Genre: Biography (mathematical)
Year Published: 1998
While I was walking to the train station yesterday, having just finished this book, I tried to think of a historical figure to compare Paul Erdős with, so that non-mathematicians could appreciate the enormity of his legacy. The best I could come up with was an unholy cross of Buddha and Bach: Buddha for his itinerant, indigent lifestyle and complete generosity; Bach for his highly prolific genius. (Now try to imagine Buddha with Bach's crazy white wig. Doesn't the imagery alone make it worth it?)
With that bizarre hybrid in mind, I admit it cannot be easy to begin to contemplate how to write a fitting biography of Erdős. There are probably a dozen directions in which an author could go. As much as I enjoyed The Man Who Loved Only Numbers, it never quite achieved whatever lofty ideal was in the back of my mind. Apparently the book grew out of a biographical story that Hoffman wrote for The Atlantic, and it shows: it retains the jumpy, floating structure of a typical high-class magazine piece instead of assuming the more linear pace of a typical work of nonfiction. Even more tellingly, we as readers are never made to think too hard in a mathematical sense: never are we given even a sketchy outline of one of Erdős's thousands of proofs, nor do we learn much more about number theory (Erdős's field) than the definition of prime numbers.
Having said all this, I'd like to reiterate that I did enjoy this book very much -- I barely put it down once I'd begun it. I simply wish that it had achieved more. This volume is a mere glimpse into the life of one of the most intriguing mathematicians to ever live (and that is saying a lot!) If someone could marry the very good, anecdote-heavy legwork that Hoffman has done with a bit more serious biographical information and a deeper insight into Erdős's mathematics, we'd have the makings of a first-rate biography. As it stands now, it feels somehow incomplete . . . part book and part fog.
Recommended? Only if you are a mathematician, or particularly fond of same.
Showing posts with label mathematical interest. Show all posts
Showing posts with label mathematical interest. Show all posts
Tuesday, June 12, 2007
Monday, June 11, 2007
The Code Book (Simon Singh)
Genre: Nonfiction
Year Published: 1999
Some people's blood races when they read stories about war. These are the people who keep a Michael Shaara book by their bedside, who participate in reenactments, who spend their Friday nights playing Risk.
But there's another side of war, one filled with warriors who don't wield guns or crouch in trenches. Their purview is communication, both protecting their government's messages and finding out what their enemies are saying. They are cryptologists, and their story is the largely unwritten side of military history. And for me, as a mathematician, that's what makes my pulse speed up, to read about those breakthroughs, especially as they so often happened as countries clashed on the battlefield.
I was actually surprised by the visceral reaction I had as I was swept up in the various races to create and break ciphers, but perhaps I shouldn't have been. No one does pop science better than Simon Singh (between this and Fermat's Enigma, he is, as far as I'm concerned, to math lit as Ina Garten is to cookbooks). I could say a thousand wonderful things about him, but the highest praise I can give him is that he is the least lazy writer I can think of. He cuts no corners; he does enormous amounts of research, including interviews with all the relevant living people; and he always ensures that difficult concepts are presented clearly, in multiple ways.
Because of his deep commitment to his readers, the average reader should be able to understand all the concepts in this book with no trouble. The final chapter, which deals with quantum physics, may be a little beyond the comprehension of non-scientists, but everything else is perfectly lucid.
I only wish that Singh would write an updated, post-9/11 version of this book. The section on privacy versus national security is already terribly outdated.
Recommended? If you're going to read one "educational" book this year, it should be this one.
Year Published: 1999
Some people's blood races when they read stories about war. These are the people who keep a Michael Shaara book by their bedside, who participate in reenactments, who spend their Friday nights playing Risk.
But there's another side of war, one filled with warriors who don't wield guns or crouch in trenches. Their purview is communication, both protecting their government's messages and finding out what their enemies are saying. They are cryptologists, and their story is the largely unwritten side of military history. And for me, as a mathematician, that's what makes my pulse speed up, to read about those breakthroughs, especially as they so often happened as countries clashed on the battlefield.
I was actually surprised by the visceral reaction I had as I was swept up in the various races to create and break ciphers, but perhaps I shouldn't have been. No one does pop science better than Simon Singh (between this and Fermat's Enigma, he is, as far as I'm concerned, to math lit as Ina Garten is to cookbooks). I could say a thousand wonderful things about him, but the highest praise I can give him is that he is the least lazy writer I can think of. He cuts no corners; he does enormous amounts of research, including interviews with all the relevant living people; and he always ensures that difficult concepts are presented clearly, in multiple ways.
Because of his deep commitment to his readers, the average reader should be able to understand all the concepts in this book with no trouble. The final chapter, which deals with quantum physics, may be a little beyond the comprehension of non-scientists, but everything else is perfectly lucid.
I only wish that Singh would write an updated, post-9/11 version of this book. The section on privacy versus national security is already terribly outdated.
Recommended? If you're going to read one "educational" book this year, it should be this one.
Sunday, May 27, 2007
A Random Walk Down Wall Street (Burton Malkiel)
Year Published: 2003 (8th ed.)
Genre: Nonfiction
The stock market is not really my thing. P/E ratios, IPOs, the EAFE index -- while those jumbles of letters may be some people's livelihoods, I've never understood them, nor made an effort to.
But at some point, I think most Americans with halfway decent incomes begin to realize that saving for retirement is a big deal, and that without some idea of how investing works, they stand to suffer a good deal of losses -- either flat-out monetary losses, or losses of opportunities to do better by themselves in the long run.
My faithful readers will note that I began to investigate the vagaries of the market with an earlier read, A Mathematician Plays the Stock Market. While I loved Paulos' book, it wasn't quite the primer on investing that I needed. Paulos had cited Random Walk in his volume, so I picked it up the last time I made a bookstore run.
Random Walk has become something of a classic in the investment field, though Malkiel's arguments are often rebutted by professional investors. Malkiel's premise is relatively simple: the stock market (encompassing both domestic equity and international equity) always gives excellent returns in the long run, but no one can determine if any one stock will give good returns. Therefore, in order to maximize your return while minimizing your risk, invest in a broad-based index fund (i.e. a fund that simply buys a large amount of stocks without buying and selling them all the time) and hold it until you need the money (i.e. for retirement or a home purchase). This is in contrast to advisers who advocate investigating specific stocks or heavily managed mutual funds -- in essence, attempting to "beat the market." Malkiel, citing several economic studies, shows that managed mutual funds mostly underperform unmanaged ones, and that there's no way of telling in advance who will be the few outperformers, so why gamble with your savings?
Now, if this were the entirety of the book, there'd be no reason for it to be upwards of 450 pages. However, Malkiel also runs through the major market "corrections" of the past four centuries (complete with snarky commentary), the tenets of the Efficient Market Hypothesis, the basic precepts of the two prevailing types of stock analysis, and, most helpfully, the types of investments that people should make, based on their age and risk tolerance. On all these counts, Malkiel does a superb job, combining hard-nosed economic analysis with funny, incisive (and often derisive) comments about everyone else in the business. See, for example:
My only hesitation in recommending this book is the somewhat worrying fact that Malkiel is a member of the Vanguard Group, the group of leaders of the eponymous corporation that is best known for being the world's leader in the sale of -- you guessed it -- index funds, the very investment Malkiel recommends all people make. This is no way negates his advice (some may even see it as putting his money where his mouth is), but I wish he had been more forthcoming about it; he only reveals this affiliation about four-fifths of the way into the book.
Recommended? Yes: the lifecycle guide to investing alone is worth the cost of the book.
Genre: Nonfiction
The stock market is not really my thing. P/E ratios, IPOs, the EAFE index -- while those jumbles of letters may be some people's livelihoods, I've never understood them, nor made an effort to.
But at some point, I think most Americans with halfway decent incomes begin to realize that saving for retirement is a big deal, and that without some idea of how investing works, they stand to suffer a good deal of losses -- either flat-out monetary losses, or losses of opportunities to do better by themselves in the long run.
