Gödel's Incompleteness Theorem

In the summer of 1930, the twenty-four-year-old mathematician Kurt Gödel proved a strange theorem: mathematics is open-ended. There can never be a final, best system of mathematics. Every axiom-system for mathematics will eventually run into certain simple problems that it cannot solve at all. This is Gödel's Incompleteness Theorem.
The implications of this epochal discovery are devastating. The thinkers of the Industrial Revolution liked to regard the universe as a vast preprogrammed machine. It was optimistically predicted that soon scientists would know all the rules, all the programs. But if Godel's Theorem tells us anything, it is this: Man will never know the final secret of the universe.
Of course, anyone can say that science does not have all the answers.
What makes Gödel's achievement so remarkable is that he could rigorously prove this, stating his proof in the utterly precise language of symbolic iogic. To come up with a mathematical proof for the incompleteness of mathematics is a little like managing to stand on one's own shoulders. How did Godel come to think of such a proof? What kind of person was he?