Ideas from 'works' by Leopold Kronecker [1885], by Theme Structure

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6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date.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
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.