[0db532a0]

Gödel’s Proof, by Nagel & Newman gives a good explanation for the semi-layman or undergrad coming across this for the first time.

Before picking up this book as an undergrad in pure maths, I still had romantic ideas about a separate platonic universe and the divine authority of mathematics to explain all human thought.

This book, along with studying the various geometries, each with a different choice of axioms not necessarily based in ‘reality’, destroyed the majority of that romance.

[cwzwarich]

Godel was himself a Platonist and didn't view incompleteness as a refutation of Platonism, rather as a restriction on the avenues of human access to mathematical truth.

[0db532a0]

I don't view it is a refutation either. I meant that the proof destroyed the greater feeling of romance I had towards mathematics.

[dasmithii]

Reading it now and enjoying it a lot. It's destroying one romance in favor of another!

[chongli]

Exactly! The beauty of life is in its flaws and limitations. Perfection is boring. Gödel opened the door to a multiverse of mathematics, all flawed in some way, yet not unworthy of study.

Mathematicians of the past sought perfection for the glory of God. Now we have the opportunity to give credit where it’s due: to our fellow human beings, many of whom devoted their lives to the craft of mathematics.

[xamuel]

Gödel's work actually echoes Christianity quite deeply. A key theme of Christianity is that humans are incapable of being good (much less of achieving perfection) on their own strength--no more than Hilbert could axiomatize all of mathematics with a consistent, computable set of axioms.

"Do not be overly righteous, and do not make yourself too wise." (Ecclesiastes 7:16)

"There is no distinction, for all have sinned and fall short of the glory of God, and are justified freely by His grace through the redemption that is in Christ Jesus." (Romans 3:22-23)

[0db532a0]

It would be interesting to see an analysis where the most fundamental results in mathematics are looked at under the light of their discoverers' ideological beliefs and psychologies.

I wonder whether Gödel would have pursued the Proof if he did not believe in an omnipotent god.

[caleb-allen]

To echo this, Godel was influenced by Cantor and Leibniz, both definitive Christian theists. Godel himself was also a theist.

Cantor believed that he had been chosen as a messenger by God to be the recipient of what was to become set theory.