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First of all, sorry if this post is not appropriate for this forum.

I have a habit that every time I read a beautiful article I look at the author's homepage and often find amazing things.

Recently I read a paper of Andrew Hicks and when I opened his homepage I found many links about his invention: Flawless wing mirrors (car mirror).

enter image description here (Image Source)

I would not be surprised if this invention was made by a non-mathematician. His mirror is an amazing invention to me because every day I see it, but didn't know its inventor is a mathematician! Anyway, I want to ask

Question 1: Are there mathematicians who have done outstanding/prominent non-mathematical work like inventions, patents, solving social/economical/etc. problems, papers in these areas, etc.?

Of course, one can say that almost all technology nowadays is based on the work of mathematicians, but I'm asking for specific contributions/innovations.

I want to ask a similar question (Maybe it will be useful for those who are looking for a job!):

Question 2: Which mathematicians are working in non-mathematical areas/companies?

Note: Please add to your answers the name and the work of the mathematician.

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    $\begingroup$ (should probably be CW, as with most big-list questions) $\endgroup$ – Noam D. Elkies Aug 20 at 15:11
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    $\begingroup$ Unabomber has to be #1 on this list. $\endgroup$ – Piyush Grover Aug 20 at 15:26
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    $\begingroup$ Not clear if it fits, but Emanuel Lasker was a Chess World Champion and a mathematician. I understand that he proved some important results in Commutative Algebra. $\endgroup$ – Nick S Aug 20 at 15:42
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    $\begingroup$ A good question here would need good delineation of "mathematician" and of "non-mathematical work". In the absence of that, I find this vague and I've downvoted $\endgroup$ – Matt F. Aug 20 at 17:32
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    $\begingroup$ The question is too vague. Before 18 century, all mathematicians had non-mathematical jobs since there were no mathematical jobs.So probably you mean modern times. It is also not clear who exactly is counted as a mathematician. $\endgroup$ – Alexandre Eremenko Aug 20 at 23:24

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Samuel Eilenberg, one of the key mathematicians of the XX Century (co-created category theory, systematized homological algebra, opened new roads in topology, etc), was a good example:

he had (at least) TWO LIVES, with only one thing in common, his short name, Sammy.

In the first one he was the mathematician, whereas in the other he was a formidable expert and collector of Chinese and far-eastern ancient pottery (and other artifacts as well). He was world-famous in his second life just like he was in his first one (when he died he donated his immense collection to NYC, you can still admire it here).

What is funny (and a bit odd ) is this: Sammy did not like to mix his two lives at all. At his funeral, the two groups (mathematicians and art collectors) collided for the first and last time. Nobody could believe that Prof. Eilenberg, the Math Genius, and Prof. Eilenberg, one of the greatest authorities in ancient eastern arts, were one and the same man.

POST SCRIPT

I have done some research on Sammy's life as art collector: apparently, he was struck by the beauty of indian art during a trip to India. From that point on, he decided that he had to assemble a collection of eastern art and craftmanship, which he did in the next 30 + years. Now I finally see what the two Eilenberg had in common: a passion for aesthetics, for the formal beauty of structures. Alex Heller wrote the following words to honor his Teacher Sammy:

As I perceived it, then, Sammy considered that the highest value in mathematics was to be found, not in specious depth nor in the overcoming of overwhelming difficulty, but rather in providing the definitive clarity that would illuminate its underlying order. This was to be accomplished by elucidating the true structure of the objects of mathematics. Let me hasten to say that this was in no sense an ontological quest: the true structure was intrinsic to mathematics and was to be discerned only by doing more mathematics. Sammy had no patience for metaphysical argument. He was not a Platonist; equally, he was not a non-Platonist. It might be more to the point to make a different distinction: Sammy’s mathematical aesthetic was classical rather than romantic.

