Steven Williams's Reviews > The Millennium Problems

The Millennium Problems by Keith J. Devlin
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This book is an attempt to explain, at least where at all possible, the seven mathematical millennium problems, which the Clay Foundation in 2000 offered a one million dollar prize for the solving of each problem. They are in order of presentation in the book: The Riemann Hypothesis, Yangs-Mill Theory and the Mass Gap Hypothesis, The P vs. NP Problem, The Navier-Stokes Equation, The Poincare Conjecture, The Birch and Swinnerton-Dyer Conjecture, and The Hodge Conjecture.

The Riemann Hypothesis involves complex analysis and if proven true would solve the pattern of the primes. The Yang-Mills Theory and the Mass Gap Hypothesis involves quantum physics and its solution would be a big help to both mathematicians and physicists. The P vs. NP Problem involves computational complexity. If P can be shown to be the same as a certain class of NP, than it would be a big boost to solving complex problems by computer computation like the traveling salesman problem, which is the solution to the shortest route of an itinerary. If not, than we will have to settle for approximate solutions. The Navier-Stokes Equation involves fluid dynamics and if solved would help in things like airplane design. It would also have a bearing on Chaos Theory. The Poincare Conjecture involves topology, which studies what stays the same in a particular geometry after twisting or stretching, but not tearing. The last two are beyond even Keith Delvin’s ability to explain, as he fully admits, so I will not even attempt describing them.

The book was okay, and I did learn something about these difficult mathematical problems. Delvin is a good expositor for the knowledgeable reader. I may have lost some of my interest for mathematical books aimed at the general reader, except books dealing with infinity, which is why I said the book was just okay. However, I am still very attracted to the philosophy of mathematical books; these books are not in the general readership category.

My recommendation is for those who have an interest in mathematics, whatever your level of competency. If you know next to nothing, you will probably be lost most of the time; if you have some type of mathematical expertise, you should do just fine, I think, even in areas of mathematics were you might not know a whole lot. For those of you who are somewhere in between, you will probably get lost at times like I did.
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Reading Progress

December 12, 2016 – Started Reading
December 21, 2016 – Finished Reading
December 22, 2016 – Shelved

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