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]