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    $\begingroup$ One might say that, because of his contributions to the theory of finite automata, he was also a computer scientist which, if we don't consider this part of mathematics, is a third domain of specialty. $\endgroup$ – Gro-Tsen Aug 21 at 0:40
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    $\begingroup$ @Gro-Tsen Then I might also add Edward Spanier to the list. Also more known as a mathematician; but published fundamental, and much cited, work in theoretical computer science; mostly with S. Ginsburg. Eilenberg's work in automata theory is clearly written and still inspirational after almost 50 years, but most TCS-Researchers know that he is a famous mathematician too. However, Spanier, I guess most TCS people do not know that he is a mathematician at all. At least it is not that well-known. $\endgroup$ – StefanH Aug 21 at 14:56
  • $\begingroup$ @StefanH A small thing, but it's Edwin, not Edward, Spanier. $\endgroup$ – Danny Ruberman Aug 24 at 1:00
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    $\begingroup$ @DannyRuberman Oh yes, I am sorry. Thank you! $\endgroup$ – StefanH Aug 24 at 11:25
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Charles Lutwidge Dodgson (1832-1898), better known as Lewis Carroll.

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    $\begingroup$ please expand, Noam :-). surely you can name a few things done/invented/made by Dodgson which you find outstanding... $\endgroup$ – Franka Waaldijk Aug 20 at 15:12
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    $\begingroup$ Well, probably his universally-known fictional books qualify for "outstanding/prominent non-mathematical work", or am I missing something? $\endgroup$ – Francesco Polizzi Aug 20 at 15:15
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    $\begingroup$ I think the issue is whether this is a prominent non-mathematical work of a professional mathematician, or a prominent mathematical work of a non-mathematician, or if that matters for this question. Certainly in this case his novels are more famous than his math. $\endgroup$ – Brady Gilg Aug 20 at 16:45
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    $\begingroup$ @BradyGilg His day job was as a mathematician. That most people don't know it doesn't make him any less of one :). $\endgroup$ – Denis Nardin Aug 20 at 16:47
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    $\begingroup$ I've also used Dodgson condensation en.wikipedia.org/wiki/Dodgson_condensation in one of my own papers. He certainly counts as a research mathematician in practice even if he technically wasn't one on paper. $\endgroup$ – Terry Tao Aug 23 at 16:53
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I have noticed, after reading all previous answers, that no woman mathematician was listed.

My first impression is that most women mathematician born before 1960 (or maybe until today), are outstanding in non mathematics areas as they must have been activist for just having the chance of studying. Many of them were not even recognized or could work as mathematicians, because universities didn't hire women professors. A sad example is that of Emmy Noether who taught for seven year without income from the university. But besides this, there are many women contributing for medicine and biology, social equity, and inclusions of minorities in mathematics. But they are ghosts, as we do not see or know them. Here is a list with some of them: https://en.wikipedia.org/wiki/List_of_women_in_mathematics

Here are two examples: Sophie- Germain, who, besides being a important mathematician of her time, contributed to elasticity theory and to philosophy - her philosophical work were admired and cited by Auguste Comte. She has struggled to study in her time but were recognized by the great mathematicians Lagrange and Gauss, even after they discovered that she was not Monsieur LeBlanc. ( Her history is worth reading: https://en.wikipedia.org/wiki/Sophie_Germain )

More recently, we have Eugenia Cheng, who is a category theorist and an accomplished pianist. She is also a writer engaged in mathematical popularization and has a column in The Wall Street Journal.

