#  cover  title  author  isbn  isbn13  asin  num pages  avg rating  num ratings  date pub  date pub (ed.)  rating  my rating  review  notes  recommender  comments  votes  read count  date started  date read 
date

date purchased  owned  purchase location  condition  format  

085738838X
 9780857388384
 3.73
 63
 Dec 30, 2010
 2012

Really, it’s my fault that mathematics gets such a bad rap. And by me, I mean math teachers in general. And by math teachers, I actually mean the pedag Really, it’s my fault that mathematics gets such a bad rap. And by me, I mean math teachers in general. And by math teachers, I actually mean the pedagogical paradigm in which most of us are embedded, and the questionable premises of the educational system that encourages such pedagogy. Math anxiety is often caused by general test anxiety, combined with a lingering sensation that there is “one right answer,” as well as a misunderstanding what math is and how we use it. Other factors: parents communicating anxiety/resisting innovative ways of teaching, and a generalized antiintellectual snobbery in our society in which those who are interested in how the world works are “geeks” and “nerds.” (This is independent of the fact that, in recent years, geekdom and nerdery has become trendy. Capitalist structures might be coopting the symbols and fashions of geek culture, but that doesn’t translate into broader tolerance or embracing of geek interests.) With How to Solve the Da Vinci Code and 34 Other Really Interesting Uses of Mathematics (I hate the title), Richard Elwes sets out to make some of the most important fields or problems in math more accessible to the layperson. This is a worthy goal. From the titles of his other books, it looks like this is Elwes’ pet cause: he likes to break mathematics into small but fascinating facts, problems, or ideas that he can explore in fiveminute chunks. As a result, this is the sort of book you can dip in and out of, say at bedtime, for a number of evenings. You don’t have to remember a lot or pay attention to a plot. Nor does Elwes demand much in the way of memory or understanding. He covers some of the basics of algebra in the earlier chapters, but even understanding those is not a requirement. This book doesn’t so much teach you mathematics as it describes the different types and fields of mathematics and some of the most interesting results or problems from them. Perhaps the most complicated concept you really want to understand is prime numbers: if you know what those are, then you’re good. Some of Elwes’ explanations are great. Within this are many “standard” explanations that I’ve seen before and skimmed—that being said, I am a mathematician and a math educator and a math enthusiast, so what’s familiar to me is not necessarily familiar to you, and this might be someone’s first exposure to Russell’s paradox or the theory of sets or graph theory. So that’s not a negative in my book, just an observation that the more mathematicallyinclined have likely come across most of the content here, in one place or another. On a related note, I want to stress that this really is a survey of mathematical results. Some chapters are longer than others, but none go into the type of depth one wants for a truly comprehensible explanation of what’s going on. To reiterate: you won’t learn a lot of math here; you’ll learn about math. Also valuable and important, but it’s a keen distinction. For me, some of the highlights were: Chapter 7, “How to unleash chaos” (chaotic systems and strange attractors); Chapter 15, “How to arrange the perfect dinner party” (Ramsey’s theorem); Chapter 18, “How to draw an impossible triangle” (nonEuclidean geometry); Chapter 19, “How to unknot your DNA” (knot theory); and Chapter 23, “How to build the perfect beehive” (2D/3D tesselation and packing). I like these chapters because they taught me something or reminded me of something I had forgotten, or Elwes’ explanations are particularly thoughtful and useful. For example, the knot theory chapter doesn’t just talk about knots—as the title implies, he mentions DNA, enzymes, proteins, etc. It’s a reminder that mathematical discoveries end up having applications in places you wouldn’t suspect. That’s another thing that this book does well. In chapters such as the one on the fourcolour theorem, or Benford’s law, Elwes emphasizes two important and related things about mathematics. Firstly, mathematical discoveries don’t always happen in isolation or as strokes of genius. We tend to tell those stories, because they are exciting. But for something like Benford’s law or the fourcolour theorem, the discoveries build on decades (or centuries) of work. Several mathematicians independently notice something cool, make a conjecture, fail to prove it, and discard it—only for another generation to succeed where they didn’t. Math is a progressive, ongoing effort. And something we don’t make clear often enough in the classroom is that new mathematical research is still ongoing at a furious pace. We present math as an accomplished, finished product: here’s how you find the missing side of a triangle; the Babylonians knew how to do it, and now you do too! But like science, mathematics isn’t a stable set of knowledge. It behoves us to raise awareness among the general public of how people research math and what we still research. Elwes points to the Clay Institute’s Millennium Prizes as one example. He also mentions a few other questions that remain open problems. While it’s true that genuine mathematics research is not for the faint of heart or the interested amateur, that tends to be true of any specialized discipline. Math is not necessarily more difficult or special in this regard. How to Solve the Da Vinci Code is not the warmest of math books I’ve read. Elwes’ tone is conversational, yes, and has a hint of humour to it. However, the broad strokes of his descriptions necessarily make them less personal than they might otherwise be. He tells a story in most of the chapters, but it’s not with the same level of vivacity that other authors often employ. Instead, his style is one step up from an encyclopedia article. Again, this isn’t really a positive or negative in and of itself—it depends on what you want from a book like this. I, personally, want to know more about the author. I want to know where they’re coming from, what interests them, and hear them tell the story of mathematics from their perspective. We don’t get that here—Elwes never inserts himself into the text—and I feel like that’s unfortunate. But others might find it more objective and informative. Would I recommend? Not for someone like me, who has read a lot of math books and studied math. For neophytes and laypeople? Maybe, depending on the person. I’d rather find a book that gets them more excited about one specific thing, rather than throw everything at them like Elwes does here. Maybe this book is best for someone who already likes math, has a passing interest or understanding of it, and wants to sort of survey the field and see what kinds of things are out there. In that case, there’s definitely 35 good ideas here. ...more  Notes are private!
 none

