at least we in Sweden do. Here it is extremely rare for even masters thesis's to be published as papers, so I would guess that it is mostly very minor stuff that would never get published at any of the larger journals. Like, for example as a freshman I got "published" as a co author for a conference contribution, but that don't count as a paper here.
  10. Dec 6, 2009 #9
    It's very field dependent. In finance and economics, getting something published is an extremely difficult process as the peer review panels consider themselves gatekeepers. Physics, mathematics, and astronomy journals peer reviewers usually have the attitude that they aren't gatekeepers, and their job is to get rid of the really silly stuff, provide a very minimal level of quality control, but otherwise let the community decide what papers are good and what ones aren't. I think that it's been mentioned that about 70% of the papers that get submitted to Astrophysical Journal eventually get published. By contrast, Nature and Science, whose policy is to only publish the cream of the crop papers, have something like a 5% publication rate.

    I think the reason that the publication rates are high are:

    1) there's often no reason that a peer review panel can give not to publish. A lot of papers in astronomy are basically, I pointed my telescope at this object, got these results, and here they are. If you are a peer reviewer, and the authors aren't obvious idiots, then what can you say? If you have a mathematician that claims to have proven a theorem, your only real excuse for not-publishing is that there is a mistake in the proof.

    2) the major journals are under the control of the professional societies, so there is no real financial reason not to publish huge journals, and

    3) finally, funding. The gate keeping in physics/astronomy happens at the grant proposal level. If you have a scientist that got a grant, did the work, and the results were decent, and the journals refuse to publish, they are going to be looking at some very serious conflicts with the NSF. Also a lot of the programs that finance undergraduate research come from NSF, and the National Science Foundation wants to see undergraduates publish.

    Personally I like the physics/astronomy system in which the journals will basically publish everything that isn't totally insane. The problem with the economics/finance system is that you have terrible, terrible inbreeding.
  11. Dec 7, 2009 #10


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    To put it into perspective, Harvard takes around 15 new Ph.D. students per year and its peers are Princeton, Stanford, Berkeley, Chicago and MIT which all take a pretty similar amount of students (or even less). You have the top students from numerous countries applying there meaning that the admissions standard is pretty much that you need to be one of the say top 5 students from the country you are applying from to have any chance. Of course, if you are from a really small country you might need to be top 1, while from China top 20 might do.

    I was the top undergrad at the top school in my country when I applied to US Ph.D. programs in math. I never even bothered applying to Harvard and Princeton, because past experience told me that everyone from my university had been rejected. I actually didn't get in to any school in the top 6 (by US News' ranking) even though I applied to four of them.

    So unless you are extraordinarily talented, you have no chance of getting into those schools. Trying to game the system by getting a high GPA is not working. You need to have your professors write a recommendation explaining that you are one of the best students they have ever had. Professors aren't stupid, so they won't write that unless there is a real reason. If you don't panic during standardized tests, then getting the requires test scores (assuming the talent) is not a problem.
  12. Dec 7, 2009 #11


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    jhooper -

    The above people are certainly right that as soon as you start your college career as an undergrad, nobody will ever care about your high school grades or SAT again.

    The other thing you need to know is not to focus too much on Harvard or any one school. Harvard in particular can afford to be EXTREMELY choosy with who they accept. Even if you have an exceptional application, there's a very high luck factor here. Besides, Harvard actually focuses pretty narrowly on just a couple fields of mathematics, and you can't possibly know now if you even like those fields.

    The point is, if your goal is to do a PhD in mathematics at a good school, then that's great. And if you want to shoot for Harvard, that's great too. Just don't focus too narrowly on that one school.
  13. Dec 7, 2009 #12
    I'd say the following resume pretty much sums up what is expected for getting into Harvard or Princeton for a mathematics Ph.D.:


    To put that into perspective, it would be very possible to complete a Ph.D. at an ordinary state university here in the U.S. and still end up with a less impressive resume than his.

    I'm sure there are people who get in without such incredible resumes, and I'm sure you don't have to have spent your childhood doing international level mathematics competitions to get in. But these are the people you would be competing against when applying to such a school.

    A few Harvard math graduate students also have Wikipedia articles:

    Last edited by a moderator: Apr 24, 2017
  14. Dec 7, 2009 #13
    No. You are confusing graduate school admissions with undergrad.

    What starts happening at the graduate level is that things start getting determined by funding. If you have a Math olympiad winner that wants to do string theory, but you want to do applied statistics with application to biomedical research, then you two aren't competing against each other. If the university just happens to have gotten a massive grant from NIH to study applied biomedical statistics, and you have background in that area, you'll win.