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    $\begingroup$ I went to a mathematics lecture by Eugenia once and she played the keyboard in the middle of it ;) $\endgroup$ – Hollis Williams Aug 22 at 0:08
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    $\begingroup$ Kovalevskaya had manifold interests and wrote a novel, but apparently it was not very good (to go by my memories of what is stated in Ann Hibner Koblitz's excellent biography, which I unfortunately don't have at hand). Perhaps we need a separate question on "first-rate mathematicians who can't focus and keep doing non-outstanding work in other fields", taking care of course not to forget elements of the set who are women. $\endgroup$ – H A Helfgott Aug 23 at 9:27
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    $\begingroup$ "Kovalevskaya had manifold interests" Pun intended, @HAH? $\endgroup$ – Gerry Myerson Aug 23 at 23:35
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    $\begingroup$ Lilian Pierce has also introduced musical interludes in her mathematical talks. She won the 2018 Sadosky Prize for research that "spans and connects a broad spectrum of problems ranging from character sums in number theory to singular integral operators in Euclidean spaces" including in particular "a polynomial Carleson theorem for manifolds". She is an associate professor of mathematics at Duke University, and a von Neumann Fellow at the Institute for Advanced Study. By age 11 she began performing professionally as a violinist. en.wikipedia.org/wiki/Lillian_Pierce $\endgroup$ – Gerry Myerson Aug 23 at 23:39
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    $\begingroup$ We will probably need a separate, (very) long list of "mathematicians who are talented instrumentalists". $\endgroup$ – H A Helfgott Aug 24 at 8:12
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Noam D. Elkies, who gave an answer to this question, is himself also an accomplished composer.

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    $\begingroup$ Interesting. Is he currently active in mathematics? $\endgroup$ – C.F.G Aug 20 at 15:37
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    $\begingroup$ OMG. He is also winner of the 1996 World Chess Solving Championship!! duo to wiki. $\endgroup$ – C.F.G Aug 20 at 15:40
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    $\begingroup$ I think it would be topologically satisfying if Noam could write something about the achievement in physics of some mathematician gmvh ;-). $\endgroup$ – Peter - Reinstate Monica Aug 21 at 8:05
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Fields medallist Cédric Villani is a French politician.

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    $\begingroup$ en.wikipedia.org/wiki/List_of_mathematician-politicians has a long list of people who "achieved notability both as academically-trained mathematicians (with a graduate degree, or published in mathematical journals) and also as elected politicians (at a state or national level)." Daniel Biss was a member of the Illinois Senate. Kathleen Ollerenshaw was Lord Mayor of Manchester. Paul Painlevé was Prime Minister of France. $\endgroup$ – Gerry Myerson Aug 20 at 23:58
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    $\begingroup$ The mathematician Borel was a cabinet member under the mathematician Painleve, who was Prime Minister of France. $\endgroup$ – Zarrax Aug 21 at 3:28
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    $\begingroup$ @C.F.G there is no shortage of deceiving, lying, hypocritical and/or illogical mathematicians. $\endgroup$ – Gerry Myerson Aug 21 at 7:33
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    $\begingroup$ @C.F.G There is nothing stopping a mathematician from asserting something he or she believes to be untrue in the hope of ultimately gaining something from this deception ("suppose for a contradiction that ... ") $\endgroup$ – Gordon Royle Aug 21 at 8:15
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    $\begingroup$ Paul Painlevé was also the first person to be an airplane passenger in France. $\endgroup$ – Richard Stanley Aug 21 at 16:28
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Omar Khayyam was a Persian mathematician, astronomer, philosopher, and poet. As a mathematician, he is most notable for his work on the classification and solution of cubic equations, where he provided geometric solutions by the intersection of conics. Khayyam also contributed to the understanding of the parallel axiom. As a poet, he gave us the Rubaiyat of Omar Khayyam – "A Jug of Wine, a Loaf of Bread—and Thou."

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    $\begingroup$ +1. Rubaiyat in MIT website? $\endgroup$ – C.F.G Aug 23 at 6:25
  • $\begingroup$ Yes, that's the one. $\endgroup$ – Gerry Myerson Aug 23 at 6:33
  • $\begingroup$ He was also one of the contributors to Solar Hijri calendar which is more accurate than the Gregorian calendar. (The GC has 1 day non-accurate after 3320 years while SHC has 1 day non-accurate after 3770 years!!) $\endgroup$ – C.F.G Aug 27 at 7:43
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Jim Simons - probably best known to mathematicians for his work on the secondary characteristic classes developed various mathematical models for market trading that have been highly successful. He is an outstanding philanthropist, using much of the income from his financial engineering work to support lots of research activities through e. g. the Simons foundation: the Simons investigators awardees list includes such names as Aaronson, Aganagic, Bhargava, Daubechies, Eskin, Kapustin, Katzarkov, Kitaev, Mirzakhani, Okounkov, Ooguri, Poonen, Rouquier, Seidel, Tao, ...

