### 1.2.5.6 Godels Theorem

A brilliant young Austrian mathematician then dealt a blow to Hilbert's plan.

If we take as an example the statement

'This mathematical assertion cannot be proved'

If it is not true then one has a contradiction and mathematics is not consistent.
If it is true then mathematics is not complete.
Thus mathematics cannot be both consistent and complete at the same time

It is said that undecideable propositions exist