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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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    $\begingroup$ Time to break out the Drake equation. $\endgroup$
    – Ryan Budney
    Commented Nov 14, 2009 at 8:35
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    $\begingroup$ On a related topic: does there exist two mathematicians with the same number of hairs on their heads? $\endgroup$
    – Douglas S. Stones
    Commented Mar 4, 2010 at 4:53
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    $\begingroup$ Doug, the answer is yes. I know several completely bald mathematicians. $\endgroup$
    – Ryan Budney
    Commented Aug 18, 2012 at 19:24
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    $\begingroup$ wow between 2009 and now MO has changed (matured) a lot!! $\endgroup$
    – Suvrit
    Commented Aug 18, 2012 at 19:33
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    $\begingroup$ @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. $\endgroup$
    – Georges Elencwajg
    Commented Aug 20, 2012 at 15:27

6 Answers 6

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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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    $\begingroup$ 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 $\endgroup$
    – Yemon Choi
    Commented Nov 14, 2009 at 9:01
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    $\begingroup$ The dead mathematicians are probably neglegable, because of the exponential growth of the mathematics community. $\endgroup$
    – shuhalo
    Commented Mar 8, 2011 at 8:03
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    $\begingroup$ 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. $\endgroup$
    – Dan Fox
    Commented Jul 16, 2011 at 9:48
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    $\begingroup$ Not all Mathematics PhDs are working mathematicians or associated with academia. $\endgroup$
    – Michael
    Commented Oct 24, 2014 at 22:31
  • $\begingroup$ I think it should be pointed out that Math Genealogy has a very generous definition of mathematics PhDs. There were 12 students in my cohort (at the maths department), but MG lists 41 in my year at my institution. Besides adjacent topics like statistics, operations research, mathematics education, and computer science, there are even dissertations listed in geophysics, biology, and development economics. That's just in one year at one university. $\endgroup$
    – R. van Dobben de Bruyn
    Commented Jun 23 at 15:39
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In an article written a few years ago ("Mathematicians in France and in the world"), 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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    $\begingroup$ 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. $\endgroup$
    – Zoran Skoda
    Commented Jul 16, 2011 at 9:23
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    $\begingroup$ One mathematician per 10,000 inhabitants, applied to a world population of 7,000,000,000, leads to 700,000 mathematicians worldwide. But perhaps France suffers from a higher density of mathematicians than the world average. $\endgroup$
    – Gerry Myerson
    Commented Apr 10, 2018 at 9:51
  • $\begingroup$ @GerryMyerson Why do you talk about "suffering"? I am living in France and hope not to make people suffer :) $\endgroup$
    – Wolfgang
    Commented Dec 14, 2021 at 22:06
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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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    $\begingroup$ 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. $\endgroup$
    – user9072
    Commented Dec 8, 2012 at 16:43
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    $\begingroup$ 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. $\endgroup$
    – Alexandre Eremenko
    Commented Dec 8, 2012 at 17:22
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    $\begingroup$ Many of those listed in MR are probably better characterized as statisticians, physicists, or electrical engineers (among other disciplines) than as mathematicians. $\endgroup$
    – Dan Fox
    Commented Apr 10, 2018 at 5:46
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    $\begingroup$ @Dan Fox: I agree. It is hard to define precisely who are "mathematicians", all these numbers are only rough estimates. $\endgroup$
    – Alexandre Eremenko
    Commented Apr 10, 2018 at 11:59
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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 (broken link http://www.bls.gov/oco/ocos043.htm, Wayback Machine). That site contains such gems about our profession as: "Mathematicians usually work in comfortable offices."

Cool.

Edit: newer link that isn't broken, yet (Wayback Machine)

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    $\begingroup$ 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." $\endgroup$
    – Michael Lugo
    Commented Nov 17, 2009 at 14:35
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    $\begingroup$ 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. $\endgroup$
    – John D. Cook
    Commented Nov 17, 2009 at 14:42
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    $\begingroup$ 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. $\endgroup$
    – Pete L. Clark
    Commented Jan 10, 2010 at 14:41
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    $\begingroup$ 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. $\endgroup$
    – sigoldberg1
    Commented Nov 3, 2010 at 7:16
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    $\begingroup$ Adding the information "Usually working in comfortable offices" could explain those low figures $\endgroup$
    – Feldmann Denis
    Commented Aug 18, 2012 at 19:44
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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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  • $\begingroup$ That particular data source was first mentioned in Nov 2009, about three years before this answer. $\endgroup$
    – David White
    Commented Jan 24 at 0:35
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Only somewhat related, I think it was Frank Adams who commented on the varying percentage of a country's population in math(s) e.g Hungary and Roumania.

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