This is a very well-written account of the most famous unsolved problem in mathematics, the Riemann Hypothesis. The author has organized it into odd-numbered chapters which have most of the math (targeted at the reader with only a high-school level background in math and no calculus background), and even-numbered chapters which have most of the history. The history is interesting enough that the math chapters could be skipped if the reader is so inclined. The math chapters are as gentle as possible given the formidable nature of the topic so many readers will find them readable. Somewhat more ambitious readers might find this book a good stepping-off point for further investigations, but be forewarned that truly comprehending this material will require a solid grounding in calculus and complex analysis, so if your background is only high-school math you probably have a minimum of two years equivalent of college math to get through first.
The Riemann Hypothesis relates to number theory, specifically the distribution of prime numbers, which is fairly understandable at the elementary level to the non-mathematically trained, so even without understanding the math behind the Hypothesis itself, most readers can still come away with an understanding of what the Hypothesis is trying to say and why it's so important.
What I found most interesting is the way in which seemingly completely unrelated areas of math and science have been found to have connections with the Hypothesis. This is true of a lot of mathematical propositions, and is perhaps the most mysterious aspect of math in general. As Shakespeare once wrote, "there's more in heaven and earth than is dreamt of in your philosophy, Horatio!" Lots more!
One minor correction: on page 54 the author expresses his awe at the ability of the great mathematician Gauss to extract the primes from blocks of 1000 integers in 15 minutes, using only a pencil, paper, and a list of primes up to 829. In fact, according to Havil in his excellent book "Gamma, Exploring Euler's Constant", on p. 174, Gauss began this task at age 15 after receiving a table of logarithms which had appended a list of primes up to one million. So what he was actually doing in those 15 minutes was just adding up the number of primes listed in the table for blocks of 1000 integers, a task even ordinary mortals could have easily acomplished.
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Book is in poor condition
Someone has treated this book with little care. It seems to have suffered water damage. There is also an inscription in permanent ink of a personal nature.
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Kishan Sharma
Chapter 1
Reviewed in India on April 12, 2024
Kishan Sharma
Reviewed in India on April 12, 2024
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