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Rating: "The Music of the Primes", Marcus du Sautoy (UK) 2003. In Italy published by Rizzoli
During the International Congress of Mathematicians, on August 8, 1900, in Göttingen (Germany), Professor Hilbert proposed to his colleagues a list of 23 problems which should (and indeed did) set the “path” of science during the newly born century. While touching (almost) all of them, the mathematician and writer, Marcus du Sautoy in the book in question describes the history of one in particular: the eighth, the most fascinating (and still unsolved) of all. Proving the Riemann Hypothesis.
“We must know, we shall know”(phrase engraved on Hilbert's tombstone: pronounced, coincidentally, in 1931 the day after the logician Kurt Gödel proved its unfeasibility, presenting the two Incompleteness Theorems)
The story narrated by du Sautoy actually begins long before the episode presented at the opening of the book: indeed, the determination of an order in the sequence of prime numbers has been a question of interest in Mathematics since its inception: and indeed the author does not fail to mention the exploits of Eratosthenes with his Sieve, of Euclid and the Proposition 20, contained in Book IX of the “Elements”, and with an important leap in time, also of Fermat with his hypothesis and Euler with his Theory of Numbers. But the first (chronologically) true protagonist of this “novel” (it is not a novel: I will then explain the quotation marks...) is Gauss with his conjecture on the Prime Number Theorem...
Other Protagonists (the main ones, not all as there are too many to mention, in Chronological Order):
-Dirichlet and Legendre and their dispute over Fermat's Last Theorem
-obviously Riemann and his hypothesis (a brief description is linked above)
-Hardy, Littlewood and Ramanujan and their work on Number Theory
-the aforementioned Hilbert and Gödel
-Siegel, Selberg and Paul Erdős (a funny story of this last one's Number) and the exodus to Princeton
-Grothendieck and the set of Prime Ideals
Apologizing if in the three paragraphs above I made mistakes, both historical and “mathematical” (after all, I am not a professional in the field but only a willing amateur and the beauty of DeBaser is that you can insult me in the comments), which I hope I have limited by putting the links, I must explain why I spoke of “Novel”.
As mentioned, this book is not at all because it absolutely has an essayistic dimension however du Sautoy performs a truly interesting operation: he does not limit himself to explaining the “specialized” path of one of the most exciting “adventures” of the scientific world but also recounts, with passion and elegance, the human stories, sometimes humorous, sometimes tragic, that happened to these marvellous minds (and forgive the Hollywood quote). Thus, it happens to be moved by reading about Riemann and his shyness (and getting angry with his housekeeper), to be thrilled by thinking of the ideals of the old Hilbert being swept away by the young Gödel, to be sorry for Turing's unjust fate and to be amazed at Grothendieck's, and so on in a race that is absolutely human...
Of course, the author cannot avoid going into specifics and therefore certain passages are not very easy (but if I managed...) but all in all he manages to make them “digestible” too.
What is depicted is Mathematics as an absolutely imaginative, fanciful, and creative activity and it is a different perspective that I think can interest everyone and for once, trust me...
Mo.
PS: this review is dedicated to Iside to whom I believe I have taken the record of Links in a single review...
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