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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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    $\begingroup$ Unabomber has to be #1 on this list. $\endgroup$ Aug 20, 2020 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, 2020 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, 2020 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. $\endgroup$ Aug 20, 2020 at 23:24
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    $\begingroup$ @Piyush if we put Unabomber on the list, then we should also make room for André Bloch, mathematician and triple murderer. en.wikipedia.org/wiki/André_Bloch_(mathematician) $\endgroup$ Aug 20, 2020 at 23:50

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Not so prominent I think but I'd like to mention that the MathTime Professional 2 (MTPro2) fonts were designed by Michael Spivak of Publish or Perish Inc., see here.

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I think, one can add Francesco Faa di Bruno to this list, see https://en.wikipedia.org/wiki/Francesco_Fa%C3%A0_di_Bruno. He is to my knowledge the only beatified mathematician.

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Gunnar Carlsson is a professor at Stanford famous for his work in K-theory, and on the Segal Conjecture in homotopy theory. He is also the President and Founder of the company Ayasdi, described as

A machine intelligence software company that offers a software platform and applications to organizations looking to analyze and build predictive models using big data or highly dimensional data sets. Organizations and governments have deployed Ayasdi's software across a variety of use cases including the development of clinical pathways for hospitals, anti-money laundering, fraud detection, trading strategies, customer segmentation, oil and gas well development, drug development, disease research, information security, anomaly detection, and national security applications.

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Per Enflo is famous for solving Banach's basis problem, Grothendieck's approximation problem, and the invariant subspace problem for general Banach spaces, and has other fundamental research in linear and non linear geometric functional analysis. He also has done research in population dynamics. A child prodigy as a pianist, he continues to give concerts in Europe and the United States, but you can hear him at home by creating a Per Enflo station on Spotify.

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Doctor Ahmed Chalabi earned a PhD from the University of Chicago in 1969, founded Petra Bank in 1977, was sentenced in absentia in Jordan for bank fraud in 1992, and (allegedly) very successfully lobbied for the 2003 Invasion of Iraq.

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    $\begingroup$ I think this one falls more under the "prominent figure who has a PhD in mathematics" category (as do a number of the other posts, to be fair)- but, wow! this guy has a wild life story! $\endgroup$ Aug 22, 2020 at 15:09
  • $\begingroup$ @SamHopkins Indeed. However, I assume that the University of Chicago would not have granted him a doctoral degree had he not made a non-trivial contribution. Perhaps I assume too much. $\endgroup$ Aug 22, 2020 at 15:10
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Abu Rayhan al-Biruni (973 – after 1050) was an Iranian polymath, physicist, astronomer, natural sciences, historian, chronologist and linguist. One of the best his achievements is a method proposed and used by him to estimate the radius and circumference of the Earth almost 1000 years ago.

He was also inventor of minutes and seconds of time.

enter image description here

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Andrew Blumberg, in addition to being an accomplished homotopy theorist, a full professor at UT Austin, and having published more than 60 papers, also works on issues related to geolocation data and privacy. For example, he worked on an amicus brief for a Supreme Court case.

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Charles Kalme, a mathematicion (Contributions to the Theory of Discontinuous Groups of Mobius Transformations, Ph.D. thesis, NYU, 1967) and pioneering chess programmer. His achievements as a chessplayer include winning the United States Junior Championship and playing twice in the United States Chess Championship. He was also a master of contract bridge.

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    $\begingroup$ The well-known mathematician Henry Peter Francis Swinnerton-Dyer was also an outstanding chess and bridge player in his student days. A variation in Ponziani's Opening that he played in 1949 is cited in 10th edition of Modern Chess Openings. $\endgroup$ Aug 29, 2020 at 12:14
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Glen E. Bredon is the author of the programs DOS.MASTER for Apple II computers, Merlin (a macro assembler) and ProSel for Apple machines. He was the professor of mathematics at Berkley and IAS and author of worthwhile math books like

Bredon, Glen E., Topology and geometry., Graduate Texts in Mathematics. 139. Berlin: Springer. xiv, 557 p. (1997). ZBL0934.55001.

and

Bredon, Glen E., Introduction to compact transformation groups, Pure and Applied Mathematics, 46. New York-London: Academic Press. XIII,459 p. $ 21.00 (1972). ZBL0246.57017.

