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I'm a student at a small LAC, and I'm considering to apply to both math and physics PhD programs. In my school, which is top 15 but do not have large (20 students in each dep.) or well-known departments for either of these fields, students did significantly better on physics PhD admission than on math PhD admission. For math, many students go instead to master's, and only one or two students can make top 40~70 PhD program per year. For physics, some students went to Caltech, Columbia, UCSB, and other high ranked programs in the last year, which was just as usual. A similar phenomena seem to happen not only in my school. Mathgre.com and Physicsgre.com list applicant profiles and admission results for each PhD program, and they show a similar tendency. For example, students accepted to top pure math PhD programs are exclusively those who got nearly 4.0 GPA, took many grad-level courses, had a significant amount of research experience and come from an undergrad institution with a renowned PhD program. On the other hand, students accepted to top physics PhD programs have more diversity in GPA, their undergrad institution, number of grad-level courses taken and amount of research experience.

What causes this difference? Or is my view wrong? If this difference actually exists, I think the following factors are among the causes:

  • Physics PhDs are funded more, and therefore more students can be afforded.
  • Physics PhDs have both theoretical and applied subdivisions, while many applied math programs exist as master's programs.
  • Math PhDs demand its applicants to take a significant number of grad-level courses, while physics ones don't.

Also, how about the situation when it comes to pure math vs. hep-th in the U.S.?

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    Is your first sentence saying that your university 1) is a small liberal arts college, 2) is one of the top 15 universities in the country, and 3) does not have a strong mathematics or physics department? I don't think all three of these can be true simultaneously.
    – Tom Church
    Commented Sep 23, 2015 at 2:46
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    I mean it's one of the top 15 LACs in the country, so it's not an university, and the ranking excludes universities. Although it has strong departments in other natural science topics, our math and physics deps are not the ones. 2) and 3) can be simultaneously true only when 1) is also satisfied.
    – Math.StackExchange
    Commented Sep 23, 2015 at 2:51
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    I'm a physicist. I'm just speculating, but it seems likely to me that a physics grad student is seen as valuable cheap labor in an experimental research group, whereas a grad student is a burden in both math and theoretical physics. In an area like high-energy particle physics, a grad student is a cog in the wheel. No originality or independence of thought is required. If you're willing to pull cables and debug software, you're an asset.
    – user1482
    Commented Sep 23, 2015 at 23:35
  • Thanks for your comment. In the U.S. is the admission for experimental hep PhD usually separated from the admission for hep-th? I'm not familiar with the process in the U.S., but many PhD programs in the U.S. seem to have the same admission process for both experimental hep and hep-th. If they are not usually separated, do students officially select their "concentration" after entering to the program?
    – Math.StackExchange
    Commented Sep 24, 2015 at 0:31
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    @AranKomatsuzaki: Usually you apply to the department as a whole, but you state a likely area of research or whether you're leaning toward theory or experiment. If you say you want to do string theory, your application may be considered more skeptically than if you say you want to be an experimentalist. In the US, there is normally a lot of coursework at the beginning of a PhD program. That coursework is an opportunity for students to get a feel for whether they would be likely to succeed as theorists.
    – user1482
    Commented Sep 24, 2015 at 15:04

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This is an attempt to gather some data supporting or refuting your hypothesis (or rather a slightly different one). Ideally, we would like a direct comparison of admission rates at top places, but I could only find limited data on admissions rates, so let me start elsewhere. At any rate, some of this data may be of interest.

The annual number of bachelor's degrees in physics is about 8000. From the AMS's annual survey, this number for math is about 28,000. This suggests there may be a lot more PhD program applicants for math. However, I don't have data separating out which math degrees are on a math ed track (or similarly for physics, though I guess the numbers are much greater for math ed), and these people are unlikely to pursue PhDs.