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    $\begingroup$ By "best known" I assume you mean best known published mathematics? The Medallion Fund, Renaissance Tech, and the Simons foundation are more well known overall by a factor of thousands. $\endgroup$ – Brady Gilg Aug 20 at 16:39
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    $\begingroup$ @BradyGilg Thanks, tried to clarify. Feel free to edit it, it is community wiki $\endgroup$ – მამუკა ჯიბლაძე Aug 20 at 16:45
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    $\begingroup$ From the known histories, the early strategies used by Medallion Fund (which became the basis for Renaissance Technologies) were derived basically by James Ax. Later strategies were created by Elwyn Berlekamp. It seems Simons' contributions were more in the business and management aspects. Not saying this to lessen him. Realistically, given the lack of success Berlekamp had later in finance, management (and hiring) practices may be more significant than actual strategies. I think this is also more inline with the intent of the question. $\endgroup$ – Chan-Ho Suh Aug 21 at 3:24
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Bertrand Russell was a mathematician well-known for his philosophical and political work.

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    $\begingroup$ Bertrand Russell was a philosopher who did also some math. His work in philosophy is still taught, his work in mathematics is not. $\endgroup$ – Michael Greinecker Aug 20 at 21:42
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    $\begingroup$ @Michael The Principia are still a well-researched subject. The interest in it is by no means just historical. $\endgroup$ – Andrés E. Caicedo Aug 20 at 23:11
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    $\begingroup$ @TimothyChow: those programming languages and proof assistants are based on descendants of Church’s type theory. Russell’s type theory was very different, and I’ve never heard of it being taught in this connection. That said, I agree that Principia continues to be very relevant. $\endgroup$ – Peter LeFanu Lumsdaine Aug 21 at 0:26
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    $\begingroup$ @NajibIdrissi My point is that by all reasonable standards Russell was a philosopher who also did some math (with Whitehead) that grew out of his philosophical work. TO me this answer reads a bit like "Edward Witten is a mathematician well-known for his work in physics." $\endgroup$ – Michael Greinecker Aug 21 at 7:40
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    $\begingroup$ You know you’ve made it when people spend inordinate amounts of time arguing whether you were a mathematician who did philosophy or a philosopher who did mathematics, all the while completely ignoring your Nobel Prize in Literature. $\endgroup$ – Dan Romik Aug 22 at 4:42
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From Wikipedia: Hermann Günther Grassmann (German: Graßmann, pronounced [ˈhɛʁman ˈɡʏntɐ ˈɡʁasman]; 15 April 1809 – 26 September 1877) was a German polymath, known in his day as a linguist and now also as a mathematician.

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    $\begingroup$ May be it should be said that he left Mathematics disappointed by the reception of his work and because his posibilities of teaching math were very low due to really bad reports, for example by Kummer. His book was almost ignored for more than two decades; now it is considered the father of linear algebra. $\endgroup$ – Xarles Aug 22 at 15:21
  • $\begingroup$ @Xarles, have you read Kummer's report, and if so, do you know if it can be found online? What you wrote is a common narrative; I also heard another one - that Kummer's report was completely accurate, and whatever in Grassmann's writing we now deem important was buried in the many pages of his unclear, unrigorous and hardly readable text. I have no opinion of my own though. $\endgroup$ – Kostya_I Aug 24 at 20:54
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    $\begingroup$ When I looked into Grassmann's book Die Lineale Ausdehnungslehre, ein neuer Zweig der Mathematik from 1844, my impression was, that he aimed to explain his ideas and results to philosophers like Kant. The second edition Die Ausdehnungslehre. Vollständig und in strenger Form begründet from 1862 seems already like a standard text on linear algebra. $\endgroup$ – Peter Michor Aug 30 at 6:19
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Felix Hausdorff wrote philosophical works, essays, poems and plays under the pseudonym Paul Mongré. Let me quote from the information of the Hausdorff Center for Mathematics in Bonn:

https://www.hcm.uni-bonn.de/about-hcm/felix-hausdorff/about-felix-hausdorff/

Hausdorff pursued, especially during the early years in Leipzig, a kind of double identity: as Felix Hausdorff, the productive mathematician, and as Paul Mongré. Under this pseudonym, Hausdorff enjoyed remarkable recognition within the German intelligentsia at the end of the 19th century as a writer, philosopher and socially critical essayist....Between 1897 and 1904, Hausdorff reached the peak of his literary-philosophical accomplishment: during this period, 18 of a total of 22 works were published under his pseudonym. These included the volume of aphorisms Sant’ Ilario: Thoughts from Zarathrustra’s Country, his critique Das Chaos in kosmischer Auslese, a book of poems entitled Ekstases, the farce Der Arzt seiner Ehre, as well as numerous essays....The play was Hausdorff’s greatest literary success, as it was performed over 300 times in 31 cities.

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Emanuel Lasker was a great mathematician and is regarded as one of the best chess players ever. If it counts.

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  • $\begingroup$ Lasker is mentioned in one of the comments on the original post. $\endgroup$ – Gerry Myerson Aug 21 at 7:28
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    $\begingroup$ I think it's appropriate for that comment to be turned into an answer, especially since it's CW. $\endgroup$ – Tim Campion Aug 21 at 11:42
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    $\begingroup$ And indeed World Chess Champion from 1894 to 1921, the longest period of time anyone has been World Chess Champion. $\endgroup$ – Rosie F Aug 23 at 11:47
  • $\begingroup$ Interesting! I knew him first as a chess player - I didn't know that he was also a mathematician. $\endgroup$ – Zubin Mukerjee Aug 24 at 19:36
  • $\begingroup$ Emanuel Lasker was a great chess player, one of the best ever, and a not insignificant mathematician: he proved a basic result on ideal theory - it's familiar (in a more general form due to Noether) to anybody who has taken a course in algebraic number theory. $\endgroup$ – H A Helfgott Sep 16 at 13:29
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Tom Lehrer published a couple of papers in mathematical statistics, and taught Mathematics at University of California, Santa Cruz for many years, but is undoubtedly better known for his three albums of humorous songs.

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    $\begingroup$ Let us not forget his work on analytic and algebraic topology of locally Euclidian metrization of infinitely differentiable Riemannian manifolds. $\endgroup$ – Aurelio Aug 21 at 14:19
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    $\begingroup$ @Aurelio : And this, he knew from nothing! $\endgroup$ – gspr Aug 21 at 14:40
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I think that the name of Archimedes immediately springs to mind. Among its inventions are the block-and-tackle pulley systems based on the lever, the screw, the parabolic reflectors used to burn Roman ships attacking Syracuse, the mechanical planetarium.

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    $\begingroup$ The story of the parabolic reflectors used to burn Roman ships attacking Syracuse is not true. It is a legend. $\endgroup$ – Philippe Gaucher Aug 23 at 14:17
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    $\begingroup$ The story is in Polybius, Plutarch and Lucian of Samosata. The Wikipedia page on Archimedes says that there are still an ongoing debate about its truth; however, some models of reflectors have been built demonstrating that the construction of such weapons was actually possible with the technology that Archimedes had at his disposal. en.wikipedia.org/wiki/Archimedes $\endgroup$ – Francesco Polizzi Aug 23 at 16:21
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    $\begingroup$ The wikipedia page mentions some experiments indeed but the weapon requires a lot of luck. A catapult or flaming arrows are far much easier to use for the same effect. $\endgroup$ – Philippe Gaucher Aug 23 at 17:38
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Gauß contributed to the development of the telegraph. Gauß was also an astronomer, metrology engineer and land surveyor.

