Full Idea
If induction was the source of our mathematical knowledge, we should proceed differently. In fact, a certain number of instances make us think of two abstractly, and we then see the general principle, and further instances become unnecessary.
Gist of Idea
Maths is not known by induction, because further instances are not needed to support it
Source
Bertrand Russell (Problems of Philosophy [1912], Ch. 7)
Book Reference
Russell,Bertrand: 'The Problems of Philosophy' [OUP 1995], p.43
A Reaction
In practice, of course, we stop checking whether the sun has come up yet again this morning. Russell's point is better expressed as: if contradictory evidence were observed, we would believe the arithmetic and doubt the experience.