0
$\begingroup$

The other day I was thinking about mathematicians in history who made fundamental contributions to both pure and applied mathematics. The examples I can think of are Newton, Gauss, Euler, Archimedes and von Neumann (I suppose you could include John Nash).

I was wondering if there were any other examples of mathematicians who excelled in their contributions to both pure and applied mathematics.

Edit: I just read a paper 'Influence of atmospheric pressure on the phenomena accompanying the entry of spheres into water' by Gilbarg and Anderson and realised that it was the same Gilbarg that wrote the elliptic PDEs textbook with Trudinger (in this case, you could even class the paper as applied physics).

Improve this question
$\endgroup$
7
  • 2
    $\begingroup$ A great example is John von Neumann, en.wikipedia.org/wiki/John_von_Neumann $\endgroup$
    – Fabrice Baudoin
    Commented Nov 9, 2019 at 17:01
  • 1
    $\begingroup$ Thanks, I did mention John von Neumann in my post though, but he is a great example. $\endgroup$
    – Hollis Williams
    Commented Nov 9, 2019 at 17:03
  • 2
    $\begingroup$ Sorry, I did not see. I will go for Henri Poincare then, en.wikipedia.org/wiki/Henri_Poincaré $\endgroup$
    – Fabrice Baudoin
    Commented Nov 9, 2019 at 17:08
  • 4
    $\begingroup$ I am not much fond of distinction between pure and applied mathematics, but I guess Kolmogorov would be another example. $\endgroup$
    – Algernon
    Commented Nov 9, 2019 at 17:12
  • 1
    $\begingroup$ I'd be more interested in contemporary mathematicians who excel at both. Harder to do it today than before. Terry Tao comes to mind. $\endgroup$
    – user35360
    Commented Nov 9, 2019 at 17:42

4 Answers 4

Reset to default
1
$\begingroup$

Very partial list: Fourier, Turing, Peter Lax, Noga Alon, Cathleen Morawetz, https://en.m.wikipedia.org/wiki/Olga_Ladyzhenskaya, Jurgen Moser,

Improve this answer
$\endgroup$
3
  • $\begingroup$ I sort of think of Ladyzhenskaya as a pure mathematician working on rigorous fluid dynamics, also what applied work did Moser do? $\endgroup$
    – Hollis Williams
    Commented Nov 9, 2019 at 17:46
  • $\begingroup$ I haven't heard of some of these before, but these are good examples, thanks for posting. $\endgroup$
    – Hollis Williams
    Commented Nov 9, 2019 at 18:33
  • $\begingroup$ I think of rigorous fluid dynamics and even KAM theory as applied Math. $\endgroup$
    – Yuval Peres
    Commented Nov 9, 2019 at 18:48
2
$\begingroup$

I think David Mumford qualifies.

Improve this answer
$\endgroup$
1
  • $\begingroup$ I didn't think of Mumford, but interesting suggestion. $\endgroup$
    – Hollis Williams
    Commented Nov 9, 2019 at 20:01
2
$\begingroup$

A further example would be Eduard Stiefel.

Improve this answer
$\endgroup$
1
  • $\begingroup$ I didn't realise that Stiefel created the conjugate gradient method, that's interesting. $\endgroup$
    – Hollis Williams
    Commented Nov 9, 2019 at 22:04
1
$\begingroup$

Examples? Almost all great mathematicians before the middle of 19th century, beginning from Euclid (who wrote not only the Elements but also a book on Optics and another on Astronomy): Archimedes, Apollonius (who introduced epicycles to Astronomy), Hero, Ptolemy,...,Kepler, Napier,..., Huygens, Newton,..., Euler, Gauss (who spent most of his career doing geodesy, astronomy, magnetism, and also invented telegraph), Cauchy, Lagrange, Jacobi, Riemann (contributions to electrostatics, ellasticity and PDE),..., Klein (his great book on spinning tops), Poincare (celestial mechanics),..., and very many 20 century mathematicians: Fatou, Weyl, Littlewood, Vladimir Arnold, Atiyah, Donald Knuth, and even Hardy (who boasted that he is a pure mathematician:-) ... too many of them to make a list of reasonable length.

I would say that before 1850, a great mathematician who DID NOT contribute to applied mathematics is a rarity.

Improve this answer
$\endgroup$
6
  • $\begingroup$ I don't really agree with this list. I asked for people who excelled in applied mathematics as well. Riemann did not make substantial contributions to applied mathematics, nor did Klein. Also Atiyah made contributions to theoretical physics, but not sure I would class him as an applied mathematician. Knuth is mainly a computer scientist and cannot be classed as having made substantial achievements in pure mathematics. Hardy did very little applied mathematics. $\endgroup$
    – Hollis Williams
    Commented Nov 9, 2019 at 21:02
  • $\begingroup$ Also some of the ancient examples such as Hero, that seems a stretch to say that they made fundamental contributions to pure mathematics, especially when many of their works have been lost. Again, Weyl did work on theoretical physics, but I class this as a separate subject and not as applied mathematics, $\endgroup$
    – Hollis Williams
    Commented Nov 9, 2019 at 21:05
  • 2
    $\begingroup$ @Tom "Knuth cannot be classed as having made substantial achievements in pure mathematics" --- I strongly disagree. $\endgroup$
    – Fedor Petrov
    Commented Nov 9, 2019 at 21:46
  • $\begingroup$ @Tom: before arguing, why you just don't look what all these named people did? Also define "applied mathematics" if you don't want to include mathematical physics. $\endgroup$
    – Alexandre Eremenko
    Commented Nov 10, 2019 at 1:30
  • $\begingroup$ @Tom: "Riemann did not make substantial contribution to applied mathematics..." Are you joking? Look at his Complete papers! And this does not include the standard textbook on PDE which he wrote with Weber. $\endgroup$
    – Alexandre Eremenko
    Commented Jan 10, 2020 at 15:53

Not the answer you're looking for? Browse other questions tagged .