Thursday, April 14, 2016

[jkgfdxox] Proportion of provable

Given Godel's Incompleteness Theorem, what percentage of true mathematical statements are provable?  Of the unprovable, what proportion are provably unprovable?

These questions can be made precise for example by placing limits on the length of the statement expressed in some specified mathematical notation, e.g., first-order logic.

Is it even possible to know the answers to these questions?

We wonder if the answer might be similar to that of real numbers: most -- almost all -- real numbers are uncomputable; perhaps most true statements are unprovable.

1 comment :

Anonymous said...

See Gregory Chaitin's work on this, "Meta-Math!".