Visions of Infinity

Visions of Infinity

The Great Mathematical Problems

Book - 2013
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A celebrated mathematician presents a fascinating history of mathematics as told through 14 of its greatest problems., and explains why mathematical problems exist, what drives mathematicians to solve them and why their efforts matter in the context of science as a whole.
Publisher: New York : Basic Books, c2013
ISBN: 9780465022403
0465022405
Branch Call Number: 510 STE NVD
Characteristics: x, 340 p. : ill. ; 25 cm
Alternative Title: Great mathematical problems

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BarryGla Aug 08, 2014

has chapters on many mathematical classical and current (CLAY) problems. Author connects these chapters together and build a coherent picture by going back and forth between the chapters. Focus is not on infinity but on various conjectures that have been and have not been resolved. Even a good chapter on P vs NP and something from physics, the Quantum Mass Gap.

johnf108 Jun 24, 2014

As with all his books, he presents a very clear description of the topics he deals with. Here for the most part the Millennium problems the Clay group has set-up prizes for.
A very good read.

nftaussig Oct 03, 2013

Ian Stewart, an emeritus professor of mathematics at the University of Warwick, makes a valiant attempt to explain fourteen of the most important mathematical problems to a lay audience. For the most part, he succeeds. However, some of the problems are sufficiently abstract (particularly, the Hodge Conjecture) that even a gifted expositor such as Stewart cannot state them in terms a lay audience can understand. However, to his credit, he does try. Some of the problems such as the Goldbach conjecture that every even number larger than 2 can be expressed as the sum of two primes are readily understood, if difficult to solve. Others, such as the Hodge Conjecture, can only be understood by a specialist. In explaining these problems, Stewart gives the reader a sense of what it is that mathematicians do. Specifically, he demonstrates how mathematicians accumulate evidence that a conjecture is true, and illustrates that crucial insights sometimes come from drawing upon seemingly unrelated branches of mathematics (such as the use of number theory in constructing regular polygons). He also conveys why the problems discussed are difficult, while not always managing to explain their importance. Readers with mathematical training will find the descriptions in the book maddeningly vague, and will, no doubt, notice errors in the text (k^2 + k + 41 is not prime if k = 40) and imprecise definitions in the glossary (he fails to specify that the integers in a Pythagorean triple must be nonzero). There is also a particularly unfortunate analogy between Ernest Rutherford's determining the shape of an atom by bombarding it with alpha particles (nuclei of helium atoms) and shooting bullets into a dark field to see what is there.

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