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).