1
 Mar 23, 2015
 Mar 25, 2015

Aug 09, 2014
 Paperback
 
0465050743
 9780465050741
 3.65
 1,040
 Oct 01, 2013
 Oct 01, 2013

I’m disappointed that so many people seem underwhelmed by the autobiographical parts of this book and feel that they are ancillary to Frenkel’s purpos
I’m disappointed that so many people seem underwhelmed by the autobiographical parts of this book and feel that they are ancillary to Frenkel’s purpose. I disagree: they are, in fact, the heart and soul of Love & Math. Without them, this would be a fairly intense treatise on deep connections between abstract algebra, algebraic geometry, and quantum physics. With them, Frenkel demonstrates how the study of mathematics and a devotion to thought for thought’s sake, to fulfil human curiosity helped him personally through antiSemitism and Soviet persecution. In some ways I was reminded of remarks Neil Turok makes in
The Universe Within
(if I am remembering correctly) about the state of education in many African countries depriving us of staggering potential intellects. How many people, poor or Jewish or otherwise unprivileged, were not as lucky as Frenkel happened to be? Frenkel’s personal recollections are also interesting because they provide a glimpse into the lifestyle and community of professional mathematicians. This is not something most people think about, even people who are scientificallyminded. There are a few famously reclusive or otherwise lonewolf mathematicians out there (though I think that most of them at least maintain some kind of correspondence with a few respected colleagues), but for the most part, twentieth and twentyfirst century mathematics is very much a group endeavour. Frenkel describes how he helped to organize new research in the Langlands Program by gathering together mathematicians from various institutions to hear their input. Belying the stereotypes, mathematics is a very social world. Ultimately, of course, the personal parts of the story are essential to Frenkel’s explanation of why he loves math. Again, I must disagree with those reviewers who pan this book because it doesn’t inspire them to love math … that was never the aim. Neither the book nor Frenkel are naive enough to believe that, I think. But I suspect one reason many people react the way they do when one reveals one’s mathematical inclinations is genuine bewilderment over the idea that a “normal” person could actually love math. As Frenkel points out, even when mathematical achievements are depicted in popular culture, the subject is always a social outsider. (In a way, it’s similar to this whole idea of left brain/right brain people. “Oh, you’re a left brain person!” and, when people find out I teach both math and English, “You’ve got a weird left and right brain thing going on!” But the truth is, a lot of people in “left brain” positions that require logical reasoning are also very creative and passionate and linguistic—and a lot of “right brain” thinkers are also organized and calculating. Humans are diverse, and the stereotypes and categories we create are not that good at classifying us.) The autobiographical elements also humanize what might otherwise be a fairly involved book. When Frenkel talks about loving math, he isn’t pulling a Cabinet of Curiosities here. Don’t get me wrong: I’m all for books explaining elementary math. But I’m pleased that Frenkel tackles much higherconcept, abstract mathematics in a nonetheless accessible and approachable way. I’ve forgotten a lot of my undergraduate math, I am sorry to say. One day I’ll delve back into ring theory and group theory for some fun. I’m pleased by how much I do remember, however. I recognized a great deal of what Frenkel explained, even though some of it still managed to escape me. So when I say Love & Math is accessible, I’m not claiming Frenkel is going to help you comprehend abstract algebra. Rather, he demonstrates some of the concepts that power abstract algebra through some clever diagrams and explanations, and he connects abstract algebra to quantum physics. I particularly enjoyed this latter endeavour. I knew that symmetry was one of the most significant aspects of group theory, but I didn’t understand the specific ways in which group theory actually underlies a good deal of the interactions between subatomic particles. So that was cool. There are many points where Frenkel basically explains the math behind the physics, then says, “Oh, and mathematicians figured this out long before physicists came along and discovered the math was useful.” That’s not to say math is more important than physics (that’s just, like, selfevident), but I love that we can build these models in math without any reference to the physical world … and then somehow, these models become useful in explaining the physical world. That is just mindboggling. As an educator, I also sympathized with another remark Frenkel makes, rather early in the book. He compares the teaching of math in high schools now to the prospect of teaching art by having students paint fences. That is, we barely get to scratch the surface of what mathematics is in high school. Frenkel speaks of quadratics with the disdain only a pure mathematician could muster. But it’s true: I don’t blame students for thinking that math is boring, because the topics we drill into them and the way we do it tends to communicate that fact. You really don’t need to know the quadratic formula—not in the days of Wolfram Alpha—but symmetry? That’s not only important but beautiful as well. Honestly, Love & Math is not going to make you love math, and it was never supposed to. It’s not going to teach you group theory or representation theory, and you probably won’t have any clue what a Riemannian Surface or a Kac–Moody Algebra is after reading the book. (Maybe you’ll understand what a group is, in some way.) If you’re really interested in learning those things, there are books and videos and courses and wikis to help you out. Instead, Love & Math is one mathematician’s story of how he fell in love with math, how it saved and defined his life, and how he feels honoured and awed that he has had the chance to give back to the mathematical community. Frenkel goes so far as to make a weird surrealist movie about loving math … and that is not my thing, but it’s clearly his thing, and I’m all for people doing their thing. So you go, Frenkel. And while you do that, hopefully some of the people who read this book come away with a better understanding of what it might mean to love math, even if they don’t quite share that feeling themselves. ...more  Notes are private!
 none

1
 May 29, 2015
 Jun 03, 2015

Aug 09, 2014
 Hardcover
 
184614678X
 9781846146787
 3.89
 2,060
 Jan 01, 2014
 2014

I math for a living. I mathed, both amateurly and professionally, at school. I math quite a bit. And as a math teacher, I like reading "pop math" book
I math for a living. I mathed, both amateurly and professionally, at school. I math quite a bit. And as a math teacher, I like reading "pop math" books that try to do for math what many science writers have done for science. So picking up How Not to Be Wrong was a nobrainer when I saw it on that bookstore shelf. I’ve read and enjoyed some of Jordan Ellenberg’s columns on Slate and elsewhere (some of them appear or are adapted as chapters of this book). And he doesn’t disappoint. I should make one thing clear: I mainlined this book like it was the finest heroin. Partly that’s because I just love reading about math, but in this case I was also days away from moving back to Canada from the UK when I started this, and luggage space was at a premium, so I was on a deadline to finish this book. I injected chapters at a time into my veins, revelling in that rush as Ellenberg charismatically and entertainingly explores the math behind a lot of everyday concepts and ideas. Unlike similar attempts, however, Ellenberg doesn’t pull the punches. He’s more than willing to go into the higherconcept ideas behind the math, and when it starts getting too esoteric or academic even for this venue, he’s always ready with a book recommendation for those interested in some further reading. Early in my reading, I tweeted I had already decided to give this book five stars because Ellenberg alludes to Mean Girls in a footnote. (Specifically, he says, “As Lindsay Lohan would put it, ’the limit does not exist!’”) That’s really all you need to know about Ellenberg’s writing style and sense of humour. Actually, I’m not all that enamoured with the footnotes in general; they interrupted the flow of my reading and the symbols used to mark them were slightly too small, so I kept missing them in the text—but that’s a design issue. The content of the footnotes themselves is often informative or, as in the case above, humorous. Ellenberg might be a university math professor, but he also has a sense of humour and an awareness of pop culture that helps to make his writing accessible. I’m impressed by the way Ellenberg effortlessly straddles pure and applied mathematics. The child of two statisticians, he clearly has a good grasp and appreciation of the way applied math drives so many areas of society. From economics to gambling, he makes passionate appeals for informed perspectives over simplistic analogies or fallacies. His first chapter criticizes analogies that promote linear thinking about taxation when the very same economists writing these analogies know that taxation probably isn’t linear. He doesn’t argue for or against an increase in taxes, but rather he points out that it’s wrong to oversimplify the concept when trying to sell it to the public. Is a curve really all that much harder to understand than a line? There’s also some great chapters on odds and the lottery, in which Ellenberg recounts how a group of MIT students set up a legitimate operation to bulk buy lottery tickets from a certain game that actually gave them good odds of winning. They made a profit, because they used math to turn a game of chance into a predictable investment strategy (which is more than we can say for the stock market). So, you know, stay in school kids. But actually, the parts about the lottery that impressed me were more towards the purer end of the math spectrum. Ellenberg started discussing, for example, how best to pick the numbers on one’s tickets so that one could maximize the chance of winning at each tier of prizes. It turns out that it’s possible to represent the way of picking these numbers geometrically (yes, as in pictures) and that it’s related to the way we create errorcorrecting codes (which allow us to send instructions to spacecraft, and compress data in JPEGs, MP3s, and on discs). He goes into quite a bit of detail about the more advanced concepts behind these ideas. Later, he points out how correlation on scatter plots corresponds to an ellipse—and we know how to deal with ellipses algebraically, which gives us a good toolset for talking about correlation algebraically too. So, How Not to Be Wrong makes an effort time and again to belie the impression that we often get in school that math consists of a series of discrete topics: arithmetic, geometry, statistics, and the dreaded algebra. We teach it that way because it’s easier to lay out as a curriculum and focus on the essential skills of each discipline. And also because we are boring. If you’re lucky, like me, then as a student you’ll start to see the connections yourself. Circles and pi start showing up everywhere, to the point where suddenly you feel like you’re being stalked, and no amount of infinite series or integration is going to save you. But really, good teachers start showing these connections as soon as possible. We fail students and leave them behind because, in our rush to equip them with the skills we’ve been told they need, we rob them of the idea that math is a creative process, instead fostering this false impression that math is a sterile, difficult, procedural slog. If it is, then you might be a computer. Ellenberg never demands a knowledge of integral calculus, of set theory, or of transfinite numbers. What he does demand is an open mind, a willingness to be convinced that not only does math have a useful place in life (it’s pretty obvious to most people that someone needs to know how to math; they just don’t see why it should be them) but that a deeper understanding of the roles and uses of math can enrich anyone’s life. One can be a believer in the power of mathematics without necessarily worshipping at its altar, and it’s this quest for adherents rather than acolytes that makes this popular math book successful. It helps that Ellenberg’s style is witty. It helps that he is passionate without sounding too evangelical. He weaves in enough history, anecdotes, and allusions to demonstrate that mathematicians’ journeys and the development of mathematics as a discipline has been just like everything else in life: alternately dramatic and dull, intense, occasionally acrimonious. We don’t like to admit it, but we mathematicians are people too. And occasionally we’re wrong, very wrong (like those nineteenthcentury French eugenicists…). The title here is tongueincheek, and How Not to Be Wrong can’t guarantee your future correctness with great certitude. All it can do is help you think more critically, more logically, but more creatively about the problems and questions that you’ll face in the future. Because mathematics is a tool for helping us to do amazing things. You can be a novice, or you can be a proficient user of this tool, but either way you’ll need to pick it up at some point to do a little handiwork. Don’t fear it: embrace it. Oh, and read this book. ...more  Notes are private!
 none

