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The Millennium Problems

3.82  ·  Rating details ·  527 ratings  ·  34 reviews
In the hands of Keith Devlin, "the Math Guy" from NPR's "Weekend Edition," each Millennium Problem becomes a fascinating window onto the deepest and toughest questions in the field. For mathematicians, physicists, engineers, and everyone else with an interest in mathematics' cutting edge, The Millennium Problems is the definitive account of a subject that will have a very ...more
Published March 7th 2005 by Granta Books (first published 2002)
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3.82  · 
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 ·  527 ratings  ·  34 reviews

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Steven Williams
Jan 10, 2017 rated it liked it
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 inv
This book is an introduction to the 7 math problems designated by the Clay Mathematical Institute as "Millenium" problems and carry an award of 1 million dollars each. The problems are mathematically dense and I was able to follow in part perhaps that first four descriptions. The 5th and 6th were tough (I basically simply read through the 6th) and the 7th was completely impossible to understand. Though I think it is the nature of these problems and not a shortcoming in the author. But still it w ...more
Jul 19, 2014 rated it liked it
Shelves: mathematics
I read this book long ago. This is probably as close as one can get to give a light overiview of the seven problems recognised by the clay institute for a million dollar prize. The author here takes up an impossible task of explaining these problems to a lay audience. Even if he didn't entirely succeed in this, this book can be used to spark someone's interest for deeper study. Worth the read at least for the chapters on Riemann hypothesis and the P vs NP problem.
Sep 09, 2011 rated it it was amazing
A very inspirational book. Now I know what math problems I should start solving.
At the beginning of the twentieth century, David Hilbert gave a talk in which he posed 23 problems in mathematics. The solutions -- or attempted solutions -- to these problems became a major part of the story of mathematics in the twentieth century. At the start of the twenty-first century, the Clay Math Institute posed seven problems to serve as a similar challenge for another century of mathematical research. Keith Devlin, a writer of popular mathematics and the "math guy" on NPR's "All Things ...more
Sep 06, 2014 rated it really liked it  ·  review of another edition
A whirlwind tour of seven of the most important and difficult unsolved problems in mathematics today (actually, one of them, the Poincaré Conjecture, has been solved since the book was written).
As an introduction, I think the book does a good job of imparting the general idea of each of the problems, even the Hodge Conjecture which in its full glory is well past my ability to comprehend without a few years of study. I recommend this book as a good starting point for getting an overall understand
Mar 24, 2007 rated it it was ok
Yeah, you just TRY explaining superalgebras to nonspecialists in a small paperback book! I give them two stars for effort, but overall this book's a wash.
Rod Innis
Sep 13, 2017 rated it it was ok
I have included in my review a couple of quotes and my comments on them. Much of the book is very hard to understand for a non-mathematician. He does give some insight into his worldview as the following quotes demonstrate.
Pages 179 & 180
"In four dimensions the bottle would not have to pass through itself. To the person in the street, an object that exists in four-dimensional space doesn’t really exist of course, but this trivial objection does not deter the mathematician. After all everyon
Deepak Kumar
May 24, 2018 rated it really liked it
It is a book that attempts to explain the 7 Millennium problems ( which can be called "extremely difficult unsolved mathematical problems for the Humankind") by using more words and less mathematics. Out of those 7 problems, fortunately, One (The Poincare Conjecture) has been solved by Grigori Perelman(who rejected the $1 million prize) in 2006.
Did I said "$1 million"? Yes, apart from achieving the satisfaction of solving an "unsolved" math problem, Clay Mathematics Institute offers $1 million
Steve Gross
Aug 08, 2018 rated it it was ok
I don't think the author is a very good explainer.
andrew y
Nov 03, 2018 rated it really liked it
Shelves: learning
The last two chapters shattered my delusion of being an amateur mathematician but the first five were pretty dope.
Ethan Gollings
May 08, 2019 rated it it was amazing
Simplistic enough to attract many but complex enough to inspire the passionate mathematician.
Mugizi Rwebangira
Jul 25, 2018 rated it liked it
Nice enjoyable survey.

Even managed to make things The Birch and Swynerton-Dyer conjecture seem somewhat understandable.

