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Answer by user6976 for Mathematicians with both “very abstract” and “very...

Pontryagin is considered one of the best both pure and applied mathematicians in the last сentury.

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Answer by alesia for Mathematicians with both “very abstract” and “very...

Jean Leray started in fluid mechanics. His work might not be applied enough for your question, but when he was made prisoner during WWII he concealed his knowledge about fluid mechanics thinking he...

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Answer by JRN for Mathematicians with both “very abstract” and “very applied”...

John von Neumann was the first person to come to my mind.He published over 150 papers in his life: about 60 in pure mathematics, 60 in applied mathematics, 20 in physics, and the remainder on special...

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Answer by Francesco Polizzi for Mathematicians with both “very abstract” and...

G. H. Hardy is well-known for his work in number theory, but also for the so called Hardy–Weinberg principle in genomics.

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Answer by Sam Hopkins for Mathematicians with both “very abstract” and “very...

David Mumford did foundational work in algebraic geometry, but then later in his career did a lot of work in the applied areas of vision (especially computer vision) and pattern theory.

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Answer by user131781 for Mathematicians with both “very abstract” and “very...

The first person who comes to mind is Hilbert, although his work on quantum mechanics might not qualify as „very applied“. But Wiener and von Neumann certainly fit the bill. Many of the prominent pure...

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Answer by bof for Mathematicians with both “very abstract” and “very applied”...

Abraham Robinson made contributions to mathematical logic (model theory, nonstandard analysis) and aerodynamics (airplane wing design).In December of 1942 Robinson wrote to his supervisors in Jerusalem...

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Answer by XL _At_Here_There for Mathematicians with both “very abstract” and...

Alan Turing is one mathematicians with both “very abstract” and “very applied” achievements: https://en.wikipedia.org/wiki/Alan_Turing

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Mathematicians with both “very abstract” and “very applied” achievements

Gödel had a cosmological model. Hamel, primarily a mechanician, gave any vector space a basis. Plücker, best known for line geometry, spent years on magnetism. What other mathematicians had so distant...

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