How many mathematicians are there?

Although we are not so numerous as other respected professionals, like for example lawyers, I wonder if we could come up with a reasonable estimate of our population.

Needless to say, the question more or less amounts to the definition of"mathematician".

Since I should like to count only research mathematicians (and not, say, high-school teachers) some criterion of publishing should be applied. But it should not be too strict in order not to exclude Grothendieck, for example, who has not published any mathematics for a long time.

An excuse for asking a question so soft as to verge on the flabby is that it might be considered an exercise in Fermi-type order of magnitude estimation.

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Time to break out the Drake equation. –  Ryan Budney Nov 14 '09 at 8:35
On a related topic: does there exist two mathematicians with the same number of hairs on their heads? –  Douglas S. Stones Mar 4 '10 at 4:53
Doug, the answer is yes. I know several completely bald mathematicians. –  Ryan Budney Aug 18 '12 at 19:24
wow between 2009 and now MO has changed (matured) a lot!! –  Suvrit Aug 18 '12 at 19:33
@suvrit: I don't see why this question is a sign of immaturity. I have opened a thread in meta where you are welcome to explain your conception of maturity. –  Georges Elencwajg Aug 20 '12 at 15:27

Current count of Mathematics Genealogy Project is 137672 (I am assuming that the PhD students that graduated are ranked as "research mathematicians"). But the problem is.. Mathematics Genealogy is mostly for universities of developed countries. There could be some really good university in Russia, China or Korea out there that doesn't give us the correct statistics. Another problem is.. Mathematics Genealogy Project counts even the dead mathematicians (like Hilbert, Hasse, Kepler and so on).. and I am assuming you want a report of living mathematicians.. but hey, I'm quite surprised by the number even 200k is pretty low for the living!

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The MGP used to be utterly inadequate for those who got their PhDs in the UK before the 1980s, it may have improved now. Also, there are odd gaps/bugs in some of the entries. It's useful and interesting but I'd be wary of using it for head counts –  Yemon Choi Nov 14 '09 at 9:01
The dead mathematicians are probably neglegable, because of the exponential growth of the mathematics community. –  shuhalo Mar 8 '11 at 8:03
I'd be careful using the MGP. I'll give some examples from my family, so I am very sure of the facts - one of my grandfathers, who was a chemist, and never published a math paper in his life, is listed in the MGP twice, as distinct persons - once as a student (his also listed advisor was not a mathematician either) and once as an advisor. My father, who is a physicist, and wrote exactly one paper that could be called math, is listed. So are 13 of his students - probably at most 1 or 2 is reasonably considered a mathematician, even if one regards many theoretical physicists as mathematicians. –  Dan Fox Jul 16 '11 at 9:48
Not all Mathematics PhDs are working mathematicians or associated with academia. –  Michael Oct 24 '14 at 22:31

In an article written a few years ago, Jean-Pierre Bourguignon estimates that there are around 80 000 mathematicians worldwide, with the AMS having about 15 000 members.

For France he says 4000 work in academia ("a reliable estimate") and about 2000 in the private sector. Since there are about 60 million inhabitants there, that's 1 mathematician per 10 000 inhabitants.

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Just to remind you also that not all research mathematicians in US are members of AMS and also many foreign mathematicians are. When I had a postdoc in US I was NOT member of AMS. I have not been in US for last 8 years and I AM now a member of AMS. –  Zoran Skoda Jul 16 '11 at 9:23

Typing "how many mathematicians" into Wolfram|Alpha, yields the information that there are 3160 mathematicians in the United States. The source listed is the US Bureau of Labor Statistics, and this site in particular (http://www.bls.gov/oco/ocos043.htm). That site contains such gems about our profession as: "Mathematicians usually work in comfortable offices."

Cool.

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That number seems too low to me. A lot of the people that many of us would think of as "mathematicians" are probably counted as teachers in this survey; the source above says that "For example, there were about 54,000 jobs as postsecondary mathematical science teachers in 2006." –  Michael Lugo Nov 17 '09 at 14:35
Maybe there are only 3,160 people who listed "mathematician" as their profession on their tax return or some other official document. How many mathematicians call themselves mathematicians? I imagine many would give their title as "professor", "research scientist", not to mention applied titles like "financial analyst" etc. –  John D. Cook Nov 17 '09 at 14:42
The number 3160 is implausibly low. Without breaking a sweat, I was able to find 260 people with PhDs and current teaching jobs at math departments in Georgia. Georgia has only 3% of the nation's population (and is, alas, not renowned as an intellectual mecca), suggesting that a more accurate number would be on the order of 10,000 or more. –  Pete L. Clark Jan 10 '10 at 14:41
See nsf.gov/pubs/1998/nsf9895/math.htm , according to which there were 10,000 highly active research mathematicians worldwide. 15k PhD level mathematicians in the US in 1996. –  sigoldberg1 Nov 3 '10 at 7:16
Adding the information "Usually working in comfortable offices" could explain those low figures –  Feldmann Denis Aug 18 '12 at 19:44

I am surprised that nobody mentioned the Math Reviews authors database.

