This is the main video
and these are the extras
and this is the theological aspect of the theorem
This theorem is a station in the history of mathematics and humankind in general.
The things started with the ancient greek philosopher and especially with Aristotle: The Uber Empiricist (Empiricism is a theory that states that knowledge comes only or primarily from sensory experience, wiki). This is that everything can be brought down to our experiences thus we can know (and prove off course) everything. Bare with me and the vagueness for a moment, it won’t be long.
Aristotle is considered the forefather of science in general, he was methodical and tried to break everything down to causality relationship.
So unanimous the scientific societies over the next centuries accepted this philosophy. This Promethean task to know and prove anything was carried out until 1931 and i don’t thing it can be better phrased than in the words of David Hilbert’s toombstone
- Wir müssen wissen.
- Wir werden wissen.
- We must know.
- We will know.
- The words were given in response to the Latin maxim: “Ignoramus et ignorabimus” or “We do not know, we shall not know”
Strong phrasing i know 🙂
So Godel came along, what he proved was that:
There will always be conjectures about numbers, that might actually be true but maybe within the axiomatic system of mathematics there isn’t a proof of that.
And since Mathematics is the base of any science this is applied to any science 🙂
Godel was what we call a bad motherfucker maybe the worst of them all.
Do check the videos from the numberphile, amazing work by Brady Haran.
The man speaking is Marcus du SautoyProfessor for the Public Understanding of Science and Mathematics at the University of Oxford.