1
 Jul 30, 2014
 Aug 02, 2014

Jul 31, 2014
 Hardcover
 
1845292812
 9781845292812
 3.77
 252
 2008
 Mar 01, 2009

To paraphrase Mr T, I pity the fool who doesn’t see the beauty of mathematics inherent in the world around us. As a teacher, I feel rather complicit a
To paraphrase Mr T, I pity the fool who doesn’t see the beauty of mathematics inherent in the world around us. As a teacher, I feel rather complicit at times in robbing children of the joy of mathematics. The systemic, industrial tone of education does not often lend itself well to the investigation and discovery that should be the cornerstone of maths; I find this particularly true in the UK, where standardized tests and levels are the order of the day. There are times when I am conflicted about how to cover subject matter. I have to find a balance between a breakneck schedule and a desire to achieve the comprehension that only comes with time and careful practice, strive to find the equilibrium between exploring interesting lines of inquiry and curtailing those lines in order to teach what’s on the test. I hope that as I become more experienced finding this balance becomes smoother. For now, though, it’s a struggle. Because the secret that everyone learns as a child and then has beaten out of them by the endless grind of daily mathematics lessons is this: mathematics is not numbers. It is not arithmetic. There, I said it. I gave my students a test today on our statistics unit, which involved data collection: designing surveys, selecting sampling methods and sample sizes, etc. As they worked through the test, a few questioned its connection to mathematics. "This is words!" they protested, as if I were somehow an imposter trying to sneak extra English content into their day. Somewhere along the line—I don’t know precisely where—they developed this notion that mathematics is solely about manipulating numbers. Really, though, mathematics is about relationships between things. Mathematics is a process for understanding the world, as well as understanding theoretical constructs that, while not directly observable in the real world, can still have useful and fascinating properties. Math can be numbers, but it’s also truth, in one of the most fundamental ways possible. This is what Robert P. Crease attempts to communicate in A Brief Guide to the Great Equations. He foregrounds each equation and carefully explains how it became a part of the great canon of mathematics. He also explains why the result is so exciting, not just to mathematicians but to the population at large. I’m pretty enthusiastic about all this crazy math stuff, but Crease manages to stoke even my considerable flames of fanaticism and set my heart racing. The way he breathlessly extols the beauty and utility of Maxwell’s equations or Einstein’s relativity … it’s like a BBC Four documentary in paper form. When it comes to books on popular mathematics, I always try to anticipate how a layperson would receive the book. As a mathematician, I don’t have a problem following the equations and explanations; it comes naturally. It still staggers me how some people are able to understand the intense nuances of some of the higherlevel mathematics involved in quantum mechanics and relativity; I’m somewhat reassured by Crease’s claims that physicists often rejected new developments that required them to learn a lot of complicated new math. Yet I still know what Crease means when he carelessly bandies around certain terminology, expecting his reader to keep up to speed based on a high school education alone. As far as pop math goes, A Brief Guide to the Great Equations is not the most friendly book. I’d probably hesitate to recommend it to casual readers, preferring maybe Zero: The Biography of a Dangerous Idea . For someone very interested in the history and philosophy of science, however, this book would appeal even if one’s math knowledge isn’t quite up to snuff. Crease recounts without fail some of the more interesting scuffles and disagreements among famous mathematicians and scientists; he also carefully lays out his own views on what constitutes a scientific revolution, and the role that developments of equations can have in revolutions. It’s easy enough to follow the history and soak up the spectacle without following the math. I don’t mean to say that you shouldn’t read this unless you’ve studied math in university. If anything, Crease hopefully sheds light on how and why people can find math such an interesting occupation. By reading these stories of how Maxwell and Einstein and Schrödinger dedicated years of their lives to these problems, one gets the sense that the problems are more interesting and worthwhile than the equations themselves indicate. Crease explains how the problems consumed and intrigued these brilliant minds in such a way that, even if one doesn’t understand the nature of the problem—or its resolution—itself, one can still appreciate the passion and dedication involved. Such passion and dedication are more universal than even the mathematics that unites the great thinkers featured in this book. One need not like math to be good at it or to succeed at it in school or in life. One need only appreciate its versatility, utility, and beauty. Crease tries and succeeds admirably in showcasing such attributes through the equations and history that he includes here. Math is beautiful. You just need to open your mind, cast aside the "but I just don’t have the brain for it", and embrace the wonderful freedom of being able to figure out how the world works. ...more  Notes are private!
 none

