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Prime Obsession: Bernhard Riemann and the…
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Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in… (original 2003; udgave 2003)

af John Derbyshire (Forfatter)

MedlemmerAnmeldelserPopularitetGennemsnitlig vurderingOmtaler
8151219,752 (4.07)5
In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark " a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic " defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark " the Riemann Hypothesis " that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows " subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many " the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof " and those who have been consumed by it.… (mere)
Medlem:B-III
Titel:Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
Forfattere:John Derbyshire (Forfatter)
Info:Joseph Henry Press (2003), Edition: 1st, 446 pages
Samlinger:Dit bibliotek
Vurdering:
Nøgleord:Ingen

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Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics af John Derbyshire (2003)

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I bought this book thinking it was a biography of Riemann. It's not. Riemann shows up for a little bit at the beginning, but the vast majority of this book is not about him. Fair enough, allegedly he kept no diary and made no friends, so there's very little known about him. But the title is exceptionally misleading.

My second concern is "who is the intended audience of this book?" Like, it goes through exceptional trouble to explain natural numbers, but a few chapters later assumes you're capable of following difficult arguments requiring calculus over infinite series. It goes on forever about what a matrix is, but then completely glosses over eigenvalues, despite using them heavily for its later arguments. The final chapter is just one huge derivation of a result that nobody outside of analysis would ever care about.

If you're a math hobbiest, this book is going to be too hard for you. If you have a math undergraduate degree, this book is going to be both too hard for you AND immensely boring at the beginning. The history presented is grantedly interesting. I'd suggest just skipping over the math bits regardless of your skill and skimming through the history. Save yourself some time and frustration. ( )
  isovector | Dec 13, 2020 |
I first read this around 2008, and re-read it (quickly) in 2020. Really enjoyed it - lots of meaty but understandable maths, intertwined with the stories of the mathematicians. In another life I would go back and read it again. ( )
  jvgravy | Jun 8, 2020 |
Un petit chef d'oeuvre alternant vulgarisation et histoire des mathématique dans un équilibre parfait. Les explications techniques sont claires infusées de manière progressive. La partie historique conte l'élaboration de l'hypothèse de Riemmann puis les tentatives pour la résoudre, le tout agrémenté par des morceaux de biographies des hommes ayant participé à cette quète. Et au centre, la fonction zêta que l'auteur nous décrit avec passion. ( )
  aipotu | Aug 6, 2016 |
An excellent coverage of the Riemann Hypothesis for the non-mathematician. ( )
  jsburbidge | Jan 12, 2016 |
Seeing as how this is my first exposure to the RH, and I'm only fairly capable in math, I can't say whether or not this is the best place to start. I feel like I have a good sense about this great mathematical problem, which is due in part to Derbyshire's simple explanations. However, I think the way the book was edited may have caused a lot of confusion. I thought it a bit erratic, with too many tangents and I didn't like being constantly referred back to old chapters. ( )
  palaverofbirds | Mar 29, 2013 |
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In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark " a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic " defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark " the Riemann Hypothesis " that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows " subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many " the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof " and those who have been consumed by it.

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