Kurt Gödel ranks with the likes of Karl Friedrich Gauss and George Cantor as among the world’s greatest mathematicians. And now, he has a full biography, that sets him within the late Austro-Hungarian Monarchy, as a Sudenten German who later moved to Austria, and as a man plagued ever more by various forms of mental illness as he aged.

One of the funniest quotes is one that stands in stark contrast to the famous Douglas Hofstadter book, “Gödel, Escher, Bach.” That is: “Bach and Wagner make me nervous.”

Not so funny is that, while Hofstadter had plenty of biographical elements about Bach, he had almost none about Escher and none on Gödel. This book remedies that in spaces.

Gödel is best known for his Incompleteness Theorem, but on the math and philosophy side, had more than that, and “informed” discussions of relativity and more in physics.

Gödel had other oddities besides comment about Bach and Wagner. He was a diehard mathematical Platonist, but others exist today. That said, he seems to have been something like a diehard Platonist period.

Spoiler

He rejected methodological naturalism, or as Budiansky calls is, scientific materialism. Philosophically, he had an ardent love affair with Leibniz, monads and all. And, he was also a Leibnizian conspiracy theorist, claiming that up to his own time, certain concepts and findings of Leibniz were still being repressed, generally by an unidentified “them.”

Related to that? He claimed “religions were bad, but religion good,” as in, questioning individual religions but affirming the value of some deeper religion. Indeed, in 1970, he claimed to have an ontological proof for the existence of God!

His mental health? Long before his suicide by starvation, he was a hypochondriac and probably had OCD.

That said, the paranoia dramatically ramped up in the last half a dozen years of his life, leaving him an incredibly tragic person. His paranoia eventually involved claims about Nazis resurgent in Austria and his own brother, before he eventually starved himself to death, including while in hospital the last couple of weeks of his life.

That’s enough to give a good taste of this book, but without getting too deep into spoiler alert territory. Even clicking open the spoiler alert won't give all away.

That said, there are a couple of errata and issues in the book.

One minor one is that Budiansky claims Wiener schnitzel is really nothing more than cotoletta alla Milanese imported from Italy in the 1850s, allegedly by Radetsky. In 2007, a linguist totally debunked this.

The larger issue is one of omission. Many ideas that many people attribute to Gödel’s Incompleteness Theorem actually come from Tarski’s Undefinability Theorem. Tarski’s theorem extends beyond mathematics into semantics in general. That said, Budiansky isn’t alone. Realistically, Hofstadter should have written “Tarski, Escher, Bach.” That said, in turn, Gödel did apparently discover this first, but never published, so the technical credit goes to Tarski. It should be noted that Hofstadter references Turing MUCH more than Tarski, and Budiansky does just as much. On the other hand, Budiansky does critique GEB, noting that Hofstadter “far outran Gödel’s proof,” while at the same time it “contained not a word about the man himself.” Budiansky gets this right, but it would have been a good place here to insert at least a small note about Tarski.

Budiansky, besides remedying that, looks at Gödel’s actual reputation today in the worlds of science and philosophy. He says that in math, most modern mathematicians have seen little reason to venture past his barrier and that philosophy (as seemingly, Gödel himself) have found his theorem limiting.