1
 Nov 27, 2013
 Nov 30, 2013

Nov 27, 2013
 Paperback
 
1408822385
 9781408822388
 3.59
 1,025
 Sep 01, 2011
 Oct 01, 2012

I came across this book while browsing the science section in Waterstones, because that’s where they hide all the good mathematics books as well, and
I came across this book while browsing the science section in Waterstones, because that’s where they hide all the good mathematics books as well, and I was looking for an appropriate math book to give to a fellow math friend for her birthday. (I opted for Ian Stewart’s Hoard of Mathematical Treasures.) Having read Dava Sobel’s explication of John Harrison and the marine chronometer in
Longitude
, I snapped this up without a second thought. Later, I discovered it was already on my toread list. Serendipity! A More Perfect Heaven is a biography of Nicolas Copernicus. As such, it reveals so much more about him than his importance to the adoption of heliocentric theory. I knew that Copernicus was a Polish mathematician who lived in the early 1500s, and that his work was largely adopted on a mathematical basis rather than a physical one. That was about it. I had no idea of his extensive involvement in the Church, including his canonry and relationships with local bishops. I didn’t know that he developed most of his theory early in his life but held off on publishing until a Lutheran mathematician showed up out of the blue to persuade him to share his theory. So in this respect, Sobel fills in some very large gaps. She brings Copernicus to life, giving names to his parents and friends, setting up the relationships and geography that would define him and influence him as he considered the movements of the heavens. As I mentioned in my review of Longitude, I’m sceptical of the “Great Man” theory of history. It’s undeniable, however, that Copernicus’ book influenced a great many astronomers and mathematicians, a case Sobel makes in the last chapters of the book, with Brahe, Kepler, Galileo, and others. Copernicus was neither the first nor the only great proponent of helocentric theory, but he was in the right place at the right time, and he had the right help, to put it forth. While most of the world wasn’t quite ready to accept it, the idea was now there, ripening in the collective unconsciousness of a generation of scientists. Speaking of which, I felt smug during much of this book. As I read about the Church’s attempts to stifle suggestions that the Earth revolves about the Sun, I mentally giggled at the amount of power religion could wield in the face of scientific discovery. But I laughed much too soon, because while it’s true that heliocentric theory has won the day, there are plenty of contemporary issues that have inherited its political controversy. The sad truth is that not much has changed in the past five centuries. Though the Catholic Church itself is much more friendly towards scientific discoveries than it once was, other elements of religion continue to push against science they see as inimical to their worldview. These deniers rail against everything from global warming to evolution to vaccines. These positions aren’t just quaint throwbacks; they’re actively dangerous. Human nature and human society has not changed all that much since Copernicus’ time, and we should not be fooled into thinking so simply because our scientific understanding has changed since then. Fortunately, A More Perfect Heaven also tells us that, eventually, science will prevail. Copernicus’ calculations were just so accurate that they became the gold standard. That wasn’t quite enough for astronomers to accept his model as fact (cognitive dissonance is a really awesome phenomenon). But it kept the Copernican ideas alive long enough to reach the ears of people like Galileo and Kepler. The former’s discovery of Jupiter’s four largest satellites was a philosophical blow to the idea that everything in the skies must orbit the Earth. The latter’s obsession with finding a beautiful mathematical explanation for certain types of orbital problems led him to expand the Copernican model based on all the data he could obtain from Tycho Brahe’s careful observations. A few centuries on, Copernicus was vindicated, and opinions began to shift. This is probably the exciting part of the story, the part that seem most relevant today. But most of the book is about Copernicus himself and his involvement in Varmia, the Prussian province of his canonry. Sobel recounts Nicolas’ various administrative duties throughout his life as a Varmian canon. I was amazed to learn of his wide interests in everything from medicine to economics, though I shouldn’t be have been so surprised. Copernicus even wrote extensively on money reform! He might not have been a Great Man, depending on your point of view, but he was a great man. Sobel departs from the typical biographical style by presenting the middle of the book as a twoact play, “And the Sun Stood Still”. She dramatizes the interactions between Rheticus and Copernicus that persuade the latter to finish and publish his overall theory. Since little in the way of documentation survives, Sobel has to take certain artistic license with this interpretation. It’s an interesting way to do it, and I was a little sceptical I would enjoy the sudden arrival of a play in the midst of a nonfiction experience. Much to my relief, the play is interesting, easy to follow, and actually rather entertaining. Sobel does it again. Like Longitude, A More Perfect Heaven is the perfect type of popular science history. It’s not too long, yet it’s amazing in its wealth of information. Sobel communicates with a passion for her subject that can’t help but be contagious. She takes the time to lay out exactly why these giants are indeed giants, people who made such a significant and lasting contribution to the way we think and operate in this world. These are the types of books that get me excited and thinking about science even as I marvel at the history of such discoveries. ...more  Notes are private!
 none

1
 Sep 28, 2013
 Sep 30, 2013

Sep 30, 2013
 Paperback
 
1444737449
 9781444737448
 3.51
 744
 Aug 01, 2012
 Jan 01, 2013

I can’t resist picking up mathy books when I’m in a bookstore. As a mathematician, I love broadening my knowledge about the field—and seeing what pass
I can’t resist picking up mathy books when I’m in a bookstore. As a mathematician, I love broadening my knowledge about the field—and seeing what passes for “popular mathematics” these days. Thinking in Numbers is a slim volume that promises to “change the way you think about maths and fire your imagination to see the world with fresh eyes”. It didn’t do that for me—but maybe that’s because I already think about maths that way. Daniel Tammet is an exceptionally talented voice when it comes to presenting the inspirational elements of mathematics, so I hope that for people who don’t quite understand why I get so excited about maths, the book does make a difference. I last wrote about why I love math in 2011. Since then, I’ve graduated from university. I’ve completed research in mathematics and had a paper published. I’ve begun teaching math and English at a high school level. All of these changes have deepened, broadened, and otherwise changed my love for math. As a student, math can be a mystery, a puzzle that demands both ruthless logic and amazing creativity, something that can tickle both the left and right hemispheres of the brain. As a teacher, I’ve tried to make my math classroom as “safe zone” where students can learn, and indeed where they can express a dislike for math, if that’s their opinion. Of course, I’m always out on a little bit of an evangelical mission to change people’s minds. But I’m not asking people to love math; I’m just asking them to reconsider whether they actually hate it, whether they are wrong when they say, “I just can’t do math”. Everyone can do math; everyone does math every day. Math is an integral (no pun intended) part of our society. And it’s just wonderful. Tammet captures a lot of these sentiments in Thinking in Numbers. This is a very unusual math book, in that it isn’t really about math. It’s a collection of 25 very short essays on topics that relate to math tangentially. There are precious few equations or formulae in this book. Instead, Tammet takes a what I might even call an intersectional approach to math. In one of my favourite essays, “Counting to Four in Icelandic,” he explores how different languages form words for numbers. Some languages, Icelandic included, have completely different words for the same numeral depending on whether what it describes is abstract or concrete (whereas, in English, we just say four regardless). In another essay, he ponders the recurrence of the motif of nothingness and synonyms for zero in Shakespeare’s works. He connects this to the spread of zero, from the Arabic world through Italy to the rest of Europe, during Shakespeare’s time. The essays are bitesized. This is a book easy to devour over the course of a few evenings: read a few essays, then put it down and mull over them before going to bed. There is a preface but no conclusion, and there is no overarching connection or theme, beyond Tammet’s obvious love for the relationship between life and math. On a related note, the topics are quite varied. There is little to suggest a pattern beyond different connections between math and life that have occurred to Tammet over the years. This might prove frustrating for people who are used to more forthright or even argumentative nonfiction. Tammet isn’t so much presenting an argument as opening the door to another perspective on the topic. It’s an invitation, not one side of a debate. Tammet’s writing style always verges on the intimate and philosophical, and he always leans on anecdotes or autobiographical details to furnish his asides. This can work well—I wasn’t familiar with his name, so his account of memorizing and reciting 22,514 decimal places of pi for a new record was fascinating. His essay expounding upon mathematical models using his mother as an example, less so. The book is at its best when Tammet takes a concrete piece of mathematics—pi, calculus, primes—and links to another field, whether it’s the literature of Tolstoy or the possibilities in a chess game. In this way, he demonstrates how math is more than just a series of problems in a textbook, and it’s not just something mathematicians, physicists, and engineers need in their daily lives. It’s this pervasiveness of mathematics that comes to the fore in this book. The dearth of equations, proofs, and even diagrams attests to this: Tammet is not out to explain mathematics. Instead, he finds and traces the connections between math and life. He talks about how an Amazonian tribe that lacks names for numbers conceptualizes the world. He examines Tolstoy’s use of calculus as an analogy for analyzing history. Having recently read War and Peace, I really enjoyed those little allusions to math. For people who only see the epic as this massive work of literature, however, it might seem strange to think that Tolstoy owes his view of history to math. Tammet teases out the cool, unsuspected ways that math can pop up and connect to parts of our lives, and it’s wonderful. Not every essay in this collection is amazing. I’d probably recommend this to most of my friends, with the caveat that they shouldn't read the book all the way through. Instead, this is a collection where it's appropriate to leaf through the chapters and read those that pique one's interest. Tammet covers enough topics that there is probably at least one essay in here for everyone. I was sceptical, when I saw the title of the book and read the brief description, that Thinking in Numbers could impress me. It looked so thin, so insubstantial, that I expected it would be too light, too far on the popular side of popular mathematics. Instead, Tammet delivers something that I wasn't anticipating at all—and it works. ...more  Notes are private!
 none