Not so much the Hodge conjecture though.
Oct 02, 2016 rated it really liked it
Quite good summaries of complex mathematical problems. It was a pleasant read.
Dec 15, 2015 rated it liked it
The Millennium Problems are seven problems in mathematics identified by the Clay Mathematics Institute as being particularly difficult and important. A one million dollar prize is offered for the solution of each problem. The awards have something of a precursor going back to 1900 when David Hilbert posed 23 problems of importance to mathematics. Almost all the Hilbert problems have been solved. Only one problem from Hilbert's list makes it onto the Millennium Problems: The Riemann Hypothesis.

Dan Cohen
Hmmm, Devlin takes on a tricky task in this book, as some of the problems described are so hard to describe (let alone solve!) that he admits that even he does not understand the problem. Having said that, he does an excellent job with some of the problems, such as the Riemann Hypothesis, and the introductory material in each chapter giving the mathematical (and physics) background is very good. He also provides biographical snippets for some of the mathematicians mentionned which helps to keep ...more
Tony Alleven
Feb 08, 2017 rated it really liked it
Well explained summary of the 7 unsolved millennium problems in mathematics. Each of these problems has a $1M prize for solving. Good luck to anyone on the Hodge Conjecture.
May 14, 2013 rated it liked it  ·  review of another edition
Shelves: books-i-own
You have to appreciate Devlin's gumption in attempting to explain the hardest problems in the mathematical world to regular joes and janes, and he does a pretty good job. But there's no getting around the fact that he pretty much punts on the last two. I mean, he *sort of* tries, but he pretty much tells the reader that it's too complicated to explain. I hoped for at least a little more attempt.
Sam Poole
Devlin tries and for that he deserves Praise. The seven millennium problems are described as simply as possible, which is still too complicated for most folks (the last two chapters sent my head spinning and were the reason I took so long to finish this!). An interesting look at complex algebra and complex systems and a fun behind the scenes glance at the histories and culture of mathematicians. Try it out but be warned, it's a challenge.
Sep 20, 2016 rated it it was amazing
Interesting read. A bit outdated if you read it in 2016 (as already one of the problems has been solved)
but generally well written and complete. The author does a great job at simplifying a lot of the maths
and transmits pretty well the spirit of each problem. The book is not dense by any means and has a lot of background information regarding the history of each problem. I recommend it to anyone that is interested in math and math history.
Geoffrey Lee
Dec 19, 2008 rated it it was ok
Shelves: mathematics
Not too much "meaningful" information is given on the subject. Also, the author makes an error when attempting to explain cohomology in the chapter on the Hodge conjecture (he has the definition for exact and closed differential forms switched).
Feb 24, 2012 rated it it was ok
Some of the areas are fairly difficult to explain and I thought the author did a decent job providing some idea what these mathematical questions are about. Still, I thought he could have been more thorough with some of them, 3.5 stars.
Ayoub Makroz
Jul 10, 2014 rated it really liked it
Clear explanation of the most sophisticated and important problems of modern mathematics. It focuses more on the importance and history of the problem, rather than the technical side. It gives also the implications of having a solution for every problem. Great Book !
Jul 09, 2008 rated it liked it
good but goes into too much detail...the diagrams are handy though. i would recommend to only read the first chapter and intro then if you want to read about a certain problem, to read that, rather than read it like a normal book.
Bradley Bartholomew
Jan 19, 2017 rated it really liked it
An interesting review of the most difficult math problems we face today and why they are important. A good pace that starts with easy stuff and moves towards the impossible.
May 31, 2010 rated it liked it
Ultimately I didn't get a whole lot of this, but I enjoyed trying. The writing is quite clear even though the subject matter isn't always...
Mar 07, 2012 rated it really liked it
All but the final two problems make good book fodder. The rest are just too arcane to make a nice story.
Chris Kemp
Nov 12, 2014 rated it liked it
Interesting book for one who has an interest in, and a little knowledge of, math. Skip the last chapter and a half if you are not a professional mathematician.
Clark Lyons
Mar 06, 2011 rated it it was amazing
This book really explains each one of the millenium problems in a way that is easy to understand. It was very informative.
Aug 25, 2007 rated it really liked it
Challenging for non-mathematicians but mind-stretching.
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Dr. Keith Devlin is a co-founder and Executive Director of the university's H-STAR institute, a Consulting Professor in the Department of Mathematics, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of differ ...more