My faithful readers will note that I began to investigate the vagaries of the market with an earlier read, A Mathematician Plays the Stock Market. While I loved Paulos' book, it wasn't quite the primer on investing that I needed. Paulos had cited Random Walk in his volume, so I picked it up the last time I made a bookstore run.
Random Walk has become something of a classic in the investment field, though Malkiel's arguments are often rebutted by professional investors. Malkiel's premise is relatively simple: the stock market (encompassing both domestic equity and international equity) always gives excellent returns in the long run, but no one can determine if any one stock will give good returns. Therefore, in order to maximize your return while minimizing your risk, invest in a broad-based index fund (i.e. a fund that simply buys a large amount of stocks without buying and selling them all the time) and hold it until you need the money (i.e. for retirement or a home purchase). This is in contrast to advisers who advocate investigating specific stocks or heavily managed mutual funds -- in essence, attempting to "beat the market." Malkiel, citing several economic studies, shows that managed mutual funds mostly underperform unmanaged ones, and that there's no way of telling in advance who will be the few outperformers, so why gamble with your savings?
Now, if this were the entirety of the book, there'd be no reason for it to be upwards of 450 pages. However, Malkiel also runs through the major market "corrections" of the past four centuries (complete with snarky commentary), the tenets of the Efficient Market Hypothesis, the basic precepts of the two prevailing types of stock analysis, and, most helpfully, the types of investments that people should make, based on their age and risk tolerance. On all these counts, Malkiel does a superb job, combining hard-nosed economic analysis with funny, incisive (and often derisive) comments about everyone else in the business. See, for example:
Curiously, however, the broke technician is never apologetic. If you commit the social error of asking him why he is broke, he will tell you quite ingenuously that he made the all-too-human error of not believing his own charts. To my great embarrassment, I once choked conspicuously at the dinner table of a chartist friend of mine when he made such a comment. I have since made it a rule never to eat with a chartist. It's bad for digestion.
My only hesitation in recommending this book is the somewhat worrying fact that Malkiel is a member of the Vanguard Group, the group of leaders of the eponymous corporation that is best known for being the world's leader in the sale of -- you guessed it -- index funds, the very investment Malkiel recommends all people make. This is no way negates his advice (some may even see it as putting his money where his mouth is), but I wish he had been more forthcoming about it; he only reveals this affiliation about four-fifths of the way into the book.
Recommended? Yes: the lifecycle guide to investing alone is worth the cost of the book.
Sunday, April 22, 2007
Innumeracy: Mathematical Illiteracy And Its Consequences (John Allen Paulos)
Genre: Nonfiction
Year Published: 1988
With A Mathematician Plays the Stock Market set firmly in my mind as one of the greatest nonfiction books I'd ever read, I set out to find more John Allen Paulos at the Penn bookstore. I knew Innumeracy was his break-out hit, so I snatched it up and began reading it that very day.
The bad news: it's not nearly as entertaining as Stock Market. The good news: it's probably a lot more important. The book is less fun because it's not as personal; it's a little more didactic and less rambling. But the fundamental idea behind the book is, in my mind, vital. As Paulos puts it:
Whew. Couldn't have put it better myself.
For anyone who has a degree in, say, mathematics, this book is not necessary to add to your shelf. But if you're one of this country's many mathphobes, the brilliant people who opted out of science and into English or sociology because the quantitative aspect of other disciplines was too scary to you, or the average people who barely passed the minimum required classes at your high school, this book is crucial. Paulos demystifies probability and statistics, subjects that arise at least every hour in most people's lives, and tries to gently lead innumerate people to the light.
Math is important, and it isn't going away. This book could help you to bridge the gap between confusion and comprehension, and that should be enough to make you want to read this.
Recommended? If you've ever uttered the sentences "I hate math" or "I'm so bad at math," you need to read this, yes.
Year Published: 1988
With A Mathematician Plays the Stock Market set firmly in my mind as one of the greatest nonfiction books I'd ever read, I set out to find more John Allen Paulos at the Penn bookstore. I knew Innumeracy was his break-out hit, so I snatched it up and began reading it that very day.