1
 Jun 2013
 Jun 02, 2013

Jun 01, 2013
 Paperback
 
0771016964
 9780771016967
 3.12
 34
 2009
 Apr 28, 2009

I read math books for fun. I realize that, right away, this puts me in an unusual portion of the population. It’s not just my fancy math degree that m
I read math books for fun. I realize that, right away, this puts me in an unusual portion of the population. It’s not just my fancy math degree that makes these books attractive. However, I do think that there are some math books written for people interested in math (whether professionally or amateurly), and then there are math books written for people who, usually thanks to a bad experience in school, have sworn off math like they said they would swear off cheap booze. Our Days Are Numbered is one of the latter. In a passionate and personal exploration of shape, algebra, geometry, and number, Jason I. Brown illuminates the fundamental mathematics behind some everyday tasks. While some people will still run away screaming, others will hopefully begin to see math in a new way. Among the topics Brown explores are: converting between units, using graphs to display data, the meaning behind averages, the role of chance in decisionmaking, networks and coincidences, prime numbers in cryptography, fractals in art, and the math behind the mystery of the Beatles’ Chord. Each chapter is bookended by a short, two or threeparagraph anecdote related to its given topic. For the main body of the chapter, Brown gradually develops some of the math behind common tasks. For example, he shows how an understanding of ratio and conversion factors makes converting between units a breeze without any memorization (aside from the factor itself, of course). Later, he explains why the Web and social networking has guaranteed that graph theory will remain a practical and important field of math for a long time. This is not really my kind of math book, and that isn’t even because of the audience or the way Brown presents the math. Rather, I read math books for the story. I’m interested in math books that take a specific topic and explore its history, its present state, and the different ways to interpret it using mathematics. Our Days Are Numbered instead covers a variety of topics. There isn’t anything wrong with this approach. However, each of these topics can be (and has been) the subject of entire, weighty tombs. It’s difficult for Brown to do them justice. Sometimes, such as with the chapter on conversion factors, he does a very thorough job. Other times, such as with his explanation of prime numbers and Internet security, he leaves something to be desired. Also, much of one’s enjoyment will hinge on how one much one likes or dislikes Brown’s writing style. As the chapter titles and subheadings demonstrate, he is a man of corny humour, easy puns, and deprecating remarks towards himself and fellow mathematicians. I can get behind the first and third attribute, and I can ignore the second. Although I think a book any longer might have begun pushing its luck, as it is, I enjoyed Brown’s conversational and easygoing style. Others will find it overbearing and intrusive, however, and there is no escape from it here. So, Our Days Are Numbered isn’t my mathematical cup of tea, but could it be anyone’s? Well, one way in which this book excels is Brown’s unrelenting insistence that math is useful, relevant, and not at all scary. As a math enthusiast and math teacher, the opposites of these sentiments besiege me constantly. I love how Brown comments on the somewhat unique reception math receives at parties: When I tell people what I do for a living, the most common response is a look of dismay, followed by “I always hated mathematics!” This statement is made with relish and without a hint of embarrassment. I don’t think there is another profession out there that gets the same response. Do people state they’ve always hated English? Music? Lawn care? I think not. Tongueincheek, Brown touches on a very crucial and deplorable fact: hating math is socially acceptable. It’s cool to disparage math and one’s ability to do math. To some extent, the aura of nerdery surrounds all of the STEM fields, but scientists and engineers get a little more recognition—people’s eyes might glaze over if one announces oneself as a theoretical physicist, but there is a little gleam of gruding respect. Mathematicians, however … what do they even do? The social acceptability of disparaging mathematics troubles me. Math is the foundation of the other three STEM fields. Science, technlogy, and engineering are all fields that require creative, passionate thinkers. Yet from an early age we send children signals that math is a dull, uncreative subject and it’s OK to hate it for being boring and irrelevant. This is nothing short of educational sabotage. It’s certainly fine for people not to like math, and I understand how parts of the educational system foster that feeling. But we should do everything we can to avoid reinforcing that notion, especially among our children. Hence the power of this book. Brown takes it as a given that math is a useful, powerful tool in the everyday world. He isn’t out to convert everyone to a science or engineering job. He isn’t trying to shoehorn calculus into a discussion of changing a car tire. (As a teacher, the incessant call to include realworld applications and contexts in my lessons wearies me at times.) He is careful not to insist that everyone uses or needs all of this math all the time—you don’t need to know how to use prime numbers in order to keep your online banking secure. But isn’t it nice to know why it is secure? Brown’s nonevangelical stance is refreshing, though it can also be a little frustrating. Our Days Are Numbered lacks a true, cohesive message, aside from the idea in the title. With no introduction and no conclusion, Brown relies on the title and the chapters to come together to create that singular idea. While not essential, some kind of introduction or metanarrative would lend additional structure to this otherwise scattered text. With brilliant mathematics, hardcore mysterysolving, and no small amount of humour, Our Days Are Numbered is a wellwritten and very successful math book. It isn’t anywhere close to my Platonic ideal of what a math book should be—but that’s me being picky. Nor do I think, in the long run, that people convinced math is uninteresting or “not for me” will find their convictions toppled by anything in here. But for anyone who is open to learning about the role of math in everyday life, there is definitely something here, waiting to be read. ...more  Notes are private!
 none

1
 Mar 05, 2013
 Mar 11, 2013

Dec 31, 2012
 Hardcover
 
1402785844
 9781402785849
 3.58
 97
 Oct 04, 2011
 Oct 04, 2011

On my last official day with my Grade 8 class, I did not want to teach them more about fractions. Instead I had asked them to submit a question they h
On my last official day with my Grade 8 class, I did not want to teach them more about fractions. Instead I had asked them to submit a question they had about mathematics—anything, from something they’d learned earlier in the year but didn’t understand to a question that had been simmering since sixth grade. The cards I got back were all across the scale, from earnest to uninterested. Quite a few were about pi. I decided to take the questions and weave them into a broader narrative about the use, purpose, and history of mathematics. I wanted to talk about how we figured out math and discuss some of the milestones in mathematical discovery. Prezi has become a pretty big deal at my university’s faculty of education, but until now I had avoided it. I decided that I should probably make at least one before I was finished my undergraduate degree. Plus, my partner student teacher had the Grade 8s make their own prezis for a history project. So I made my first prezi to talk to Grade 8s about math. Part of my goal as a teacher is to expose my students to the wider world of mathematics, to impress upon them that math is more than just skills and concepts they learn out of a textbook in the fulfilment of curriculum expectations. I want to make the usefulness and purpose of all that math explicit—and I want to go even further and show that math can be beautiful. Finally, it’s important to provide a sense of history and context to all this math. Because the history of mathematics—and the lives of those caught up in it—is intensely fascinating. Or at least I find it so. Stories of love, betrayal, comedy, and tragedy pervade story of math. Because doing math is ultimately an act of discovery and of creativity—and those acts are what make us human. Amir D. Aczel recognizes this in A Strange Wilderness, which is a history of mathematics disguised as a biography of mathematicians. He makes it his mission to relate the stories behind the math, such as Pythagoras’ travels and interesting diet to Archimedes’ famous bathtub epiphany. (Lucky for me, my Grade 8s had not heard the Eureka! story, despite having just concluded their unit on fluids. So I got to tell it to them for the first time!) This is a laudable goal, and one that coincides with my own. Owing to the way it’s taught in school, we often treat mathematics like received wisdom, far more than we do even science. Mathematical concepts just exist, passed down to us by the teacher and the textbook. It’s difficult, if you don’t actually go out and look for it, to realize that someone had to ask the questions and make the leaps that gave us these concepts. These people were all living, breathing individuals at some point in history, with the same mundane concerns as any human being. For reason, though, through a combination of genius and effort and luck, they made a lasting contribution to our wealth of knowledge as a species. Aczel brings a wealth of knowledge and enthusiasm to this endeavour. I discovered a lot of cool things about names I already knew, and I met a few fresh faces as well. I marvelled at the chain of events that led to people like Isaac Newton becoming the juggernauts of their day. Newton’s mother, after abandoning him for a new husband, apparently pulled him out of grammar school to live on a farm. It was only through the intervention of his uncle that he returned to finish his education and end up at Cambridge. I shudder to imagine how history would have played out differently if Newton had stayed on a farm! Of course, a book this size can’t do justice to the history of mathematics or all the mathematicians involved in it. Aczel seems to do his best to hit the high notes. That being said, he makes some curious decisions about who to leave out. In particular, the book seems to start off strong but lose steam, and by the time we reach the twentieth century, great minds like Lebesgue, Zermelo, Russell, Hilbert, and Gödel get cameos if they’re mentioned at all. I don’t know if this is just a consequence of the rather dense nature of twentiethcentury mathematics compared to the previous centuries or if Aczel was worried about the complicated nature of the math. Certainly he focuses less on the math itself and more on the mathematicians, as is the case with the final mathematician, the reclusive Alexander Grothendieck. I guess you can’t please everyone, of course, and Aczel does his best while trying to keep the book to a manageable length. As you might be able to tell, I’m passionate about the history of mathematics. While I’m sure Aczel is too, I have to confess that the stories in this book come across much drier than they should. Maybe it’s a result of reading so many short biographies back to back—it’s just a steady diet of mathematical dessert. Whatever the reason, as much as I enjoyed A Strange Wilderness in small doses, it took me longer to read than I expected. There’s something to be said for books with narrower scopes and their ability to take a detailed look at the lives of a select few. In combination with other resources, for it is certainly not exhaustive, A Strange Wilderness is a fine book on the history of mathematics. People who aren’t that familiar with (or comfortable) with math shouldn’t have a problem reading this book. Aczel will often discuss the details of the mathematics that his featured geniuses discovered. However, he characterizes the most esoteric items (like group theory) in very general terms, and even when he gets a little more specific (such as with his discussion of Leibniz and Newton’s calculus), it’s never too technical. The math in this math book consists mostly of shoutouts, an understanding of which is far from essential for enjoying this book. As usual, it comes down to what you want out of your mathematics book. If, like me, your interest in the history of mathematics burns bright and you’re familiar with quite a few of these lives already, then there are probably better books dealing with more specific topics. You can certainly discover new things in this book, but it won’t blow you away. This is definitely a good starting point, however, for those who know that mathematics has some interesting stories to tell but just aren’t sure where to find them. ...more  Notes are private!
 none