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  • $\begingroup$ Really????????? $\endgroup$ – C.F.G Aug 20 at 17:39
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    $\begingroup$ @C.F.G Well, I don't think it was the fundamental theorem of algebra or quadratic reciprocity that got his name attached to the unit of magnetic flux density. $\endgroup$ – Andreas Blass Aug 20 at 17:48
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    $\begingroup$ Major inventions are not usually made by a single person (there were lightbulbs before Edison), and the telegraph is no exception. But Gauss made an essential contribution. $\endgroup$ – Michael Renardy Aug 20 at 21:19
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    $\begingroup$ @C.F.G : Is it a coincidence that your initials are the same as Gauss's? If not, your astonishment is a bit amusing! $\endgroup$ – Timothy Chow Aug 20 at 23:15
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    $\begingroup$ Some details are at en.wikipedia.org/wiki/… $\endgroup$ – Matt F. Aug 21 at 1:28
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Paul Painleve was briefly prime minister of France on two separate occasions, as well as holding many other government posts including Minister of Defense. In mathematics, he is best remembered for his contributions to nonlinear differential equations.

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    $\begingroup$ I mentioned Painlevé in a comment on the answer that proposed Villani. $\endgroup$ – Gerry Myerson Aug 21 at 7:30
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    $\begingroup$ Before being mainly involved in politics (mostly $\ge 1910$), Painlevé had (1897-1906) a significant involvement in defending Alfred Dreyfus, see Des mathématiciens dans l'affaire Dreyfus (French) $\endgroup$ – YCor Aug 21 at 16:20
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Frank Ryan earned a math PhD from Rice for the dissertation "Characterization of the set of asymptotic values of a function holomorphic in the unit disc." He published two fundamental papers on the set of asymptotic values of a function holomorphic in the unit disc in Duke Mathematical Journal. [the papers, not the unit disc, were in the journal] He was an assistant professor at the Case Institute of Technology, 1967-71. He has an Erdős number of 3. He was also a lecturer in mathematics at Yale University, 1977-86.

But he is best-known as a quarterback in the National Football League, 1958-70. He led the Cleveland Browns to an NFL title in 1964.

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    $\begingroup$ John Urschel played in the NFL for a couple of seasons, and has some publications in Mathematics. $\endgroup$ – Gerry Myerson Aug 21 at 8:02
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Persi Diaconis is an accomplished magician, in addition to his mathematical career.

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I think Greg Egan (sci-fi author) qualifies. He has a few papers on arxiv, and made the news for his work on superpermutations, which motivates the title 'Mathematician'. He is also an occasional MO-user.

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    $\begingroup$ I think Egan would be a great answer to a different question, of people whose profession is not "mathematician" doing good maths $\endgroup$ – Yemon Choi Aug 20 at 18:08
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    $\begingroup$ @YemonChoi why don't you ask that as a separate question? I'd answer Aubrey de Grey. $\endgroup$ – Nik Weaver Aug 20 at 23:05
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    $\begingroup$ @NikWeaver : That question arguably already exists. $\endgroup$ – Timothy Chow Aug 20 at 23:18
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    $\begingroup$ @TimothyChow and Egan and de Grey are both answers there! Never mind, then. $\endgroup$ – Nik Weaver Aug 21 at 0:16
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I'm surprise no-one has mentioned Isaac Newton. He spent almost half his career outside academia fighting against forgery at the Royal Mint. He was also an MP and wrote a huge amount on biblical chronology, alchemy, and theology.

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Ron Graham's mathematical work is probably familiar to most users of this website.

In his youth, he won a title as California state trampoline champion. In 1972 he was elected president of the International Jugglers' Association.

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Harald Bohr was a member of the Danish national football team for the 1908 Summer Olympics, where he won a silver medal. The semi-final against France was 17-1.

