The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics

Capa
Macmillan, 2003 - 340 páginas
An engaging, informative, and wryly humorous exploration of one of the great conundrums of all time In 1859 Bernhard Riemann, a shy German mathematician, wrote an eight-page article giving an answer to a problem that had long puzzled mathematicians. But he didn’t provide a proof. In fact, he said he couldn’t prove it but he thought that his answer was “very probably” true. From the publication of that paper to the present day, the world’s mathematicians have been fascinated, infuriated, and obsessed with proving the Riemann Hypothesis, and so great is the interest in its solution that in 2001 an American foundation put up prize money of $1 million for the first person to demonstrate that the hypothesis is correct. The hypothesis refers to prime numbers, which are in some sense the atoms from which all other numbers are constructed, and seeks to explain where every single prime to infinity will occur. Riemann’s idea—if true—would illuminate how these numbers are distributed, and if false will throw pure mathematics into confusion. Karl Sabbagh meets some of the world’s mathematicians who spend their lives thinking about the Riemann Hypothesis, focusing attention in particular on “Riemann’s zeros,” a series of points that are believed to lie in a straight line, though no one can prove it. Accessible and vivid, The Riemann Hypothesis is a brilliant explanation of numbers and a profound meditation on the ultimate meaning of mathematics.
 

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LibraryThing Review

Procura do Utilizador  - palaverofbirds - LibraryThing

The funny thing about this book, for me, is that it claims to simply be a study of how the Riemann Hypothesis has been scrutinized, fought over and beloved by mathematicians. It is not supposed to be ... Ler crítica na íntegra

THE RIEMANN HYPOTHESIS: The Greatest Unsolved Problem in Mathematics

Procura do Utilizador  - Kirkus

British author Sabbagh (A Rum Affair, 2000, etc.) looks at a major unsolved problem in pure math and the men working to solve it.In 1859, the German mathematician Bernard Riemann stated his solution ... Ler crítica na íntegra

Índice

Prologue
3
Prime Time
13
Gorgeous stuff
30
New Numbers for Old
46
Indian Summer
63
Very probably
85
Proofs and Refutations
104
The Bieberbach Conjecture
116
No simple matter
202
Taking a Critical Line
214
Abstract Delights
231
Discovered or Invented?
249
Whats it all about?
263
TOOLKITS
277
Logarithms and Exponents
279
Equations
284

In Search of Zeros
132
The Princeton Tea Party
148
A Driven Man
163
The Physics of Mathematics
177
A Laudable Aim
188
The Euler Identity
292
De Brangess Proof
311
Further Reading
327
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