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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 Ref
'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]
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |