Matt's Reviews > Gödel's Proof

Gödel's Proof by Ernest Nagel
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really liked it

I don't read much math these days, so when I do read it, it's a little like climbing a steep wall following a winter of sitting in front of a computer. You discover a lot of soreness in muscles you scarcely remember you ever had in the first place.

The long and the short of it is that once upon a time, I sorta understood Godel's incompleteness theorem, and after this modest reading, I sorta understand it again. Success!

More importantly for me, it was fun to try to connect neurons in my poor fuzzy brain, and for a math aficionado, entering a world where it's assumed that conclusions are merely the logical consequences of initial assumptions and nothing more is a bit like diving into mom's meatloaf -- familiar and comforting.

Godel's theorem itself is supposedly the big revelation that upset the 19th century mathematics apple cart. As the authors explain, his proof showed that "no final systematization of many important areas of mathematics is attainable," a potentially unsettling proposition. But it may be a somewhat comforting assertion. Who would want to have it all figured out anyway? And gravity still works, and the sun still comes up every day, so I think we'll all get by.

As for its readability, math forever has a big problem in that it's *designed* to simplify reason, so when it itself becomes very complex, it can be difficult to impart. By the same reasoning, if you try to simplify a very complex proof, leaving out a lot of the messy details while trying to explain the rest in plain English, you're necessarily going to miss a lot and there will be important details that are missing.

In this book, the concepts are simplified and the details are left out. On the plus side, it's pretty readable for a math book, and the main conclusions are pretty easy to follow. On the minus side, there will necessarily be points to question. They do have a lot of footnotes, which offers some middle ground.
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Reading Progress

Started Reading
May 25, 2009 – Shelved
May 25, 2009 – Finished Reading

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