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Prime Obsession (Derbyshire)
Jan. 7th, 2010 01:47 pmStill finishing up books from 2009...
I was complaining to D several weeks ago that the last time I read a math book for fun was probably back in high school. D listened, thought a bit, and said, "You know, you should try Prime Obsession."
Yup, he was absolutely right. This book is made of complete awesome, and I was totally addicted to it, reading it when I should have been unpacking (or sometimes trying to do both at once) and finishing it in under a week (which is kind of unheard of for me and nonfiction books). It is about the Riemann hypothesis, and told in two strands: the mathematical and the personal. Derbyshire breaks down all the math as simply as possible -- if I hadn't seen it done, I would've thought it was impossible to explain the Riemann hypothesis ("All nontrivial zeros of the Riemann zeta function have real part 1/2.") requiring no more math than, really, elementary algebra (he explains everything else, including the concept of series, complex numbers, logs, analytic continuation...) -- though if that's all the math background you have, it will be significantly harder slogging than if you have a bit more (I would recommend knowing the general concepts of complex numbers, logs, infinite series, and having a nodding familiarity with at least the concepts of calculus). Along the way you'd be introduced to lots of fascinating math tidbits, like the divergence of the harmonic series (Derbyshire makes it sound a lot more interesting than I just did) and chaos.
My personal background is such that I know up to calculus/linear algebra really well (I skimmed most of the early mathematics chapters in this book), and have, or used to have, a nodding familiarity with complex analysis. I had been taught the Riemann hypothesis (in the words I use above) in my complex analysis class, but had no idea why it was so very interesting. There's a point where Derbyshire introduces what he calls the "Golden Key," at which point my mouth hung open and I said to D, "Holy crap! ...I clearly knew NOTHING about the Riemann hypothesis! ...Wow!" Even so, I found a couple of the chapters near the end fairly dense (and so did D, who I suspect knows quite a bit more complex analysis than I do). So, um, yeah, I really recommend it if you know some math, though the early math chapters will be pretty trivial for you. It does make me want to find a book at a slightly more advanced level, though.
But you can even read it without any mathematical knowledge or background whatsoever, and it's still an awesome book. Derbyshire has decoupled, to a certain extent, the math and people/context chapters (even and odd respectively), so you can fairly easily skip any of the math you don't want to look at and just read the interesting stories about the personalities involved. I find his style extremely entertaining; even the endnotes are fun (there's one where he explains multiplying negative numbers against themselves that ends with a funny and rather adorable punchline from his small son). And mathematicians are an amusing lot; some of the stories he cites are mathematical classics that I'd heard before (e.g., the mathematician G. Hardy used to mail postcards before travel saying he'd solved the Riemann hypothesis, because he knew God would never let him die with such glory!) and some were new, but all were amusing!
Really, really highly recommended, especially for math nerds (though presumably not if you already know tons about the Riemann hypothesis).
I was complaining to D several weeks ago that the last time I read a math book for fun was probably back in high school. D listened, thought a bit, and said, "You know, you should try Prime Obsession."
Yup, he was absolutely right. This book is made of complete awesome, and I was totally addicted to it, reading it when I should have been unpacking (or sometimes trying to do both at once) and finishing it in under a week (which is kind of unheard of for me and nonfiction books). It is about the Riemann hypothesis, and told in two strands: the mathematical and the personal. Derbyshire breaks down all the math as simply as possible -- if I hadn't seen it done, I would've thought it was impossible to explain the Riemann hypothesis ("All nontrivial zeros of the Riemann zeta function have real part 1/2.") requiring no more math than, really, elementary algebra (he explains everything else, including the concept of series, complex numbers, logs, analytic continuation...) -- though if that's all the math background you have, it will be significantly harder slogging than if you have a bit more (I would recommend knowing the general concepts of complex numbers, logs, infinite series, and having a nodding familiarity with at least the concepts of calculus). Along the way you'd be introduced to lots of fascinating math tidbits, like the divergence of the harmonic series (Derbyshire makes it sound a lot more interesting than I just did) and chaos.
My personal background is such that I know up to calculus/linear algebra really well (I skimmed most of the early mathematics chapters in this book), and have, or used to have, a nodding familiarity with complex analysis. I had been taught the Riemann hypothesis (in the words I use above) in my complex analysis class, but had no idea why it was so very interesting. There's a point where Derbyshire introduces what he calls the "Golden Key," at which point my mouth hung open and I said to D, "Holy crap! ...I clearly knew NOTHING about the Riemann hypothesis! ...Wow!" Even so, I found a couple of the chapters near the end fairly dense (and so did D, who I suspect knows quite a bit more complex analysis than I do). So, um, yeah, I really recommend it if you know some math, though the early math chapters will be pretty trivial for you. It does make me want to find a book at a slightly more advanced level, though.
But you can even read it without any mathematical knowledge or background whatsoever, and it's still an awesome book. Derbyshire has decoupled, to a certain extent, the math and people/context chapters (even and odd respectively), so you can fairly easily skip any of the math you don't want to look at and just read the interesting stories about the personalities involved. I find his style extremely entertaining; even the endnotes are fun (there's one where he explains multiplying negative numbers against themselves that ends with a funny and rather adorable punchline from his small son). And mathematicians are an amusing lot; some of the stories he cites are mathematical classics that I'd heard before (e.g., the mathematician G. Hardy used to mail postcards before travel saying he'd solved the Riemann hypothesis, because he knew God would never let him die with such glory!) and some were new, but all were amusing!
Really, really highly recommended, especially for math nerds (though presumably not if you already know tons about the Riemann hypothesis).