    Yes this means that a lot of graduate admissions depends on politics and luck, but I don't really see this as a bad thing. It's good education for the "real world" in which pretty much everything is politics and luck.

    And politics is not necessarily a bad thing. Without some political pressure, what would eventually happen is that all of the big name schools would get all of the money and get even bigger. One good thing about the way that science research is done in the US is that there is tremendous pressure to "spread the money around" so that difference between Harvard and everyone else is less than you would think. The large state universities have enough funding to attract professors from Harvard, who then turn their departments to "Harvard West" and the NSF and the NIH *explicitly* set up their grant funding to try to spread the money to as many congressional districts as possible.

    For that matter Harvard does the same thing with undergraduate admissions. Part of the game is that if it was clear that you just couldn't get into Harvard at all, it makes Harvard a lot *less* powerful, so the really big name universities set things up so that you have a shot at getting in.
    Last edited: Dec 7, 2009
  15. Dec 7, 2009 #14
    I was under the impression this thread was about people wanting to become research mathematicians applying to the pure mathematics Ph.D. program at Harvard. I don't think the Harvard Ph.D. program in mathematics would be of any interest whatsoever to the person wanting to do biomedical research.

    Please correct me if I'm wrong. I certainly don't want to spread misinformation. But my understanding is that the Harvard Ph.D. program in math is simply intended only for people who want to do pure mathematics, with a few exceptions due to faculty interests (e.g., game theory and evolutionary dynamics, and even this is treated in a very purely mathematical way at Harvard). I wouldn't think either of your two hypothetical applicants would ever actually be applicants to this particular program.
    Last edited: Dec 7, 2009
  16. Dec 7, 2009 #15
    But the Harvard offers a Ph.D. in biostatistics as well as one for statistics. There is also a Ph.D. program in the school of engineering in applied mathematics. Yes, people that tend to be math competition gurus tend to avoid these "applied" programs, but that's why it's a *lot* easier to get into them.

    The question was getting a Ph.D. in mathematics from Harvard. Biostatistics and statistics are mathematics. It's from Harvard.
  17. Dec 7, 2009 #16
  18. Dec 7, 2009 #17


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    A Ph.D. in mathematics means a Ph.D. from the math department. Period. It's quite well known that getting into applied math or stats is a lot easier. The brightest people tend to go to pure math programs regardless of interests as the transition from pure to applied is not too hard while the other way around is. Let's put it this way: I can take a stats article and understand it in a few weeks or days by just having a basic background in measure theory, but there's no way I can understand a recent article from say algebraic topology or number theory in a few weeks.

    Now pure math is such that after a typical undergrad most people really don't have a clue what they want to specialize in. The admissions committee knows this and most people tend to change their interests during their first year. The simple reason for this is that it's very hard to get in touch with cutting edge research as an undergrad, because you simply don't have the preparation to read papers from major journals.

    Of course, if you state on the application that you want to do something that no one is doing at the school you are applying to, you are probably doomed. However, if your interests are say anything from number theory, differential geometry, algebraic geometry, algebraic topology, you can be pretty sure that there's a few possible advisers at the department, so it really boils down to a comparison of your stats compared to the others and less or no politics.
  19. Dec 8, 2009 #18
    So statistics isn't "real math". Who made those rules? (Seriously.)

    It's actually not easier. Its just harder in a different way. If you have a international math olympiad winner with no biological experience going against someone with a pre-med/math degree, the person pre-med is more likely to get into the Harvard biostatistics program. But that doesn't count. So why doesn't it count?

    If you want to know why "number theory" is somehow "better" than "biostatistics" well that's basically politics. Not that there is anything wrong with that, expect that you have to realize that the politics can change. One thing that really changed big time at MIT is the swing in power from physics/"pure math" to biology/economics/management.

    But if you don't have any biology or statistics background, you'll apply those principles in ways that give you total gibberish. Also, I very, very seriously doubt that with a few weeks of reading that you can set up a drug trial that will pass the institutional review board, and if you try, you'll be lucky if you don't kill anyone. Again, you might say that doesn't, count, but my reply again is "who made up those rules?" And more important, why should I submit to those rules if it doesn't help me.

    There's lots of politics. The decision of which stats are more important and which stats are less important is a political decision. Why is number theory "better" than biostatistics? The reasons for that are political and economic, and it's important to realize that since you can then change the situation so that the politics and economics works in your favor.

