Answer by Per Alexandersson for Mathematicians with both “very abstract” and...
What about James Simons, of the Chern–Simons form, and working in topology and with manifolds.He is perhaps more known for his more applied works, making tons of money from the stock market and funding...
View ArticleAnswer by Nik Weaver for Mathematicians with both “very abstract” and “very...
Israel Gelfand ... was a prominent Soviet mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis ...The...
View ArticleAnswer by Mark L. Stone for Mathematicians with both “very abstract” and...
James MunkresVery abstract: Obstructions to the smoothing of piecewise-differentiable homeomorphisms (doi:10.1090/S0002-9904-1959-10345-1)Very applied: Munkres assignment (a.k.a. Hungarian) algorithm...
View ArticleAnswer by Piyush Grover for Mathematicians with both “very abstract” and...
Jerrold Marsden made major contribution to symplectic geometry but also was a key contributor to problems in celestial mechanics and numerical methods.
View ArticleAnswer by Thomas Sauvaget for Mathematicians with both “very abstract” and...
Vladimir Arnold's work ranges from the very abstract (cohomology ring of the colored braid group, symplectic topology, Maslov Index, real algebraic geometry, invariants of plane curves,...) to the...
View ArticleAnswer by Francois Ziegler for Mathematicians with both “very abstract” and...
I have a friend to whom De Rham was famous for completely different reasons — as author of a “corner-cutting algorithm” used in Computer Aided Geometric Design (of car bodies).
View ArticleAnswer by Cliff AB for Mathematicians with both “very abstract” and “very...
Ronald Fisher is considered an establishing figure in the field of modern statistics. A story I've heard goes that his work in statistics was mentioned to a biologist, who responded "He worked in...
View ArticleAnswer by Michael Hardy for Mathematicians with both “very abstract” and...
Some things Kolmogorov did were fairly "pure", but he is one of the eponyms of the Kolmogorov–Smirnov test.
View ArticleAnswer by JCK for Mathematicians with both “very abstract” and “very applied”...
How about Arne Beurling? Complex and harmonic analysis on the "very abstract" side, breaking nazi codes on the "very applied". See https://en.wikipedia.org/wiki/Arne_Beurling and...
View ArticleAnswer by xuq01 for Mathematicians with both “very abstract” and “very...
Thierry Coquand works mainly in formal topology, constructive algebra, and foundations, but he was one of the early authors (and namesake!) of the Coq proof assistant. In fact, most people probably...
View ArticleAnswer by einpoklum for Mathematicians with both “very abstract” and “very...
Pafnuty Liebovich Chebyshev contributed to probability and number theory, among other matters - but also worked on steam engine "linkage" design. I also remember being told that he had developed a...
View ArticleAnswer by polfosol for Mathematicians with both “very abstract” and “very...
I am surprised that no one has mentioned Terence Tao yet. Speaking of his very abstract achievements in math to the audience of this site is like carrying coals to Newcastle. But he has some cool...
View ArticleAnswer by fosco for Mathematicians with both “very abstract” and “very...
Steve Vickers works on topos theory and pointfree topology, but alsoHe was responsible for the adaptation of the 4K ZX80 ROM into the 8K ROM used in the ZX81 and also wrote the ZX81 manual. He then...
View ArticleAnswer by Francois Ziegler for Mathematicians with both “very abstract” and...
Several known for “pure” work have rather applied contributions to geometrical optics:Carathéodory (1937) Geometrische OptikChaundy (1919) The aberrations of a symmetrical optical systemWhittaker...
View ArticleAnswer by Martin Argerami for Mathematicians with both “very abstract” and...
James Glimm did his Ph.D. in C $^*$-algebras, where he made long-lasting contributions. He switched fields soon after, and (as Wikipedia says) he has been noted for contributions to C*-algebras,...
View ArticleAnswer by Geoff Robinson for Mathematicians with both “very abstract” and...
Perhaps Helmut Wielandt might be mentioned. As well as his work on finite group theory, he has a famous theorem on doubly stochastic matrices, and another elegant proof (albeit of a previously known...
View ArticleAnswer by user8253417 for Mathematicians with both “very abstract” and “very...
Frank Garside (he doesn't have a wikipedia page but he has this https://en.wikipedia.org/wiki/Garside_element) was responsible for solving the conjugacy problem in the braid group, and then became the...
View ArticleAnswer by user150544 for Mathematicians with both “very abstract” and “very...
George Dantzig is known for his work in Linear Programming, including coining the Simplex algorithm. But his PhD was accidentally in Statistics.
View ArticleAnswer by bof for Mathematicians with both “very abstract” and “very applied”...
Stanisław Ulam is best known for his work on the Manhattan Project, but his contributions to pure mathematics include pioneering work on measurable cardinals and formulating the reconstruction...
View ArticleAnswer by Gerry Myerson for Mathematicians with both “very abstract” and...
Littlewood is best-known for his pure math research, but during the first World War he worked on ballistics. I suspect there were others who put aside pure math for more applied topics during the wars.
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