1
 Apr 12, 2012
 Apr 24, 2012

Jan 02, 2012
 Hardcover
 
1926851099
 9781926851099
 3.20
 197
 Jan 01, 2011
 Mar 29, 2011

Do you ever feel like you have let down a book, not the other way around? That if you had been smarter, funnier, prettier, then the book wouldn’t have
Do you ever feel like you have let down a book, not the other way around? That if you had been smarter, funnier, prettier, then the book wouldn’t have broken up with you by text message and started dating your friend, who really isn’t all that much prettier than you and has terrible taste in clothing and music and restaurants anyway? No? Just me? OK. I kind of feel that way about Napier’s Bones. I first heard of this book from a “Big Idea” piece on John Scalzi’s blog. It sounded amazing: mathematics as magic! People, called numerates, who can see and manipulate numbers. I had a coworker this summer who has a form of synesthesia where numbers move around for her, and I was really curious about this phenomenon. Derryl Murphy’s concept reminds me of that, and of course as a mathematician myself, I’m fascinated by the idea of being able to manipulate numbers in a very real way. So I was excited for this novel and bought it new a few months later. Alas, this is one of those times when the premise is far superior to the execution. For the first few chapters, this is an OK book. Indeed, my mathematical interests had me positively tingling as I read about Dom’s acquisition of an adjunct, the shade Billy, and his newlyminted status as a fugitive from a shadowy opponent. It was an in media res opening that promised Murphy would keep the action going right until the last page. For the most part, he delivers on this promise, which is one reason I decided to go with two stars instead of one. I have many criticisms of Napier’s Bones, but “dull” is not one of them. The cracks are tiny but appear early. Murphy loves his exposition, and although Jenna is by no means a minor character, her primary role for the first half of the novel is as a listener to Dom’s Mr. Expositionpants (TVTropes). The action/travel sequences are really just what happens in between the lengthy conversations in which Dom explains how numbers behave, how numerates manipulate them, how mojo enters into the equation, etc. Jenna nods and smiles. It’s the most unsatisfactory way to explore a mythology and a magical system; I wish Murphy had put as much effort into unfolding his universe as he did constructing it in the first place. The real trouble begins about halfway through, when Jenna and Dom get rescued from nearcertain death by a mysterious, defrocked priest who introduces himself as Father Thomas. It turns out that John Napier is back from the dead, has possessed someone important to Dom or Jenna, and is after some of his old artifacts in a quest for ultimate power. Fair enough. I mean, his name is in the title, so I was expecting Napier to show up—in body or in spirit—at some point, and I was pretty sure Napier’s actual bones would be an important part of the story. I have no problems with this. Once again, however, I take issue with how Murphy communicates all this information. (And I could have done without being told, almost every time his name comes up, that Napier invented logarithms. I get it.) Father Thomas explains why it is so important for Dom and Jenna to hop on a flight he has booked them to Scotland. And then we never see Father Thomas again. When you introduce a character for a single chapter whose only purpose is to provide major exposition and a plane ticket, you are doing something wrong. So Dom and Jenna hop the pond to Scotland, where they gallivant across the countryside, searching for several important artifacts. They meet another ally in their quest, in the form of intelligent numbers who collectively choose to call themselves “Arithmos”. I wish I were making this up. When the talking numbers enter the story is where I draw the line and where Napier’s Bones goes from slightly flawed to outright bad. Murphy’s interesting idea about numbers being a form of magic degenerates into a messy equivocation of magic and quantum mechanics. With each chapter, he introduces new rules—and exposition to go along with those rules—and more conditions for victory (or failure) on the part of Dom and Jenna. I dislike it when magical systems don’t feel consistent but instead appear to change based on the needs of plot. Speaking of which, the ending itself is somewhat of a literal deus ex machina, at least as far as I can tell. By the time we got that point, I was not so interested in the story any more. The plot had become hard to follow, and my emotional connection to Dom and Jenna was tenuous. This is probably the dealbreaker, in my book, even though it is the most subjective part of the relationship between reader and story. I can handle oppressive levels of exposition and poorlyconstructed systems of magic. But ultimately a story is about the reader connecting to a character (or characters), and that did not happen here. Napier’s Bones is just a mess. Its narrative is jumbled, chaotic, and confusing. Its themes are feeble and spread thinly across a book that is longer than it needs to be and still feels far too short. The “magical system” that underlies the story is unsatisfactory and, worse, feels completely arbitrary. The characters start off as interesting and actually become less welldefined as the story progresses. For all of these reasons, I had a difficult time feeling anything more than ambivalence toward this book. Is it me? Did I do something wrong, Napier’s Bones? Am I too mathy for you—was that voice in my head going, “This isn’t why mathematics is magical!” too loud? Did I say the wrong thing in front of your parents on that one Saturday night when I was tired from a long day at work and they dropped by, despite the fact I told you to tell them Saturdays weren’t good for me, and I would prefer that they give us advanced warning so I could at least tidy up the place, because it’s not like you ever bother to do it? Just … give me a sign, please. I can change. Maybe it’s better if I just see some other books for a while, you some other readers. We can get some perspective. A lot of perspective. ...more  Notes are private!
 none