The bad news: it's not nearly as entertaining as Stock Market. The good news: it's probably a lot more important. The book is less fun because it's not as personal; it's a little more didactic and less rambling. But the fundamental idea behind the book is, in my mind, vital. As Paulos puts it:
At least part of the motivation for any book is anger, and this book is no exception. I'm distressed by a society which depends so completely on mathematics and science and yet seems so indifferent to the innumeracy and scientific illiteracy of so many of its citizens; with a military that spends more than one quarter of a trillion dollars every year on ever smarter weapons for every more poorly educated soldiers; and with the media, which invariably become obsessed with this hostage on an airliner, or that baby who has fallen into a well, and seem insufficiently passionate when it comes to addressing problems such as urban crime, environmental deterioration, or poverty.
Whew. Couldn't have put it better myself.
For anyone who has a degree in, say, mathematics, this book is not necessary to add to your shelf. But if you're one of this country's many mathphobes, the brilliant people who opted out of science and into English or sociology because the quantitative aspect of other disciplines was too scary to you, or the average people who barely passed the minimum required classes at your high school, this book is crucial. Paulos demystifies probability and statistics, subjects that arise at least every hour in most people's lives, and tries to gently lead innumerate people to the light.
Math is important, and it isn't going away. This book could help you to bridge the gap between confusion and comprehension, and that should be enough to make you want to read this.
Recommended? If you've ever uttered the sentences "I hate math" or "I'm so bad at math," you need to read this, yes.
Wednesday, April 18, 2007
A Mathematician Plays the Stock Market (John Allen Paulos)
Genre: Nonfiction
Year Published: 2003
This is one of the most helpful books I've read in years. Paulos, a professor of mathematics at Philadelphia's own Temple University, gives his readers a broad rundown of the stock market, game theory, behavioral finance, and basic statistics. Although I am a mathematician by training, I knew next to nothing about the world of finance before starting this book, but I consider myself relatively well-informed now about the very basic structure of the market.
But -- and here's the great part -- this is the most enjoyable work of nonfiction I've read in years. Paulos is amazingly funny, and manages to cram in asides and jokes that take what could easily have been a primer and make it into a wonderful read instead. I found myself laughing out loud, something I rarely do while reading. (One quick example: "I thought news stories in November 2002 recounting New York Attorney General Eliot Spitzer's criticism of . . . analyst awards were a bit superfluous. Spitzer noted that the stock-picking performances of most of the winning analysts were, in fact, quite mediocre. Maybe Donald Trump will hold a press conference pointing out that the country's top gamblers don't do particularly well at roulette.")
Here's the catch (isn't there always one?): this is not a book for the mathphobes among us. If you hate the idea of being taught something about covariance or chaos theory, skip this book. But if you're intellectually curious and open-minded, and you have a thorough mathematical grounding (say, up to precalculus at least), don't miss out on this one.
Recommended? If you can stomach the math, then don't hesitate!
Year Published: 2003
This is one of the most helpful books I've read in years. Paulos, a professor of mathematics at Philadelphia's own Temple University, gives his readers a broad rundown of the stock market, game theory, behavioral finance, and basic statistics. Although I am a mathematician by training, I knew next to nothing about the world of finance before starting this book, but I consider myself relatively well-informed now about the very basic structure of the market.
But -- and here's the great part -- this is the most enjoyable work of nonfiction I've read in years. Paulos is amazingly funny, and manages to cram in asides and jokes that take what could easily have been a primer and make it into a wonderful read instead. I found myself laughing out loud, something I rarely do while reading. (One quick example: "I thought news stories in November 2002 recounting New York Attorney General Eliot Spitzer's criticism of . . . analyst awards were a bit superfluous. Spitzer noted that the stock-picking performances of most of the winning analysts were, in fact, quite mediocre. Maybe Donald Trump will hold a press conference pointing out that the country's top gamblers don't do particularly well at roulette.")
Here's the catch (isn't there always one?): this is not a book for the mathphobes among us. If you hate the idea of being taught something about covariance or chaos theory, skip this book. But if you're intellectually curious and open-minded, and you have a thorough mathematical grounding (say, up to precalculus at least), don't miss out on this one.
