Single Idea 12461

[catalogued under 6. Mathematics / A. Nature of Mathematics / 1. Mathematics]

Full Idea

The thesis that every mathematical problem is solvable - we are all convinced that it really is so.

Gist of Idea

We believe all mathematical problems are solvable

Source

David Hilbert (On the Infinite [1925], p.200)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.200


A Reaction

This will include, for example, Goldbach's Conjecture (every even is the sum of two primes), which is utterly simple but with no proof anywhere in sight.

Related Ideas

Idea 17892 For clear questions posed by reason, reason can also find clear answers [Gödel]

Idea 9812 In mathematics, if a problem can be formulated, it will eventually be solved [Badiou]