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Here is some mathematical work by someone better known for other work.

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    $\begingroup$ Isn't this the exact reverse of what the question is asking for? $\endgroup$
    – Yemon Choi
    Aug 20, 2020 at 18:07
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    $\begingroup$ @YemonChoi Indeed, this answer should be reformulated as “Karl Marx wrote political texts that have gained some measure of celebrity”. 😁 $\endgroup$
    – Gro-Tsen
    Aug 21, 2020 at 0:59
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    $\begingroup$ Does any of this go beyond philosophical ramblings about basic definitions? Legit question -- I haven't seen the entire work. $\endgroup$ Aug 21, 2020 at 6:20
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    $\begingroup$ Karl Marx and the Foundations of Differential Calculus by Hubert Kennedy gives a nice discussion of Marx's investigations into calculus. At the time, the received view of the derivative (following Leibniz) was a ratio of infinitesimals, which today we would find lacking in rigor. Marx perceived this difficulty and took some nontrivial steps toward a modern rigorous account. $\endgroup$ Aug 29, 2020 at 19:14
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I think, John F. Nash fits in this category, because of 1994 Nobel Memorial Prize in Economic Sciences. (I am not aware the details of his work, I just know this because of "A beautiful mind" movie!)

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    $\begingroup$ The work Nash received the Nobel memorial prize for was from his Princeton PhD-thesis in mathematics. This was not non-mathematical work. $\endgroup$ Aug 20, 2020 at 21:44
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    $\begingroup$ @MichaelGreinecker: thanks for comment. So I should delete this answer but I think it is better to not to do that for those don't know this fact like me!! $\endgroup$
    – C.F.G
    Aug 21, 2020 at 14:18
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Although it is difficult to say exactly what Thales accomplished, if you take what he's given credit for it is immense. By your criteria he would qualify as an answer.

Although he lacked the rigor of proof, he was the first mathematician we attribute a mathematical result to - namely Thales' Theorem used to get the distances of ships at sea.

He was also the first philosopher. With his contention that everything is water we have the first theory that says everything is one.

Also with his contention that everything is water we have a testable claim. This makes him the first scientist.

He also was an astronomer, predicting the eclipse of May 28th, 585 BC.

He even dabbled in business, by legend. There is a famous story attributed to Aristotle, and others, about him. If true, Thales predicted the weather and foresaw a good olive harvest for the coming year. He then bought all the olive presses at a discount, and rented them out during the harvest. This would be the first recorded use of futures to turn a profit.

Legend has it that Thales was an engineer.

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  • $\begingroup$ I think Joseph of Genesis preceded Thales in the use of futures. Seven good years, followed by seven lean years, and all that. But there's no record of Joseph making any mathematical contributions, Thales has him beat there. $\endgroup$ Aug 30, 2020 at 9:36
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    $\begingroup$ Wikipedia is incorrect then. I've also seen other sources that cite Thales as well. The old testament reached its current form in the Persian period (538-332 BC). Thales came before that. I suppose if you believe the Bible is to be taken as a real account, then that reference would be older. However, I don't think you'll find a scholar that would argue that Thales wasn't real. $\endgroup$ Aug 30, 2020 at 9:59
  • $\begingroup$ Wikipedia? Who said anything about Wikipedia? $\endgroup$ Aug 30, 2020 at 12:17
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    $\begingroup$ From wikipedia, with their source on the topic: "This first version of the story would constitute the first historically known creation and use of futures, whereas the second version would be the first historically known creation and use of options." George Crawford, Bidyut Sen – Derivatives for Decision Makers: Strategic Management Issues, John Wiley & Sons, 1996 ISBN 9780471129943 $\endgroup$ Aug 30, 2020 at 12:41
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There is Bertrand Russell, a logician, who had another career as a philosopher as well as an anti-war protestor. He helped publicise what was happening in Vietnam - in fact, according to Paul McCartney of the Beatles, at one point he lived on the same square or street with Russell and he had knocked on his door to introduce himself and Russell proceeded to tell him all about the war. This is, according to Paul McCartney, how the Beatles became involved in the anti-war protest movement, in particularly against the war of aggression by the USA on Vietnam.