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    $\begingroup$ Interesting result!!! $\endgroup$ – C.F.G Aug 23 at 14:09
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    $\begingroup$ Interestingly, Harald Bohr played professional football also together with his older brother, Niels, who also had a prominent science career. $\endgroup$ – Uri Bader Aug 30 at 10:05
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I am on the fence regarding whether this question should stay open, but while it does, I thought the following example might be of interest: Peter Rosenthal, perhaps best known to mathematicians for his work on subspace lattices of operator algebras (see e.g. his book with Heydar Radjavi), developed a 2nd career/mission as a lawyer.

Wikipedia link: https://en.wikipedia.org/wiki/Peter_Rosenthal

Link from comments: 2014 profile in the Toronto Star

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    $\begingroup$ While he definitely seems to be vocal about being left-wing, the causes he represent are more often regarding basic human rights than left-wing. E.g., he has represented many cases of police brutality; see this beautiful piece on Toronto Star: thestar.com/news/crime/2014/01/05/… $\endgroup$ – auniket Aug 21 at 2:42
  • $\begingroup$ @auniket thank you for the clarification. I must admit that originally I omitted the adjective and then added it at the last-minute in a confused effort at sign-posting, since I couldn't remember the details that I'd heard from friends on the Canadian scene $\endgroup$ – Yemon Choi Aug 21 at 2:49
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Per Enflo, a Swedish mathematician known for solving the so called ``basis problem'', one of the problems from Scottish book (about the existence of Schauder basis). Besides being a mathematician he is also known as a talented pianist.

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Mathematician Eric Temple Bell

President of the MAA, 1931-32
Author of the book Men of Mathematics
Bell numbers, Bell polynomials
etc.

Also was a successful science fiction author under the pseudonym John Taine.

See the fascinating book
Reid, Constance, The Search for E.T. Bell, MAA spectrum, The Mathematical Association of America, 1993

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Martin Hairer has written a widely used professional audio editing software "Amadeus Pro" (https://www.hairersoft.com/).

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Nikolai Durov, who launched Telegram with his brother Pavel Durov, has some works on Arakelov geometry.

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Joseph Fourier was also an Egyptologist.

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    $\begingroup$ He was a bit more than just that. Excerpts from hiw biography on wikipedia include: "He took a prominent part in his own district in promoting the French Revolution, serving on the local Revolutionary Committee. ... Fourier accompanied Napoleon Bonaparte on his Egyptian expedition ... Cut off from France by the British fleet, he organized the workshops on which the French army had to rely for their munitions of war ... In 1801, Napoleon appointed Fourier Prefect (Governor) of the Department of Isère in Grenoble, where he oversaw road construction and other projects." $\endgroup$ – HJRW Aug 22 at 11:03
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    $\begingroup$ @HJRW Equally, one should also mention Gaspard Monge, who was on the same expedition to Egypt, similarly held political appointments during the Revolution and all the while also is known for his results in geometry and as being the father of optimal transport. $\endgroup$ – mlk Aug 23 at 6:34
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In addition to his work in number theory, Carl Størmer made important contributions to the study of the aurora borealis. Here he is conducting an experiment rather far from his blackboard:

Størmer conducting an experiment

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Otto Iulievich Schmidt is now best remembered for his polar expeditions and a geophysical institute in Russia bears his name. The English wikipedia does not mention it, but he was also one of the founders of the modern theory of groups and had a strong influence on A.G. Kurosh.

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    $\begingroup$ Oh -- that's the Schmidt from Krull-Remak-Schmidt! $\endgroup$ – darij grinberg Aug 21 at 20:07
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Gian-Carlo Rota in addition to being an influential combinatorialist was a philosopher, and his philosophical writing was not in the tradition often thought of as being closest to math ('analytic philosophy') but was rather inspired by phenomenology. Apparently this heterodoxy caused some consternation from e.g. his colleagues in the philosophy department at MIT.

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