Kurt Gödel’s Brilliant Madness

As an anxious person who deals with hypochondria and germaphobia I could relate to some of this (I have in the past also kept journals of my temperature taken several times per day, for example). That he was able to achieve what he did in spite of all of these mental health obstacles is all the more amazing.

> “you simply cannot […] find the concentration necessary for research if you read twice a day [about] things […] which touch the basis of the civilization of your country as well as your personal existence”.

Kind of feels like the recent couple of years in the US. Only we don't just get news twice a day, we're constantly inundated with it. The same advice is given now, only it includes not just avoiding the news but also social media - in my experience it's pretty essential advice.

The thing about mathematics and logic is that logic went from being a branch of philosophy to a branch of mathematics and once logic was formalized it could then be described in terms of mechanical calculation. The proof of the halting problem took less than a page in my college text on Language, Automata and Machines and some version of the proof of Gödel's Incompleteness Theorem take little more space. But that's now that the properties of computation are well established and can be hand-waved away.

So a lot of what Kurt Gödel did was follow a fairly inevitable progression before anyone else. And it is one of those ironies the result, that the-provable and the truth are far apart, did not please such a brilliant idealist.

Edit: From wikipedia: "Mathematical logic emerged in the mid-19th century as a subfield of mathematics, reflecting the confluence of two traditions: formal philosophical logic and mathematics (Ferreirós 2001, p. 443). "Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the last [nineteenth] century with the aid of an artificial notation and a rigorously deductive method."[3] Before this emergence, logic was studied with rhetoric, with calculationes,[4] through the syllogism, and with philosophy. "

https://en.wikipedia.org/wiki/Mathematical_logic#History

Great read.

> Kurt Gödel, only a year beyond his PhD, announced a result which would forever change the foundations of mathematics. He formalized the liar paradox, "This statement is false" to prove roughly that for any effectively axiomatized consistent extension T of number theory (Peano arithmetic) there is a sentence σ which asserts its own unprovability in T. John von Neumann, who was in the audience immediately understood the importance of Gödel's incompleteness theorem. [...]

> In the next few weeks von Neumann realized that by arithmetizing the proof of Gödel's first theorem, one could prove an even better one, that no such formal system T could prove its own consistency. A few weeks later he brought his proof to Gödel, who thanked him and informed him politely that he had already submitted the second incompleteness theorem for publication.

Gödel did have some grounds for paranoia.

Wittgenstein [1937-1944] had shown that Gödel failed to prove

incompleteness of the foundations of mathematics. Gödel was

aware of this failure but tried to bluff past it claiming that

his incompleteness result was not for the foundations of mathematics.

Contrary to [Gödel 1931], he claimed decades later

that his result was for a limited first-order theory of the

natural numbers [Wang 1987].

However, the failure may have secretly weighed on his mind.

There is more information here:

"Gödel failed to prove inferential undecidablity or incompleteness in foundations"

https://professorhewitt.blogspot.com/2021/03/godel-failed-to...

Adele Thusnelda Porkert: An absolute hero in the world of math and science.

I remember reading some short bios that (with a wink and nod) mentioned Godel had a relationship with a cabaret dancer. I remember absolutely detesting it.

Making a life with a genius, obsessive compulsive individual doesn’t seem very easy to say the least.

Nevermind the importance of the individual to society, and the implied responsibility that came with it.

Crazy to see that he was perpetually afraid of being poisoned and starved himself to death.