Hilbert and Decartes

I had lunch today with a Sun colleague, Larry Freeman, who drew an interesting parallel between Hilbert and Descartes.

Neither Descartes, despite his influence on philosophy, was the best of philosophers, nor Hilbert, similarly influential in mathematics, was the greatest among mathematician. They were both creative artists in their practice but neither was outstanding in the practice of their art. (For example, I would give Brouwer and von Neumann higher marks as mathematicians, even if the latter was Hilbert's student at one point in his varying career. However, Hilbert's early work on axiomatization, say The Foundations of Geometry {Grundlagen der Geometrie}, stands apart in its creative simplicity and importance. By the way, Constance Reid's Hilbert is one of the best autobiographies I've ever read of a scientist or a mathematician.)

What made both special was the questions they asked and the puzzles they brought to philosophy and mathematics.

Depending on what you think about "puzzles" whether true or imaginary, you may value their work differently.

, ., , .

Comments:

Sometimes questions are more important than answers ...

Posted by sA on May 16, 2005 at 10:45 AM PDT #

I agree. Nevertheless, in the mechanics of their art, they were not as skilled as others who competed and bettered them in many ways. Both had interesting life stories. Hilbert did not want to become a mathematician just prior to entering his university career, and I agree, it is a bit unfair to say that he didn't make any significant contributions, beyond and above asking questions. He did. For example, I have noted his foundations of geometry.

Posted by M. Mortazavi on May 16, 2005 at 03:37 PM PDT #

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