Indeholder "Preface", "Zero. The Gauntlet is Thrown", "One. The Music of the Primes: The Riemann Hypothesis", " Appendix 1. Euklid's proof that there are infinitely many primes", " Appendix 2. How do mathematicians work out infinite sums?", " Appendix 3. How Euler discovered the Zeta function", "Two. The Fields We Are Made Of: Yang-Mills Theory and the Mass Gap Hypothesis", " Appendix. Group Theory: The Mathematics of Symmetry", "Three. When Computers Fail: The P versus NP Problem", "Four. Making Waves: The Navier-Stokes Equations", "Five. The Mathematics of Smooth Behavior: The Poincaré Conjecture", "Six. Knowing When the Equation can't Be Solved: The Birch and Swinnerton-Dyer Conjecture", " Appendix: Notation for infinite sums and products", "Seven. Geometry Without Pictures: The Hodge Conjecture", "Further Reading", "Index".

"Preface" handler om at Clay Institute i maj 2000 annoncerede syv priser på hver en million dollar for løsningen på syv vanskelige og vigtige matematiske problemer. Det gav efterspørgsel på en bog om problemerne. Faktisk mindst to, for Clay Institute bad Keith Devlin og Ian Stewart om at skrive en generel introduktion til hvert problem i den officielle problemformulering. Denne bog er anderledes, for ideen er blot at give en ide om hvad de syv problemer går ud på. Udover Clay Math Institute bogen kan man også finde en film på www.claymath.org som forsøger det samme.
"Zero. The Gauntlet is Thrown" handler om ???
"One. The Music of the Primes: The Riemann Hypothesis" handler om ???
" Appendix 1. Euklid's proof that there are infinitely many primes" handler om ???
" Appendix 2. How do mathematicians work out infinite sums?" handler om ???
" Appendix 3. How Euler discovered the Zeta function" handler om ???
"Two. The Fields We Are Made Of: Yang-Mills Theory and the Mass Gap Hypothesis" handler om ???
" Appendix. Group Theory: The Mathematics of Symmetry" handler om ???
"Three. When Computers Fail: The P versus NP Problem" handler om ???
"Four. Making Waves: The Navier-Stokes Equations" handler om ???
"Five. The Mathematics of Smooth Behavior: The Poincaré Conjecture" handler om ???
"Six. Knowing When the Equation can't Be Solved: The Birch and Swinnerton-Dyer Conjecture" handler om ???
" Appendix: Notation for infinite sums and products" handler om ???
"Seven. Geometry Without Pictures: The Hodge Conjecture" handler om ???
"Further Reading" handler om forslag til yderligere læsning.
"Index" er et almindeligt opslagsregister.

Clay Mathematical Institute udlovede i 2000 syv priser på hver en million dollar. Til hver pris hørte en lille opgave med at løse et matematisk problem, som ingen tidligere havde løst. ( )

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. ( )

As someone who spends no time ever trying to solve these things, I found it to be a really approachable summary of what the problems were and roughly the techniques that one must be fluent in to stand a reasonable chance of understanding them 'really well'. Gave good references for further reading too. I liked Devlin's style, he was conscious not to get too bogged down whilst not being so high level as to be irritating (I thought anyway). If you read this book within a week or two I;d suggest its one fo the few times anyone would ever think about all 7 major problems in quite such quick succession (well - 6 now after Poincare's conjecture was proven - can I get a refund for that one?)... ( )

Keith Devlin takes on a daunting task in The Millennium Problems: explain the problems that the Clay Mathematical Institute in 2000 labeled the seven most important unsolved problems in modern mathematics to an audience of non-mathematicians. Given the difficulty of this problem, Devlin succeeds as well as could reasonably be expected.

Devlin organizes the book from most comprehensible to least, beginning with the relatively straightforward Riemann Hypothesis dealing with the distribution of prime numbers (though ease in understanding is not ease in solving; this is the longest-standing of the Problems, first proposed in 1859.) He works his way through the classic algorithmic question of P vs NP and the Poincaré Conjecture (proved in 2006, after the publication of this book) to the utterly opaque Hodge conjecture, where he effectively throws up his hands in despair at even attempting to explain the problem.

The book assumes an interest in math (why else would anyone read it, after all?), but not much knowledge of the field. This was actually rather baffling; Devlin has no qualms about introducing the fundamentals of complex analysis or group theory, but doesn't assume the reader knows or remembers differential calculus. I thus found myself skimming impatiently at some points while being baffled at others. It's probably safe to assume that people who didn't take any math at all in college wouldn't touch this book, so why the coyness about high school calculus?

As a physicist and astronomer by training, it was difficult for me to understand why some of these problems matter. P vs NP is obviously tremendously important to modern computing, and the Navier-Stokes equations of fluid mechanics have clear real-world applications (and their inclusion in the list of problems validated my longstanding opinion that quantum mechanics and general relativity are childs' play compared to the terrors of fluid dynamics), but what will it actually mean, even to mathematicians, whether the Hodge conjecture is true?

This review may seem fairly critical, but overall The Millennium Problems is a very interesting read; the task it tackles may just be nearly as difficult as some of the problems it describes. ( )

About what one would expect. An adequate but not great overview of the seven million dollar problem sponsored by the Clay institute.
The final chapter was intriguing in that it hinted at connnections between differential forms (which I care about) and algebraic geometry (which I've tried to avoid caring about); but as always with these books, the fact that they are pitched so low makes them frustrating. ( )