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I think that this might be exploring the analogy's breaking point.

It can be quite easy to draw a clean line between theoreticians and implementors in other fields. Biologists and veterinarians, physicists and engineers, etc. But who was the last major computer science theoretician who wasn't also a skilled programmer or system architect (or both)? Alonzo Church?

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After looking through all the Turing Award winners, my answer is Stephen Cook - a CS mathematician who did nothing on engineering, discovered the concept of NP-completeness.