    There is something called "playing to lose" and I'm amazed that so many people are interested in doing this. Now if I'm in a head-to-head competition in which I'm trying to get scare resources like money, power, prestige, then the first thing to do is to set up the competition so that it's something that I'm good at rather than something that I'm bad at.
  20. Dec 8, 2009 #19
    Something that is pretty relevant here is the sociology of status hierarchies. There is the analogy of the shark. In the right environment the shark is the most dangerous predator around and is the top of the food chain. If you change the environment, then you end up with shark on the beach flopping around being a danger to no one.

    What's interesting is that if you change the environment then you can massively change the status hierarchy. Someone that's a great number theorist could make a lousy statistician or physicist, and vice-versa. One cool thing about the US is that there are so many ways of changing your environment, so that you can end up on top, if that's what you want, or you can end up on the bottom, if that's what you want.
  21. Dec 8, 2009 #20
    They expect some combination thereof along with the ability to think.
  22. Dec 8, 2009 #21
    That is the most impressive undergraduate cv I have EVER seen. 10 points for anyone who can find a better one.
    Last edited by a moderator: Apr 24, 2017
  23. Dec 8, 2009 #22


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    I think in your haste to get defensive, you may have missed eof's main points.

    When someone says he wants a PhD in math, he means A MATHEMATICS PHD, pretty much always. This is no slight against related fields. It's just what the words mean.

    This means that your posts about biostatistics and biomedical research and whatever the crap else just aren't relevant.

    BTW, you said, "it's a *lot* easier to get into them." Then just a couple posts later you said, "It's actually not easier." Which is it?
  24. Dec 8, 2009 #23
    And since when is number theory and algebraic topology mathematics and statistics and biostatistics not mathematics? If you do your dissertation in statistics how is that worse than doing your dissertation in algebraic topology?

    Who decided that mathematics Ph.D. includes algebraic topology but not statistics? (Probably some professor of algebraic topology.)

    This isn't a rhetorical question. I'm really curious why you think statistics isn't "real" math. Is numerical analysis "real math" or not?

    It's true that in academia that people that do algebraic topology and number theory end up higher in the food chain than people that do statistics and numerical analysis. But I work in a financial firm, and people that do statistics and numerical analysis end up much higher on the food chain than people that do algebraic topology and number theory. Also in academia, your social status increases if you write papers that no one but specialists can understand. In any sort of industrial environment that will get you fired.

    Why is it that mathematical physics is usually considered "real math" whereas biomedical physics isn't?

    What about applied mathematics and statistics?

    It depends who you are.
  25. Dec 8, 2009 #24
    Also you have to realize that you are talking to a physicist with some legal background. One thing that both physicist and lawyers think pretty deeply about is what words mean, and more importantly who defines the meanings of words. I don't think it's totally crazy to argue that someone that gets a Ph.D. from the department of applied mathematics in the school of engineering from Harvard has got a mathematics Ph.D. from Harvard.

    If you define mathematics as "things that the faculty at the Department of Mathematics at Harvard teaches" that's seems to me a very odd definition. Now you can define words to mean whatever you want them to mean, but I just don't see that definition as being particularly useful or accurate, since other schools like MIT or NYU structure their math departments differently. So you end up with the weird situation of something being "not mathematics" at Harvard Square, but then if you get on the Red Line and go to MIT (which doesn't have a separate applied mathematics department or statistics department), then the exact same thing is considered "mathematics."


    So if you want to get a "mathematics Ph.D.' I suppose the first thing that you want to do is to see how the different schools classify things, and if you define "mathematics Ph.D." as a degree given by the mathematics department and you happen to be interested in numerical analysis, then I suppose this means that you should apply to MIT and NYU and not Harvard.

    And since my degree is from MIT, I don't think I'd be too off if I take the MIT definition of mathematics over the Harvard one :-) :-) :-)
    Last edited: Dec 8, 2009
  26. Dec 8, 2009 #25


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    Well, of course there is an obvious difference between fields like algebraic topology and fields like biostatistics. Someone in algebraic topology is seeking to answer questions of mathematics. Someone in biostatistics is seeking to answer questions of biology, and using mathematics to do it.

    I agree with some of what you say, but it's all beside the point, really. When someone asks about a mathematics PhD, he almost surely is not thinking of biostatistics. All this other stuff is just not relevant to the question, regardless of your philosophical views on what is mathematics.
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