Currently it has about 650000 authors. I suppose that about 50% of them are dead, which gives an estimate of 300-400 K living mathematicians. Of course, as it was noticed in the question, it is hard to establish a criterion, whom do we call mathematicians. I think about 1/3 or 1/2 of the people in this database are those who published only one paper.

Such sources as Math Genealogy project are much less reliable, because they do not include most Soviet, Chinese and other mathematicians. But it also includes people who defended a PhD in mathematics, published one paper (or even did not publish anything) and switched to some other activity.

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MR also (in particular since the somewhat recent expansion) includes various journals that are not or not only mathematics. So, that not too few of these authors should not be mathematicians but scientists in other fields. –  quid Dec 8 '12 at 16:43
My experience shows that there are not too many non-math papers included in MathRev (much less than in Zentralblatt). But of course the distinction between a mathematician and a person doing mathematics in some other field is sometimes fuzzy. –  Alexandre Eremenko Dec 8 '12 at 17:22

Here are yearly totals from the Mathematics Genealogy Project. (This is as of August 2012.)

Year              # of Math PhDs known to MGP
---------------------------------------------
1960                593
1961                674
1962                863
1963                1002
1964                1203
1965                1309
1966                1439
1967                1549
1968                1762
1969                1949
1970                2031
1971                1986
1972                2057
1973                1997
1974                1997
1975                1922
1976                1859
1977                1830
1978                1911
1979                1922
1980                1873
1981                1822
1982                1939
1983                2012
1984                1966
1985                2023
1986                2102
1987                2267
1988                2526
1989                2703
1990                2884
1991                3009
1992                3328
1993                3419
1994                3650
1995                3764
1996                4034
1997                4053
1998                4181
1999                4065
2000                4275
2001                3932
2002                3815
2003                3807
2004                3919
2005                4751
2006                4445
2007                4332
2008                4194
2009                3877
2010                3714
2011                3235
2012                1372
------------------------
Total 1960-2012   139143


For comparison, the total number of records in the MGP at this time is 163611.

Also, this (undated) AMS page says there are 35800 members of the four main U.S. mathematics professional societies.

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By definition mathematician is a person who holds phd in mathematics. Per Wikipedia only 2.94% of population in US out of 310 million hold phd in anything. And math phd's are very rare. By estimation I would assume that only 0.001% of total population would hold phd in mathematics. So that does end up as around 3100 mathematicians in US. Many of the math teachers in high school or community colleges may not be holding phd in math. So technically they are not mathematicians.

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As the question said, it depends on the definition of mathematician. Would you exclude a high school teacher who contributes to MathOverflow from the (scope of a) technical definition of mathematician, even if they have published mathematics without a Ph.D.? Gerhard "Not A High School Teacher" Paseman, 2011.07.16 –  Gerhard Paseman Jul 16 '11 at 8:04
@Amit: Every year about 1200 new Ph.D. degrees are awarded in mathematics in the U.S., according to the AMS surveys which are published in the Notices. Personally I think the number of mathematicians is approximately the number of research papers published in mathematics per year. This makes the number approximately 100 000 which is consistent with the data mentioned by me and others above. –  GH from MO Jul 16 '11 at 8:12
Come on, there are many of us who hold physics Ph.D. and from mathematical physics drifted into pure mathematics and some of us hold academic positions as mathematicians. So the definition is incorrect. –  Zoran Skoda Jul 16 '11 at 9:20
This "by definition a mathematician ... holds phd in mathematics" is very culturally specific. It also excludes Birkhoff and Gleason. This is certainly not what is understood in the US, though it is perhaps not so far off what is understood in Spain (the only other culture I know well enough to comment). On the other hand, as a way of establishing a crude upper bound on the number of active mathematicians, counting math PhDs seems reasonable. The number of those who should be considered "mathematicians" who don't have a math PhD is presumably (?) small compared to the total. –  Dan Fox Jul 16 '11 at 9:55
The definition would also exclude Jack Edmonds. –  Andrew D. King Aug 21 '12 at 21:36