1
 Feb 07, 2012
 Feb 10, 2012

Mar 29, 2011
 Paperback
 
1841196509
 9781841196503
 3.37
 279
 Sep 12, 2003
 Feb 01, 2010

My two teachables, the subjects which I will be qualified to teach when I graduate from my education program in May, are mathematics and English. When
My two teachables, the subjects which I will be qualified to teach when I graduate from my education program in May, are mathematics and English. When I tell people this, they usually express surprise, saying something like, “Well, aren’t those very different subjects!” And it irks me so. They’re not, not really. Firstly, mathematics and English are both forms of communication. Both rely on the manipulation of symbols to tell a tale. As with writers of English, writers of mathematics have styles: some are elegant yet terse, seemingly expending little effort while getting their point across with an admirable economy of symbols; others are expansive and eloquent, elaborating at some length in order to furnish the reader with an adequate explanation. Secondly, as with English, mathematics is very much grounded in philosophy and history, and it is a subject that is open to deep, almost spiritual interpretation. If you balk at that last idea, don’t worry. You’ve probably had it drilled into your head since elementary school that in mathematics there is only one correct answer! How could such a reassuringly logical subject be open to interpretation? Despite its apparent objectivity, mathematics is just another human endeavour, and like all our mortal works, it is vulnerable to our flaws, foibles, and fits of passion. Mathematicians can be just as stubborn and argumentative, if not more, than other people. There are many famous follies and feuds in the history of mathematics, and that is one of the reasons I enjoy learning about it so much. Infinity is one of the mathematical concepts most central to those feuds. It’s one of the areas where math rubs up against the spiritual realm—for, as some mathematicians and philosophers have wondered, what is infinity if not God or some kind of greater being? So it seems natural to look at our shifting views on the infinite along the continuum of the history of maths. In A Brief History of Infinity, Brian Clegg does just that, following the classical, somewhat Eurocentric development of math from Greece to Rome, then zigzagging down to the Middle East and India before flying back to Britain, France, and Germany. As with most tricky math concepts, the trouble with infinity begins with its definition. One must be very careful with definitions in math—for example, it is not enough merely to say that infinity means “goes on without end”. After all, the surface of the Earth has no “end”, but that does not mean the Earth has infinite surface area! Rather, the surface of the Earth is unbounded. Grasping the idea of infinity as “not finite” is easy enough, though: there is no “last” counting number, because you can always add one to the largest number you can conceive, and suddenly you have a new largest number. So infinity is a quicksilver of a concept: intuitive and easy to grasp, yet also elusive and far too fluid for some mathematicians to handle. The Greeks, with their mathematics strictly confined to the geometric figure, would have no dealings with the infinite. Infinity confused Galileo, who nevertheless bravely meditated upon it in his final days. And the shadow of infinity hangs over the controversy of the calculus that caused the divide between Newton and Leibniz, and correspondingly, between Britain and the Continent. The story of infinity gets even more interesting after that. In general, I love the history of mathematics during the 1700s and 1800s. So many brilliant minds pop up during that time: as Newton and Leibniz exit, Euler and Gauss enter. Later, Cauchy and Weierstrass formalize the concept of the limit, which does away with any need for infinity in calculus at all! There are plenty of names and plenty of stories—and this is where A Brief History of Infinity starts to lose its edge. The first few chapters of this book are fascinating. Clegg devotes a lot more space to the Greek philosophers than others might, going so far as to mention some of the more obscure ones, like Anaxagoras. He provides a considerably detailed development of Zeno’s paradox (well, paradoxes) and a nice, if basic, grounding in the idea of an infinite series. Clegg lays the ground well for what will come in later chapters, all the while emphasizing the reluctance of the Greek philosophers to abandon the solidity of numbers found in the real world. But as we get closer to those magical two centuries following the great Newton–Leibniz schism, the story of infinity gets more complicated as more people get involved. This book is very similar to Zero: The Biography of a Dangerous Idea . In my review of Zero, I praised the author’s ability to stay focused: The story intersects with the lives of many famous mathematicians, but the obvious slimness of this book testifies that Seife managed to distill only what was necessary about their lives in his quest to explain the mystery of zero. To be fair to Clegg, this book is almost as slim as Zero. And although he happens to go off on many a tangent, he at least has the ability to find his way back on track quickly enough—that is, his tangents are interesting and informative. He sometimes seems to go into more detail than is strictly necessary to get the point across, and once in a while he waxes melodramatic—as is the case when he links Cantor’s madness to his study of infinity. Overall, however, Clegg’s writing is crisp and clear. I’m also impressed by the detail and depth of Clegg’s explanation of the math. He goes so far as to list and briefly elaborate upon each of the axioms of ZermeloFraenkel set theory! I was half expecting him to mention the Banach–Tarski paradox after that—he doesn’t quite get there, but he does explain the difference between ordinals and cardinals, develop the continuum hypothesis, and even mention Gödel’s Incompleteness Theorem. He tackles whether imaginary numbers are truly all they’re cracked up to be. And he even discusses nonstandard analysis—we didn’t even learn about that in university. Don’t let my awe scare you away, though. Rather, think of it like this: if you are not particularly mathematical and read this book, you will gain a wealth of knowledge. You will be fun at parties! If you are particularly mathematical, then depending on how much you like the history of math, you might already be familiar with most of these anecdotes. But the book will still be fun to read, and chances are you will learn at least one or two new things. So I would recommend A Brief History of Infinity to most people—perhaps not with the same zeal that I do Charles Seife’s Zero, but with a similar hope in mind. I hope this book, or at least my review of this book, demonstrates why I find math, as well as the history of math, so fascinating. It’s not just all about numbers, solving for x, and finding the One True Solution. Mathematics is a subject with a long and storied past, one that is fun to explore by looking at the humans who progressed—or regressed—throughout the centuries. A Brief History of Infinity is a book in this mould. While its organization and its focus leaves something to be desired, its scope and ambition do not. ...more  Notes are private!
 none

1
 Dec 19, 2011
 Dec 23, 2011

Jan 08, 2011
 Paperback
 
0140296476
 9780140296471
 3.94
 5,619
 2000
 Sep 2000

My grade 11 math teacher gave this to me, and I remember reading it and loving it. Here I am, three years later, returning to Zero for a second read.
My grade 11 math teacher gave this to me, and I remember reading it and loving it. Here I am, three years later, returning to Zero for a second read. No longer the gullible high school student (now a gullible university student!), I'm apt to be more critical of Zero. Nevertheless, it stands up to a second reading and both inspires and informs. Imagining a world without zero is probably difficult for most people. It was especially difficult for me, as a mathematician who grew up learning calculus and understanding that zero is just another number. Even with Charles Seife leading the way in the first chapter, I still have trouble comprehending this idea that entire civilizations rose and fell—and achieved great things in between—without the concept of a mathematical zero. In that respect, Zero acts as a history of the development of an idea, one that began in Babylonia and spread, via Alexander the Great, to India, where it flourished. Seife's history is necessarily balanced between East and West in this case, as it's impossible to discuss mathematics without discussing India. That being said, I would have liked to learn about how China regarded zero, even if Chinese mathematicians contributed no new developments to the number's importance as their absence from this book seems to imply. This one oversight overlooked, Zero is not your typical history book that starts in ancient Egypt or Greece and insists everything we know flows from there. What's admirable about Zero is Seife's ability to focus on zero. The story intersects with the lives of many famous mathematicians, but the obvious slimness of this book testifies that Seife managed to distill only what was necessary about their lives in his quest to explain the mystery of zero. I'm not trying to imply, "Short books are easier for nonmathematical people to understand," but that's part of the attraction. Although it's heavier on the equations than I remembered, I would still feel comfortable recommending Zero to my nonmathematicallyinclined friends. Firstly, Seife's writing is accessible, even when loaded with equations. As long as you have some basic arithmetic left over from high school, you can follow along. And I'd definitely recommend this book to high school students, like I was when I first read it: it's one of those books that opens the mind. Secondly, the narrow focus acts like a window into the history of mathematics. I have A History of Mathematics sitting next to Zero on my desk, and while the former is more complete, I somehow suspect the latter is more appropriate for a general audience. In other words, Zero is a good gateway drug. Where Zero starts to show its seams is in Seife's rhetorical ability, which stretches itself thin even over so thin a volume. He's too dramatic for my taste, especially as he recounted the attitudes and fate of the Pythagoreans. And he's always eager to remind us of how "powerful" zero is. While I agree that zero is a pretty cool number, the constant refrain felt somewhat forced after a while, pulling me out of the book instead of keeping me comfortably ensconced in this little tutorial. Seife devotes only cursory glances at the philosophical arguments offered for or against the acceptance of zero; he tells us about Aristotle's rejection of zero but goes into little detail. While I'm sure he wanted to avoid turning the book into a text on Aristotelian philosophy, I feel like there are gaps here that, if not filled, could have been covered with a more attractive carpet. Not perfect, not as mindblowing as some mathematical literature I've read, Zero makes it mark because it's adequate at explanation without going overboard. I'm not sure what else to say: if you're interested in the subject, this is a good place to start. And even if you're not, hey, it's only 250 pages. What have you got to lose? Nothing. Zero! ...more  Notes are private!
 none