What about actual numbers of PhD students? I didn't see 1st year PhD numbers in physics for recent years but this slightly dated data puts it around 3000 new grad students in physics/astronomy (with about 93% aiming for PhDs), whereas the AMS annual survey has around 3600, and around 5000 if you include masters programs. (Stats and biostats is separate with around 2000, I guess including masters.) These statistics also say the number of physics versus math phd's awarded in recent years are pretty similar (about 1500-1600 for physics compared to 1400 for math). So there may be many more "potential" PhD applicants in math, but both math and physics students seem to compete for roughly the same number of slots in grad programs. (I don't know about how many of the PhD enrollments were domestic BS/BA holders, but we might guess the numbers are comparable as about 54% of enrollments were US citizens.)

So the above data tenuously supports your hypothesis. Can we check this with some actual admission rates?

For physics schools, this website has grad school admission rates. For top schools, the admissions rate seems to be around 10-15% (though Penn State seems to be an anomaly). Unfortunately, I don't know such a nice tool for math schools, but a few math departments mention their admission rates. Northwestern is around 17% (about the same as for their physics program, 16.4%). Notre Dame's is around 20% (a little lower than their 26% for physics).

These were all I could easily find and I'm afraid it's not enough to make any real conclusions, but I might speculate that top math phd programs are only somewhat more competitive than top physics ones if at all. (And in terms of undergrad research experience, I would guess that's more common in physics than in math.)

Edit: One qualitative issue for why you're seeing what you're seeing could be that top schools in math get lots of applications and if an admissions committee isn't familiar with a department, it doesn't know how to evaluate a transcript or the letters of recommendation from there, so it will tend to play it safe and accept students from places it's more familiar with. This is one reason why it's very helpful for students at small, relatively unknown schools to do programs like REUs (or a master's first) where a letter writer from there can compare you with a wide range of students. That said, I know many people who have gone straight from small, relatively unknown schools directly to top math PhD programs.

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  • I really appreciate your effort to gather all these data. I'm surprised to see some of the facts you mentioned and from your link. 1) # of physics bachelor's is only 8k/y. This sounds like physics is one of a few least popular majors among the departments which exist in almost every colleges in the U.S. Maybe media is exaggerating difficulty of physics, and youngsters were discouraged. 2) Acceptance rate of physics programs are much higher than expected (I thought ~5% for top ones). While top math PhD programs enrollment are roughly 20/r, physics
    – Math.StackExchange
    Commented Sep 24, 2015 at 4:08
  • PhD seems to have more capacity. 3) Some of lower ranked programs have pretty low acceptance rate. Penn state, while it's ranked high, is probably not for me. 4) This may be a well-known fact, but about a half PhD students in math and physics can't get PhD. The following list of universities attended by math PhD students at Harvard and UC Berkeley gave me an idea of how prestige of undergrad institution matters in admission for math PhD (because better education nurtured better students). reddit.com/r/math/comments/296e60/…
    – Math.StackExchange
    Commented Sep 24, 2015 at 4:12
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    That only 8,000 bachelor's degrees are awarded to physics students at American universities annually made my eyes pop out. I would have guessed a much larger figure. So a big +1 for presenting hard data.
    – Pete L. Clark
    Commented Sep 24, 2015 at 5:01
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    Another point to consider is that people that end up in physics departments come from a variety of backgrounds. I'm a physicist myself but we have plenty of chemists, materials scientists, IT guys and the odd mathematician in my department. I would guess it's mostly only mathematicians trying to make it to maths PhD programs.
    – Miguel
    Commented Sep 24, 2015 at 6:24
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    @AranKomatsuzaki Regarding your point 4), I'm guessing that most of the PhD students at top schools can get PhDs. At Caltech in math, almost everyone who started finished, and those who didn't were usually the ones who decided it wasn't for them during their 1st year, so I don't think that's as bleak as it seems. Also, see edit about undergrad institution.
    – Kimball
    Commented Sep 24, 2015 at 12:29

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