Thursday, January 25, 2024

Journey to the Edge of Reason

"That he is an important man is shown again and again, but he is a little crazy."
-Oskar Morganstern

Kurt Gödel (1906-1978) is famous as the mathematician who proved that mathematics doesn't quite work. The result is known as the Incompleteness Theorem, and before Gödel's proof, mathematicians assumed anything you could say with elementary mathematics (from 2+2=4, e.g., and on up) could be proven either true or false. It might be hard, it might be impossible for me or you, but it could be done. In 1930 Gödel demonstrated it can't. 

You can create mathematical statements, using math no more complicated than addition and equality, whose truth is unprovable.

Gödel was born in Brno, now in the Czech Republic, but then the largely German-speaking town of Brünn in Austria-Hungary. His father owned a textile factory and was reasonably well off. After the breakup of Austria-Hungary at the end of World War I, financially the Gödels were better off with their money in Czechoslovakia, but when it came time for young Kurt to go to college, in 1924, he went to Vienna, the old imperial capital, which still had the best universities. (It was also becoming uncomfortable in Czechoslovakia for German speakers). 

Budiansky is clearly in love with Vienna. (Understandable.) He spends quite a lot of time on the atmosphere in Vienna, citing figures whose connection to Gödel is pretty non-existent--Joseph Roth, Robert Musil--but whose interest to readers is large. Vienna was Gödel's home for roughly fifteen years, and a large portion of his important work was done there, so it's appropriate enough.

But Vienna was becoming problematic. Gödel wasn't Jewish, but his friends were; as things got worse, the sort of mathematics that Gödel did got labeled 'Jewish mathematics' (What's that?) and after Anschluss, the university wasn't going to allow that sort of math any more. Gödel did a semester as a fellow at Princeton's Institute for Advanced Study when it opened in 1933--Einstein was one of their first hires--and though Gödel didn't much like Princeton, his friends there kept suggesting he come back.

He was subject to paranoid fantasies (though one of his mathematical colleagues was assassinated by a right-wing student, so maybe not entirely paranoid).  His girlfriend Adele was married and under Catholic Austrian law she couldn't get divorced, so the two of them couldn't leave the country as married. Also he was inclined to be apolitical, and was politically naive. 

But after Anschluss in 1938, German law applied in Austria, allowing divorce and remarriage. Kurt and Adele married. Gödel was still sluggish about the need to leave, but after much prodding he did, ultimately taking a full-time position at the Institute for Advanced Study.

And became close friends with Einstein

Through the forties, he continued to do mathematics, working with Oskar Morganstern and John von Neumann. The later years he taught (though he was a terribly shy teacher) and continued to suffer periods of paranoia.

And why was I interested in a biography of Kurt Gödel you might ask?

I read Hofstadter's Gödel, Escher, Bach around when it came out, devoured it more like. It was probably the first serious non-fiction book I read on my own. There were various essays in 2019 for the fortieth anniversary of the book, and I thought about rereading it then, but didn't, but when I saw about the new biography of Kurt Gödel, I was primed to be interested. The biography was well done. The proof of the Incompleteness Theorem is relatively (...?) easy to understand, but Budiansky saves the explanation of that for an appendix, where he does a pretty good job, and otherwise you can read the biography without math.

And am I about to reread Hofstadter? Well, if you look closely you can see a purple bookmark there...

Austria. Could be the Czech Republic, I suppose, but no, not really. Vienna is where it happens. Last year's Austria book for the challenge was another biography of an intellectual who left in the 30s and came to the U.S., Victor Gruen.


  1. You certainly find some very interesting books! I've heard of Kurt Godel in connection with Einstein, but never about his proof. and I'm thinking I'd probably really like this book. :D

    1. It's a pretty fascinating time period--the U.S. gained so much from all these people that were driven out by the Nazis.

  2. I'm such a dunce when it comes to mathematics but the story sounds interesting. It's inspiring to know that everything cannot be explained by an equation. I have Gödel, Escher & Bach but I've never read it. Should I? Or will my head explode, lol?! Great review!

    1. I'm a hundred pages into Gödel, Escher & Back and I'm finding it pretty good still. It's not easy (but easier than St. Augustine!) and he lightens it by having the regular dialogs between Achilles and the Tortoise that are funny but on-point.

      I used to be math, but not any more!

  3. I kinda wondered if that book might have been the impetus for your recent reading! (I've not read it myself, but have seen it on so many people's bookshelves, likely all smarter people than me. heheh) Funny how our interests persist in life even when some of the inclination or talent or whatever exists more in the past than the's nice to still read about these things.

    1. We'll see! If I still have it in me to read the Hofstadter or not...