I just wondered -- what is the typical age of a PhD recipient? A bit of Googling turned up this table from Inside Higher Ed, which conveniently sorts by discipline; it reports on an NSF brief. Mathematics and physics are tied for second lowest median age at 30.3; chemistry is the only discipline that's lower, at 29.6.
The table I linked to also gives the median time from getting the bachelor's degree to getting the PhD; by subtraction one can get some number that is a "typical" age of bachelor's degree receipt for students who eventually get a PhD. The median time from bachelor's degree to PhD in mathematics is 7.9 years. Subtraction, 30.3 - 7.9, gives 22.4 as a "typical" age (the difference of medians, which isn't really meaningful) for students getting a bachelor's degree who eventually go on to get a PhD in math. (The highest typical age at bachelor's degree is 25.3, for people getting PhD's in education.) This is the minimum among all eighteen disciplines covered here. It's hard to imagine a median much lower than that given the age at which students typically enter formal education and the number of years it takes.
I interpret this as saying that students who get PhD's in mathematics are less likely to take time away from formal education between high school and college or to take longer than the traditional four years to graduate from college. I'd be interested to see if this is because students who spend time away from formal education "lose" whatever mathematics they knew and have trouble picking it back up again; it's a popular conception that mathematics is more "hierarchical" and so this is more of a problem there than in other fields. (Not having much experience with other fields, I can't say.)
Also, chemistry has a median registered time to degree (time from entering a doctoral program to receiving the PhD) of 6.0 years; the next lowest is mathematics at 6.8. Why is chemistry such an outlier?
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I took some math grad courses in 2004 (Lie Algebras and Topology, which was H-level for non-18) after not having taken any math since 2000. They were hard, but math is always hard. I don't think that not having done math for 4 years made them any harder. (Of course I was doing a PhD in Computer Science at the time, but not super theoretical CS).
I've been working in the industry for about two years and trying to get back to college next winter term... it is difficult to get back to math, is all I can say to you! (but still very enjoyable) :)
If I remember correctly, MIT wants its PhD students to finish within four years.
Do people in chemistry enter doctoral programs with a Master's Degree already in hand? (Or would that already have been accounted for?)
I don't think it has as much to with skill as interest and exogenous circumstances. Once a student leaves the confines of academia and gets used to real pay and other aspects of grown-up life, there is a subtle attitude shift that colors future decisions. Couple that with the fact that graduate study in mathematics is a lot less "useful" than, say, engineering or computer science and you get one of the main contributors to the pattern, I think.
PS: Of course, such trends are always coarse in that every rule has many exceptions!
@Anonymous:
That coloring is often not quite so subtle. I weighted eight years after graduating from high school to start studying math (and, for a while, physics), and somehow thought it'd be good to also start a big family simultaneously.
I'm still working on my baccalaureate degree, after a lot of part-time and intermediary no-time university attendance. I expect to graduate next spring, after 12 years have elapsed. 20 years after graduating high school.
I think there's something to the hierarchical argument, but (luckily or as a product of poor education policy) much of "higher" mathematics starts from the foundations and works up, so ready application of the half-angle trigonometric identities isn't quite as important as in, say, the second quarter of the freshman calculus sequence.
Um...
s/weighted/waited
Chemistry students do not typically have an MS when beginning the PhD. I suspect the short median time is due to a combination of some short dissertation projects (in theory and synthesis) and a relative paucity of long degrees (because students are traditionally supported on research assistantship after 1-2 years, the advisor has a vested interest in rapid progress).
I'm an exception, FWIW. After high school, I quit college before completing any classes. When I was 26, I decided to go back and eventually settled on math. I'm now 29, and will be finishing in December (3 years; I was fortunate enough to be able not to work simultaneously).
I had forgotten or never knew lots of things; I was smart but a very poor student in high school. But here I started with Calc I and caught up pretty quick.
Here's the crazy (for me) part... I will be applying to graduate school this fall/winter. This means I will be starting when I am 30. Starting a PhD this late seems to be very rare in math. In fact I have yet to learn of a single person who has done it. I have met PhD students in other disciplines that are older (I worked with one who was over 40), but not math.
For me, the drawbacks were mostly related to how long it would take to get a career started. Plus the long distance moves and so on... It seems crazy, but it's what I want. But I don't really know what's different about math than other disciplines in this respect.
Honestly, I think there's less jobs for someone with a B.S. in Math or Physics than there are for people with bachelor degrees in similar fields (engineering, cs, chem/bio).
Based on what, Maggie? My conversations with former math students and various hiring manages seem to indicate that, for instance, a math B.S. with a good bio supporting sequence is more desirable than a straight bio major for bioengineering firms.
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