Richard Tieszen

Simply Gödel by Richard Tieszen covers Kurt Gödel’s life and work in an accessible manner. Considering the accomplishments of Mr. Gödel this is no mean feat. Around the Turn of the Twentieth Century, that is, around 1900 or so, the Mathematician David Hilbert established his famous 23 problems that he felt needed to be solved, or to prove that no solution would be forthcoming. Namely, his second problem was to “Prove that the Axioms of Arithmetic are Consistent.” Gödel managed to show that this was impossible using the tools of Arithmetic alone.

However, the book does not merely cover this element of Gödel’s life; it discusses in great detail his relationships with other thinkers of the time and how his opinions were formed. This leads to Gödel’s perfectionism and his holding back on publishing. As I mentioned in the opening sentence of this review, this book covers the life and work of Kurt Gödel; this also includes his personal relationships, especially the one with his wife. Gödel met Adele Porkert Nimbursky 10 years before they married, but Kurt’s parents had some issues with her. The book does not dance around from topic to topic but treats each event in a chronological manner.

The book contains thirteen chapters, with three of those chapters focusing on the Incompleteness Theorems. It also develops the idea of what a System of Logic is and the underlying principles to that idea. With a lucid style and careful prose, Tieszen shows the depth of his research into Gödel’s life. Furthermore, I enjoy the fact that Tieszen goes over the symbols of Formal Logic and explains their meanings. This is extremely helpful to me since I don’t know what a backward E is supposed to indicate, for example. I also like how the problem is laid out by Tieszen. He defines the issues of crafting something in formal logic and compares it to a Computer Programming Language. The syntax and grammar must be established beforehand and so on.

Speaking of computers, Turing is mentioned several times as well. The Turing machine is the classic mathematical construct that defines what any computer is capable of. Limitations on size and time are disregarded. Inconsistency is just another word for Contradiction in the case of logic. As the book covers Kurt Gödel’s life in detail, it also discusses his Completeness Theorem, the one he submitted for his Doctoral Thesis.

The book does its best to explain Gödel’s work in a format that is understandable, but I don’t know if many people would understand. If you have heard of Kurt Gödel, I imagine that you are somewhat familiar with Logical Systems, Zermelo-Fraenkel Set Theory, and other things. However, if you are someone that just wants a mindlessly enjoyable biography, this book might not be for you. I enjoyed the book quite a bit, especially since it does not stop at the Incompleteness Theorems, but covers the aftermath of them as well.

While I have read “On The Formally Undecidable Propositions of Principia Mathematica and Related Systems,” from what I recall of it, I only knew that it was important, I couldn’t make head nor tail of it. This book, Simply Gödel, helps to define what Gödel says and how he says it. That is the long and short of it.… (más)

"Tieszen’s Simply Gödel is a remarkable achievement—a handy guide with the impact of a philosophical tome. It’s all here: elegantly lucid discussions of Kurt Gödel’s epochal discoveries, a sympathetic account of the eccentric genius’s life, focused discussions of his encounters with his astonished peers, and a visionary peek into the future of mathematics, philosophy, and the on-rushing specter of robots with minds. A compact masterpiece, brimming with fresh revelations."
—Rudy Rucker, author of Infinity and the Mind… (más)