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I have always read about the geniuses of Alan Turing and Kurt Gödel . Many websites mention their works in logic as revolutionary. I want to understand their works, but I don't exactly know the way through which I should go in order to understand their work. To be precise, I want to know the prerequisites required to learn their theories. I hope that members here can suggest the correct way.

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4 Answers 4

For a (freely available) route into Gödel, you could always try my notes, Gödel Without (too many) Tears.

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Yay! Notes by Peter Smith! I'll download and read too. Herr Peter is damn pro. You should also cite your Introduction to Gödel Theorems, Herr Peter. –  Vÿska Jun 10 '13 at 2:56

The website www.logicmatters.net has a student guide to teaching yourself logic.

There is also a free textbook called "A Problem Course in Mathematical Logic" by Stefan Bilaniuk if you can find it. The link I had to it seems to be broken.

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I suggest starting with Godel, Escher, Bach: an Eternal Golden Braid by Douglas Hofstadter, if you haven't read that book yet.

I think it's a good first option because there's a nice curve to the book as ideas become progressively more intricate. Even if you can't get everything towards the end or can't manage to read it all the way through, I guarantee that you will get a lot out of it.

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This may not be the most direct route to understanding the mathematics behind their works. GEB is not primarily about the math of Turing and Godel, and is more about the author's views concerning consciousness and such. –  user64480 Jun 9 '13 at 18:15
    
@user64480: While the author of GEB does go into thoughts on mind and whatnot, the book is primarily a spin on Goedel's proof, and how such thinking has influenced information systems. So, yeah, it is about the math of Goedel (with some Turing sprinkled in). –  Ron Gordon Jul 12 '13 at 3:08

For a very gentle history and introduction to Leibniz, Gödel, and Turing, I recommend Martin Davis' The Universal Computer: The Road from Leibniz to Turing. As I recall, it was accessible to a motivated high school student (U.S.) but managed to convey the basic logic, computability and mathematical ideas. It's a short, easy, fun read even if its target audience is below your level. By the way, Martin Davis is more than qualified to present this material.

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