Ideas from 'works' by Leopold Kronecker [1885], by Theme Structure
green numbers give full details 
back to texts

unexpand these ideas
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 outofdate. 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.