Recommended? If you can stomach the math, then don't hesitate!
Thursday, January 18, 2007
The Math Instinct: Why You're a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs) (Keith Devlin)
Genre: Nonfiction
Year Published: 2005
I'm a mathematician by training, so when the holidays roll around, I often find myself in possession of several new books that somehow incorporate math. Since mathematicians tend to be below-average writers (myself, I hope, excepted), a lot of these turn out to be well nigh unreadable. (A noteworthy exception is Fermat's Enigma, one of my all-time favorite books in any genre.)
The Math Instinct, however, is extremely readable -- not surprising, as the author is a commentator on NPR's Weekend Edition and has written many books for a general audience. In fact, at times I almost felt I was being condescended to a bit . . . but you can't trust the opinion of a mathematician on that point.
Devlin's point in writing this book is to illustrate the many ways in which complex mathematics are performed by various members of the plant and animal kingdoms, ostensibly to make math seem a little less daunting to the public, but also to showcase how natural selection can really produce some amazing results. My favorite example is that of the Tunisian desert ant that can wander far from its home in multiple directions and then walk straight home instead of retracing its path. That's a trig problem, dear readers, and while Devlin makes it clear that it's erroneous to think of an ant as doing trigonometry, you can think of its daily walk as a trig problem that nature has enabled it to solve instinctively.
Devlin catalogues this sort of mathematical behavior in all sorts of animals, and this is interesting, if it's the sort of thing you're into. (It is for me, but again, as a mathematician, I don't feel I can really speak for the general public at this point.) Where the book really gets intriguing, though, is towards the end (Chapter 10 out of 13 total), when Devlin takes on the idea of mathematics as an innate process.
He cites fascinating studies that show, for example, that young Brazilian street vendors are able to mentally perform complicated arithmetic problems, but are utterly unable to reproduce those results on math exams, because of the dichotomy of "street math" versus "school math." Devlin comes to conclusions about math education that I think would be very interesting and informative for anyone who's in the education field, as well as anyone who feels that they're a smart person, but just "doesn't get" math.
Recommended? Sure! It's fun, it's easy, and people will think you're smart if they see you reading it on the subway.
Year Published: 2005
I'm a mathematician by training, so when the holidays roll around, I often find myself in possession of several new books that somehow incorporate math. Since mathematicians tend to be below-average writers (myself, I hope, excepted), a lot of these turn out to be well nigh unreadable. (A noteworthy exception is Fermat's Enigma, one of my all-time favorite books in any genre.)
The Math Instinct, however, is extremely readable -- not surprising, as the author is a commentator on NPR's Weekend Edition and has written many books for a general audience. In fact, at times I almost felt I was being condescended to a bit . . . but you can't trust the opinion of a mathematician on that point.
Devlin's point in writing this book is to illustrate the many ways in which complex mathematics are performed by various members of the plant and animal kingdoms, ostensibly to make math seem a little less daunting to the public, but also to showcase how natural selection can really produce some amazing results. My favorite example is that of the Tunisian desert ant that can wander far from its home in multiple directions and then walk straight home instead of retracing its path. That's a trig problem, dear readers, and while Devlin makes it clear that it's erroneous to think of an ant as doing trigonometry, you can think of its daily walk as a trig problem that nature has enabled it to solve instinctively.
Devlin catalogues this sort of mathematical behavior in all sorts of animals, and this is interesting, if it's the sort of thing you're into. (It is for me, but again, as a mathematician, I don't feel I can really speak for the general public at this point.) Where the book really gets intriguing, though, is towards the end (Chapter 10 out of 13 total), when Devlin takes on the idea of mathematics as an innate process.
He cites fascinating studies that show, for example, that young Brazilian street vendors are able to mentally perform complicated arithmetic problems, but are utterly unable to reproduce those results on math exams, because of the dichotomy of "street math" versus "school math." Devlin comes to conclusions about math education that I think would be very interesting and informative for anyone who's in the education field, as well as anyone who feels that they're a smart person, but just "doesn't get" math.
Recommended? Sure! It's fun, it's easy, and people will think you're smart if they see you reading it on the subway.
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