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I know about Manjul Bhargava, a mathematician and a Fields Medal winner who is a tabla player. Are there any other mathematicians who have had such a musical background?

By "musical background", I mean those who have had played musical instruments.

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    $\begingroup$ Einstein played the violin, though I thibk ge'd be the first to say that he didn't have a 'musical background.' $\endgroup$ Dec 2, 2020 at 21:19
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    $\begingroup$ What does it mean to "have a musical background"? If you just require them to know how to play an instrument, there will be lots of answers. If you have stricter requirements (professional-level player), it should be specified more clearly. $\endgroup$ Dec 3, 2020 at 7:45
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    $\begingroup$ That definition may be a tad broad, as I think that most American grade-school students learn to play an instrument in a class. Presumably there ought to be some distinction between a casual, everyday familiarity with a musical instrument and being notable as a musician. $\endgroup$
    – Nat
    Dec 3, 2020 at 13:12
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    $\begingroup$ @Nat I strongly agree. Even if you add a condition like having performed the instrument publicly in a concert, that still would be true for about a third of any math department I have been working in. $\endgroup$
    – mlk
    Dec 3, 2020 at 15:09
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    $\begingroup$ Actress Natalie Portman plays the piano (and did so on-screen in at least one film: Mr. Magorium's Wonder Emporium), and she holds a doctorate in mathematics. Granted neither of those are what she's most known for, so it might be a stretch to call her either a mathematician or a musician. $\endgroup$ Dec 3, 2020 at 15:24

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The MacTutor Article Mathematicians and Music provides an overview of this relationship.

Amongst those mathematicians who were accomplished players and had performed in public, the article includes:

Mathematicians who were also composers with published works include:

  • Herschel (also an accomplished violinist, hautboyist, organist, and conductor)

Mathematicians who wrote on the subject of music and its analysis include:

The article comments on the common belief that mathematicians tend to make good musicians, noting recent statistical analysis which suggests that:

... in only about 2 per cent of the cases considered was there any appreciable correlation between talent for music and talent for mathematics; they found also that the percentage of males lacking in talent for music but showing a talent for mathematics was comparatively high, about 13 per cent.


EDIT 30, July 2022.

Boltzmann, a mathematical physicist if not a mathematician, was a trained classical pianist who studied piano with none other than Anton Bruckner. Although he never performed for a paying audience he would frequently entertain friends, students, and colleagues by performing Liszt's piano transcriptions of the Beethoven symphonies. Whenever living in Vienna he was in regular attendance at the concert halls and theatres.

Here is Boltzmann's decidedly musical, if somewhat corny reaction to Maxwell's 1866 paper, On the Dynamical Theory of Gases:

First the variations in velocity develop majestically, then the equations of state enter on one side, the equations of motion on the other; ever higher surges the chaos of formulas. Suddenly, four words sound out: 'Put $\text{N} = 5.$' The evil demon $\text{V}$ vanishes, just as in music a disruptive figure in the bass abruptly falls silent...

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Einstein was a violinist, though I think he'd be the first to say he wasn't a musician.

Eugenia Cheng is a mathematician who specialises in higher category theory. She is also a concert pianist specialising in Lieder and art song. She was awarded the Sheila Mossman Memorial award from the Associated Board of the Royal School of Music and was the first recipient of the Brughtin & Hove Arts Council award for the musician of the year.

Interestingly, according to Wikipedia, Iannis Xanakis, a French-Greek musician who incorporated mathematical modelling, such as stochastic processes and game and set theory into his compositions. Though, personally, I think this goes way back to Duchamp and his notion of 'found art'.

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  • $\begingroup$ I'd argue that Einstein also would be the first to say he wasn't a mathematician. $\endgroup$
    – mlk
    Dec 3, 2020 at 14:49
  • $\begingroup$ @mlk: I'd argue that everybody else would see him as a mathematician as well as a physicist ... $\endgroup$ Dec 5, 2020 at 14:49
  • $\begingroup$ Well I don't. Wikipedia also doesn't call him a mathematician. Now don't get me wrong, he was most certainly more than just proficient in using mathematics, but as far as I know he only ever used it as a tool for doing physics and even then he preferred his thought experiments. $\endgroup$
    – mlk
    Dec 5, 2020 at 17:41
  • $\begingroup$ @mlk: Wikipedia is not everyone else. The average man on the street when faced with a mathematical physicist or a mathematician interested in physics isn't going to be able to distinguish between them. Thats what I say what I did. Mathematicians have thought experiments - they call them conjectures. $\endgroup$ Dec 5, 2020 at 17:47
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Per Enflo (see Wikipedia for a longer summary)

concert pianist, mathematician (solutions for the basis problem, the approximation problem, the invariant subspace problem in Banach space theory )

At a certain point in his life, he had to choose between the two. He reasoned that the likelihood of ever reaching the top as a concert pianist was small, compared to the same thing in mathematics. He chose mathematics. But throughout his life, despite being a professor of mathematics, he continued to do piano performances. When I knew him (maybe 1980's) he still spent two hours a day practicing on the piano.

The basis problem was placed in the Scottish Book by Banach. The prize offered was a live goose. Enflo did, indeed, receive the prize.

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There's always Tom Leher. I think he counts as a musician and mathematician.

https://www.youtube.com/watch?v=UQHaGhC7C2E ("Lobachevsky". It's satire, by the way)

https://www.youtube.com/watch?v=yhuMLpdnOjY (Poisoning Pigeons in the Park)

https://www.youtube.com/watch?v=zGM-wSKFBpo (The Elements)

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