CONCLUSION
The world of mathematics fell apart when Gödel’s Theorems came to the forefront of the field. For most of the history of mathematics, it was assumed that any true statement could be proven as true. Gödel remains history’s first to realize the flaw in such an assumption.
More recently, Gödel’s Theorem has begun to be applied to fields outside of mathematics. This is done in an effort to explore if there exist statements in Physics, Philosophy, Computer Science, and Computer Science which are true, but have no proof, or that an entire system on which the field rests is broken (for a philosophy oriented reading see source 10). Statements that may claim this status seem increasingly more common than in years past.
The year after the publishing of the Paris-Harrington Theorem, 1978, Gödel passed away in Princeton, New Jersey. His Incompleteness Theorem remains his finest accomplishment and he fortunately lived to see it strengthened. Gödel proved that the system in which all statements can be proven is an inconsistent system. Thus for mathematics to be consistent, for it to have any purpose, it must be incomplete.
To read more about the life of Kurt Gödel, see source 7.
