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I was initially skeptical about this book, because in the early chapters I felt like Seife sometimes presented questionable anecdotes as fact. The story presented here is about much more than math: there's history, philosophy, religion, and modern physics too. Plus, for the chapters that I knew the most about, I lamented the lack of footnotes, which isn't really a fair criticism of a popular science work. The book quickly won me over, though, and I often found myself reluctant to put it down. Much of the material was already familiar to me, but Seife brought it all together into a satisfying overview of the evolution of western thought. I would recommend this even to people who don't particularly like math; it's not very technical and is full of information that would be interesting to anyone.
I'm glad I read the book, but I wish it had been shorter, more concise, and stopped at chapter 6. The first 5 or 6 chapters are pretty good and I enjoyed the discussion of zero and infinity and how they developed and were incorporated in Eastern and Western mathematics and thought. Like other reviewers, I do think the author over-states his case a bit, which weakens his argument. The language is a bit hyperbolic and the last few chapters seem disconnected and tangential. The author is at his best when he is succinct and clear in his premises and propositions. Personally, I think the book could have been an article or
The infinite density of the black hole is a division by zero. The subject of the book could be described as "the metaphysics, physics, and mathematics of 'zero and the void, infinity and the infinite'." The mathematical concepts of zero and infinity are often conflated with analogous metaphysical and physical concepts, and this makes the text confused, unclear, and occasionally annoying.No topic is given a lot of attention. The big bang creation from the void is a division by zero. Topics include the use of zero as a placeholder in mathematical notation, Zeno's Achilles-paradox of motion, infinite addition, infinite division and the infinitely small, zero as a cardinal number and as an ordinal number, the void as a metaphysical and physical concept, God and the infinite, perspectival drawing and the vanishing point of "an infinite zero", vacuum and atmospheric pressure, infinitesimals, tangents, volume and the calculus, irrational numbers, imaginary numbers and complex numbers, projective geometry, Cantor's infinities, absolute zero temperature, zero-point energy, black holes, worm holes, strings, and the big bang. "Zero is behind all the big puzzles in physics. The infinite energy of the vacuum is a division by zero. Yet dividing by zero destroys the fabric of mathematics and the framework of logic - and threatens to undermine the very basis of science." (214)
A totally fascinating book. Debunks Aristotle and the West's rejection of the concept of the void and infinity. I already have someone who wants to borrow it.
Zero: The Biography of a Dangerous Idea I love the sciences and math has always amazed me. I can only marvel at what would be possible these days if Newton and his peers had been around these days to add to string theory, relativity etc. However, the first half does a great job of showing how something we take for granted (zero), had to be introduced into the world a number of times before it became standard in the ways of thinking.
At last a book has explained in a understandable way the concepts of calculus, relativity, point theory, string theory and quantum mechanics. I had planned on giving this to my daughters 8th grade math teacher who loves math, but again, only the first part is relative to math people at the basic level. I did well in calculus and physics, but understanding concepts and doing well in class aren't always the same.
While the illustrations are lacking in number and detail, those that are there do a good job of explaining the concepts. I liked the hyperbole and the comments that made this read entertaining and enlightening. If you don't have a background in the sciences, you may want to pass as the second half of the book gets into science that isn't easy.
Those that look at calculus and marvel that someone could actually come up with the concept, will realize what imagination the great thinkers had and our technological leaps are made possible only because people saw things in a different manner. Given the number of so called skeptics these days who hogwash creative thinking and new science, it is easy to imagine the pressure from the church and other outside influences that had vested interest in keeping these discoveries quiet.
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