Laurent Schwartz, a french mathematician known for his work was on distributions, was also an anti-war activist and who focused on labour activism as well on the colonial war in Algeria.

Grothendieck, who needs no introduction, was also an ati-war activist, focusing on what was then occuring Vietnam. His fater was a revolutionary socialist.

Smale was also another anti-war activist; also Solzhenitsyn and many others.

Sofia Kovalevskaya was one of the first handful of female mathematicians. She was also a writer, having written a well-received autobiography, A Russian Childhood in where she reveals she met Dostoyevsky as a young woman and did not think much of him.

Likewise, Lewis Carroll, also a logician and who wrote the best-selling Alice's Adventures in Wonderland.

Also Abdus Salam, who was a mathematical physicist and had a second career setting up the Triest Centre of Mathematical Physics to help te Third World get on to its feet.

And a special mention for Walter Sisulu, who studied a science degree, but after joining the ANC, was imprisoned several times, and was finally imprisoned on Robbens Island with Nelson Mandela and sentenced to twenty-five years - the same sentence as Nelson. He rose to become the ANC's Secretary-General and Deputy President of the organisation.

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    $\begingroup$ mathoverflow.net/a/369713/90655 $\endgroup$
    – C.F.G
    Nov 27, 2020 at 16:26
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    $\begingroup$ Russell is previously mentioned here. Carroll is mentioned here. $\endgroup$ Nov 27, 2020 at 16:26
  • $\begingroup$ @Noah Schweber: But with very little detail - they deserve better than that. Besides Kovalevskaya and Sisulu are not mentioned. $\endgroup$ Nov 27, 2020 at 16:28
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    $\begingroup$ Solzhenitsyn was not a mathematician. Carroll hardly one, to be honest. Sisulu only studied science, but never worked as a mathematician. There are many students in mathematics (the majority, in fact) who pursue careers not related to mathematics after graduation, so according to your view they would all qualify as answers to this question. $\endgroup$
    – Alex M.
    Nov 27, 2020 at 21:25
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    $\begingroup$ This is a community wiki big-list question for a reason. (1) If you feel some other answer has insufficient detail, add that detail to that answer, do not put it in a new answer. (2) Ideally, each answer should only give one example. If you have more people, put each in a separate answer. $\endgroup$ Nov 28, 2020 at 8:42
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It has been noted already that Noam Elkies is an accomplished composer.

What I find at least as extraordinary about him is that he can hum-whistle some of Bach's two-part inventions. (Anecdotal "evidence", will remove this answer if it is false.)

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Albert Einstein's contribution to differential geometry was significant. One could mention also Einstein's tensor notation.

On the other hand, Einstein was an inventor, he had several inventions (patents) to his credit.

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    $\begingroup$ He wasn't a mathematician I think. $\endgroup$
    – C.F.G
    Nov 27, 2020 at 20:09
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    $\begingroup$ One of his papers on math? $\endgroup$
    – C.F.G
    Nov 27, 2020 at 20:14
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    $\begingroup$ Mathematics can be recorded also outside of papers in mathematical journals. Differential geometers would direct you to Einstein's results on the affine connection. $\endgroup$
    – Wlod AA
    Nov 27, 2020 at 20:34
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    $\begingroup$ The probability theory, classical mechanics, the special relativity theory, ... ... ... are all mathematical theories these days. $\endgroup$
    – Wlod AA
    Nov 27, 2020 at 20:38
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    $\begingroup$ What is the definition of a mathematician? Who is educated in math or did some math research. Isn't? $\endgroup$
    – C.F.G
    Nov 27, 2020 at 20:41
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Professionally, Pierre de Fermat was a lawyer; he had also contributed to physics.

