Wednesday, February 18, 2009

Quote of the day ...

The main difference between Mac Lane and me, as I see it, is a matter of temperament. He is by temperament a reductionist, and I am not. He believes that the reduction of mathematical concepts to their abstract logical components is the main road of progress in understanding. I prefer to deepen my understanding of abstract components by building them up into concrete structures. I do not deny the power and the beauty of reductionist science, as exemplified in the axioms and theorems of abstract algebra or algebraic topology. But I assert the equal power and beauty of constructive science, as exemplified in Gödel's construction of an undecidable proposition or in Gentzen's construction of an enlarged domain for mathematical logic.

Freeman Dyson, reply in the NYRB to a letter from Saunders Mac Lane: 'A Matter of Temperament'.

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