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Triangle of Thought Hardcover – January 1, 2001

ISBN-13: 978-0821826140 ISBN-10: 082182614X

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Product Details

  • Hardcover: 179 pages
  • Publisher: Amer Mathematical Society (January 1, 2001)
  • Language: English
  • ISBN-10: 082182614X
  • ISBN-13: 978-0821826140
  • Product Dimensions: 6 x 9 inches
  • Shipping Weight: 12.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #1,179,880 in Books (See Top 100 in Books)

Editorial Reviews

About the Author

Alain Connes is one of the founders of non-commutative geometry. He holds the Chair of Analysis and Geometry at the Collège de France. He was awarded the Fields Medal in 1982. In 2001, he was awarded the Crafoord Prize by The Royal Swedish Academy of Sciences.

André Lichnerowicz, mathematician, noted geometer, theoretical physicist, and specialist in general relativity, was a professor at the Collège de France.

Marcel Paul Schützenberger made brilliant contributions to combinatorics and graph theory. He was simultaneously a medical doctor, a biologist, a psychiatrist, a linguist, and an algebraist.

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Most Helpful Customer Reviews

10 of 11 people found the following review helpful By Jaume Puigbo Vila on February 10, 2008
Format: Hardcover Verified Purchase
The goal of this book is "to enable a broad but enlightened audience to bridge the growing gap between the subtleties of these advances (meaning quantum mechanics, relativity and Gödel's theorem), usually accessible only to specialists, and the often unbelievably deformed images of them presented by popularized accounts".

I must disagree. Although the reader will attend an interesting dialogue between some of the top minds of the XXth century and Alain Connes is one of the greatest living mathematicians, it is difficult to follow a great part of this conversation if you are not familiar with advanced mathematics and physics. The publisher could have made the reading easier by including a lot of sidebars as Scientific American does. On the other hand I have read quite a number of books by very good scientists on the topics mentioned (therefore they could not be deformed images) and these books are much more accessible than "Triangle of Thoughts". If you have read the other Connes co-authored book, "Conversations on Mind, Matter and Mathematics", the level of accessibility of this one is similar.

That said, the book is worth reading and there are sections which are quite readable like that on Cosmology, on game theory or even on Gödel's theorem. Alain Connes introduces a distinction between primordial mathematics and axiomatic mathematics which he considers an (limited) instrument of comprehension at our disposal. Gödel affirms that any sufficiently rich axiomatic system contains truths that are not provable and it has the curious consequence that you can add a countertruth to an axiomatic system which will be free of contradiction if the former system was non contradictory.

That the book needs some editing is clear.
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By Kevin Roberge on December 30, 2013
Format: Hardcover
This sort of casual conversation that wanders across these three passions of mine: physics, philosophy and mathematics, is rare. As you read these great minds jump all over deep topics and the history of their development. The conversation is inspiring for its depth and breadth and I recommend reading this along with your cup of coffee. To appreciate all the references, at least in passing, it would be helpful to have some graduate work in physics or mathematics coupled with a broad interests. The layperson is likely to find many references that are unfamiliar to them. However you can gloss over those passages or pause and do a little background research in the meantime before returning to the passage. This is just another example of why Alain Connes is one of my new mathematical heroes.
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