Henry Poincare, Solomon Lefschetz, and Raoul Boot were into engineering when they were young.

Hugo Steinhaus was serious about applications, e.g. about the different feet shapes in order to help shoe designers. The famous Steinhaus slogan was

                    A mathematician will do it better.

In particular, Steinhaus patented longimeter.

Karol Borsuk invented a successful game during WWII, and it helped him to survive in those hardship years.

Stan (Stanisław) Ulam was the main inventor of the H bomb. He has also invented cellular automata.

Israel Gelfand at his mature stage turned his interests toward biology and medicine.

Rene Thom in his later years became seriously interested in too many things to mention here.

Several American mathematicians, including John Milnor, worked on DOD contracts.

Topologist James Munkres made a significant contribution to the assignment problem -- it's even called Munkres assignment algorithm or Kuhn–Munkres algorithm.

A parallel processor invented by a mathematician in the US, and the technology that followed, had an impact on the fall of communism.

Greg Kuperberg was an early pioneer in the field of computer games when he was in his teens; this helped him to pay his tuition at MIT.

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    $\begingroup$ Did Fermat do anything prominent as a lawyer? Did Poincare, Lefschetz, Bott do anything prominent when they were "into" engineering? Did Thom do anything prominent in the unmentionable areas that interested him? Did Milnor et al do nonmathematical things on those DoD contracts? Isn't the assignment problem mathematics? Any details on the mathematician who invented a parallel processor, and how it impacted communism? $\endgroup$ Nov 29, 2020 at 4:21
  • $\begingroup$ @GerryMyerso, it's mixed. OP said outstanding/prominent. But there were over 30 answers before mine, and the average level for these 30+ is way below outstanding/prominent, and overall I believe that also clearly below my answer. ### My weakest case was wonderful Bott who indeed was simply an engineering student. ... Munkres did an algorithm (Erdos would call it computer science, not mathematics). $\endgroup$
    – Wlod AA
    Nov 29, 2020 at 7:10
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Stan Wagon, whose work was featured in several Mathoverflow posts (e.g. an unexpected image, Gaussian prime spirals), has also an entry in Ripley's Believe It or Not due to his Square Wheel Bike.

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Marcel-Paul Schuetzenberger (https://en.wikipedia.org/wiki/Marcel-Paul_Sch%C3%BCtzenberger) is also an interesting example (he started as a physician).

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I see nobody mentioned about John Forbes Nash, who obtained Nobel prize in Economic science for his contribution to economy. Further German Mathematician Carl Fredric Gauss, Von Neumann etc both were not only prominent mathematicians but also prominent physicist as well.

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    $\begingroup$ Gauss was already mentioned, mathoverflow.net/posts/369701/revisions (I think von Neumann was already mentioned, too). $\endgroup$ Oct 21, 2020 at 12:25
  • $\begingroup$ @GerryMyerson, But Prof John Nash was not mentioned. $\endgroup$
    – MAS
    Oct 21, 2020 at 13:18
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    $\begingroup$ Actually, Nash was mentioned in this answer of C.F.G: mathoverflow.net/a/369703 $\endgroup$ Oct 21, 2020 at 14:17
  • $\begingroup$ @JeremyRickard, I am confused who answered first , he or me.I answered 10 hours ago. During my answer i searched with keyword nash but got no link. That is why i answered as you see my first sentence. Anyway let it remain.I will help $\endgroup$
    – MAS
    Oct 21, 2020 at 14:56
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    $\begingroup$ @M.A.SARKAR: I posted my answer 2 month ago. $\endgroup$
    – C.F.G
    Oct 27, 2020 at 18:51
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