Ideas of Leopold Kronecker, by Theme

[German, 1823 - 1891, Professor of Mathematics at Humbolt University, Berlin. Taught Cantor.]

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6. Mathematics / A. Nature of Mathematics / 1. Mathematics

12427	All of mathematics is properties of the whole numbers
	Full Idea: All the results of significant mathematical research must ultimately be expressible in the simple forms of properties of whole numbers.
	From: Leopold Kronecker (works [1885], Vol 3/274), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 09.5
	A reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date. Natural numbers have a special status, but not sufficient to support this claim.

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers

10091	God made the integers, all the rest is the work of man
	Full Idea: God made the integers, all the rest is the work of man.
	From: Leopold Kronecker (works [1885]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Intro
	A reaction: This famous remark was first quoted in Kronecker's obituary. A response to Dedekind, it seems. See Idea 10090. Did he really mean that negative numbers were the work of God? We took a long time to spot them.