85

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.

Georges Elencwajg
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    Time to break out the Drake equation. – Ryan Budney Nov 14 '09 at 08:35
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    Presumably one could use MathSciNet in some way to estimate the number of research mathematicians. – Michael Lugo Nov 14 '09 at 15:32
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    On a related topic: does there exist two mathematicians with the same number of hairs on their heads? – Douglas S. Stones Mar 04 '10 at 04:53
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    Do theoretical computer scientist, who approached the topic from C.S., count as mathematicians? What about theoretical biologist, physicist, simulation sciences? – shuhalo Jan 09 '11 at 23:02
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    Doug, the answer is yes. I know several completely bald mathematicians. – Ryan Budney Aug 18 '12 at 19:24
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    wow between 2009 and now MO has changed (matured) a lot!! – Suvrit Aug 18 '12 at 19:33
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    @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
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    This question has been closed, then reopened. There is a thread on meta about that. – Georges Elencwajg Aug 22 '12 at 11:16
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    @RyanBudney I looked at this comment thread and thought "Wow, Ryan Budney is on a roll!". Then I saw that your two comments were $3$ years apart... – Steven Gubkin Oct 24 '14 at 21:47
  • There are mathematicians in different sense: 1. mth. PhD 2.mth research publication 3.referred to by MR 4.listed by MGP ... There are errors, they partially cancel out, one gets an idea in one way or another. I'd also consider a *recognized mathematician: independently* refereed to her/his mth research by 10 or more different mathematicians (this is not circular). – Włodzimierz Holsztyński Oct 24 '14 at 23:06
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    There are 831 MO user pages + 5 participants on page 832. Thus the number of mathematicians is: $\ 831*36 + 5\ =\ \mathbf {29921}.\ \ $ That's it! :-) – Włodzimierz Holsztyński Oct 24 '14 at 23:11
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    Too few of them. – Sylvain JULIEN Oct 25 '14 at 07:26
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    @GeorgesElencwajg I did not take Suvrit's comment as sarcasm, maybe a little tongue in cheek, but not a serious criticism. – j0equ1nn Mar 18 '16 at 23:24
  • If we modify the "Single electron universe" to mathematicians, we could argue that all mathematicians are the same up to isomorphism and therefore in practice all mathematicians are instances of the same mathematicians rippling through the Quantum Mathematical Field. In such case, I propose the canonical mathematician to be von Neumann. – Asaf Karagila May 31 '18 at 12:38
  • Not just the Drake equation (@Ryan), sometimes one feels that the Fermi paradox applies. – Jukka Kohonen Jan 24 '24 at 10:33

7 Answers7

43

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.

Todd Trimble
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Thomas Sauvaget
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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 09:23
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    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. – Gerry Myerson Apr 10 '18 at 09:51
  • @GerryMyerson Why do you talk about "suffering"? I am living in France and hope not to make people suffer :) – Wolfgang Dec 14 '21 at 22:06
28

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.

Alexandre Eremenko
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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. –  Dec 08 '12 at 16:43
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    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 08 '12 at 17:22
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    Many of those listed in MR are probably better characterized as statisticians, physicists, or electrical engineers (among other disciplines) than as mathematicians. – Dan Fox Apr 10 '18 at 05:46
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    @Dan Fox: I agree. It is hard to define precisely who are "mathematicians", all these numbers are only rough estimates. – Alexandre Eremenko Apr 10 '18 at 11:59
24

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!

Jose Capco
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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 09:01
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    The dead mathematicians are probably neglegable, because of the exponential growth of the mathematics community. – shuhalo Mar 08 '11 at 08:03
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    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 09:48
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    Not all Mathematics PhDs are working mathematicians or associated with academia. – Michael Oct 24 '14 at 22:31
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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)

Martin Sleziak
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Kevin O'Bryant
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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
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    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
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    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
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    See http://www.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 03 '10 at 07:16
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    Adding the information "Usually working in comfortable offices" could explain those low figures – Feldmann Denis Aug 18 '12 at 19:44
  • @Pete Georgia Tech might single-handedly make Georgia an overachieving state, but even 10,000 seems low. – Andrew D. King Aug 21 '12 at 21:43
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    The link is broken, but the current data says (from 2016) there are only 2730 of us: https://www.bls.gov/oes/current/oes152021.htm Sad :( – Kimball Mar 28 '18 at 02:13
  • I have added links to Internet Archive to prevent link rot. There are several versions available. The closest ones to the date of the original post are from November 2, 2009 and December 30, 2009. – Martin Sleziak Apr 10 '18 at 05:58
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    The Labor Department has a standard survey that they use to gather information about various occupations, which is where the notes like "comfortable offices" come from. I was once asked to participate in this survey and filled out a very long questionnaire about my job, including things like the average number of hours per week spent climbing ladders! – Nate Eldredge Feb 12 '20 at 13:27
12

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.

Kevin Walker
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2

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.

Jim Stasheff
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-2

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.

Amit
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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 08:04
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    @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 08:12
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    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 09:20
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    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 09:55
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    The definition would also exclude Jack Edmonds. – Andrew D. King Aug 21 '12 at 21:36
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    Sir Peter Swinnerton-Dyer also never received a PhD. – Adam P. Goucher Mar 11 '18 at 16:34