Surprisingly to me, Garrett Birkhoff also did some very applied mathematics (Wikipedia says "During and after World War II, Birkhoff's interests gravitated towards what he called "engineering" mathematics."). I have his book Hydrodynamics in front on me, and it has plots of experimentally-determined results, photos of objects plunging through water, but also sections on group theory and a Lie algebras. Of course, he also coauthored Algebra with Mac Lane, and is well-known for lattice-theoretic work. He also worked on computational mathematics and numerical linear algebra.