2
 Jan 23, 2010
 Jan 23, 2010

Jan 23, 2010
 Paperback
 
0385665776
 9780385665773
 2.92
 130
 Sep 06, 2007
 May 12, 2009

This is perhaps the first time I have condemned a book for its concept but applauded it for its content. Writing a book that examines the integers 1 t
This is perhaps the first time I have condemned a book for its concept but applauded it for its content. Writing a book that examines the integers 1 to 9 on a perchapter basis is just silly. It's also impossible; the properties of these numbers are inextricably bound up in the properties of all other numbers. Andrew Hodges knows this, and indeed makes no attempt to conceal the fact that the structure of this book is a lie. In each chapter, Hodges gleefully digresses into topics that have only the most tenuous of connections to their titular number. Some of these topics are very interesting and worthy of entire books in their own right. Hodges covers electromagnetism, quantum chromodynamics, Fermat, Fibonacci, and some cryptography too. But One to Nine's incredible breadth is, somewhat predictably, also a weakness. Hodges provides able summaries of these topics, but in his whirlwind tour of the first nine positive integers, he can't cover the topics in much depth. Although Hodges' explanations of some fairly complicated mathematical concepts are accessible, I don't think people would find them very helpful. It doesn't help that Hodges jumps from topic to topic, and even from thought to thought, with the pace of a frenzied beaver on speed. And while I've never been high, reading parts of this book made me feel like I imagine being high would feel: "to consider Twoness is to confront broken symmetries in a world crammed with them." Um . . . OK, sure. "Twoness?" Really? Hodges' writing is a bizarre mix of airy and wistful. His attempts to come off as jaunty are merely jarring, owing to his constant transitions from one topic to another. And, oh my, I have never seen so many rhetorical questions in my life. Excess and superfluous much? As a result, Hodges undermines the very effect essential to a popular mathematics text: the sense of wonder that mathematics evokes. He tries for it, and once in a while gets close. But before the monotonous tour guide can say, "And we're moving. . ." Hodges has gone off on a parallel track, and you're forced to catch up rather than stick around and appreciate the beauty of what's just been covered. One to Nine did little to augment my admiration of number (and much diminished any remaining shred of interest in Sudoku). Hodges also makes sporadic references to Desperate Housewives, climate change, and Alan Turing. Alan Turing, I can understand, because his contributions to cryptography, computer science, and mathematics are pretty important. That doesn't quite justify Hodges' obvious hero worship, however. While mathematics has a role to play in answering questions about climate change, Hodges never actually addresses that role. Climate change just gets mentioned, much like Desperate Housewives (allusions to which I am at a loss to explain at all). Then in the last chapter, the book abruptly shifts from its focus on the properties of number into a polemic about mathematics in education and how Alan Turing met an untimely end. In both cases, Hodges makes some good points. Yet I don't appreciate being ambushed by such arguments at the end of the last chapter of the book. All of this makes for a rather dense barrier to the main event. It's clear that Hodges knows what he's talking about. He just didn't convince me of his ability to talk about it well. Nevertheless, despite his meandering through the mathematics, Hodges does make it possible to eke a semblance of erudition from this book. I'm not sure it's worth the effort. One to Nine is by no means a bad book, but it does not excite me or delight me in the way that a book like A Short History of Nearly Everything does. Maybe it needed more Twoness. ...more  Notes are private!
 none

1
 May 29, 2010
 Jun 2010

Dec 25, 2009
 Paperback
 
0312427808
 9780312427801
 3.94
 14,447
 Jan 01, 2003
 Feb 03, 2009

**spoiler alert** After a somewhat bumpy relationship with literary fiction for the past few weeks, The Housekeeper and the Professor delivers an enjo
**spoiler alert** After a somewhat bumpy relationship with literary fiction for the past few weeks, The Housekeeper and the Professor delivers an enjoyable experience that reassures me some literary fiction is sublime. Full disclosure: I am studying mathematics, so I do find the subject matter in this book fascinating. I understand that less mathematicallyinclined readers might not, but I don't see that as an excuse for enjoying this book any less. The Housekeeper and the Professor isn't a textbook, nor is it a treatise. Most of the math is high school level, and one doesn't need to pay attention to it to follow the story. Instead, one must focus on the emphasis on mathematics and the way the characters in the book embrace it. The Professor never misses an opportunity to observe an interesting relationship between two numbers or educate the Housekeeper or her son, Root, about some sort of mathematical proposition. Ogawa perfectly captures the way I feel about math, the reasons why I'm studying math in the first place. There's something transcendent about this search for truth through numbers . . . math allows us to express aspects of the universe that would otherwise remain invisible. You don't have to be a math genius to comprehend this, as Ogawa demonstrates with her character of the Housekeeper. I'm not just fond of these people's titles. Ogawa is very stingy with her names: a famous baseball player gets one, and Root's designation is more of a nickname than a title, but everyone else is out of luck. The Housekeeper and the Professor are exactly that; the former has a "Director" as her boss and the latter has a "sisterinlaw" as a minor antagonist. Most of the time, when a character lacks a name, that means he or she is minor and unimportant. Obviously this is not the case here, and by making almost everyone nameless, Ogawa manages to make it feel normal. Still, the lack of names can make it hard to establish identity. While I contend that Ogawa succeeds at this for all three of the main characters, I understand how one could find it difficult to empathize with them. The characters' namelessness is fitting considering the novel's subject matter. Like the mathematics that he studies, the Professor is an abstraction. In fact, owing to his condition, he is a Professor of Mathematics—and that's all he is. His memory loss has shrunk his world such that math is the only thing he has left. He grasps numbers because they haven't lost their meaning for him like the rest of the world has: whether it's 1975 or 1990, 220 and 284 will still be amicable numbers. To some degree, one can say the same for the Housekeeper. After her young pregnancy, she takes up the only work she knows how to do; since then, this has been her life. Hence, these titles are fitting enough identities for the characters. They would be stifling if Ogawa failed to develop the characters beyond their titles; fortunately, that's not the case. For a story set in Japan, The Housekeeper and the Professor is completely accessible to the Western audience. I could almost forget its setting and think it takes place in North America. The most important relationship, in my opinion, is the one between the Professor and Root. It takes on the qualities of a fatherson relationship that anyone will recognize. Not only does the Professor educate Root and challenge him, but Root in turn looks after the Professor, cares for him, and rekindles the Professor's love of baseball. This shared enthusiasm for baseball is one of the few ways in which the Professor ever comes close to transcending the eighty minute barrier on his memory. By this I mean that, whenever Root engages the Professor in a discussion about baseball, the fact that Enatsu has long since left the Tigers seldom matters . . . suddenly the Professor has something other than mathematics he can talk about to a likeminded person, and his little world has just grown bigger. Root matures considerably throughout the book. At first, the Professor's manner startles him, but he quickly grows accustomed to the rituals he must endure. Soon, he becomes not only fond but protective of the Professor. At one point, the Housekeeper has to leave to buy cooking oil. She is worried about leaving Root alone with the Professor, but Root assures her that it's fine. However, when she returns, Root has accidentally cut himself with a kitchen knife. It isn't a big deal, but after, Root is cold toward his mother. When she asks why, he says, "I'm mad because you didn't trust him. I'll never forgive you for that." It's a small scene, but it's significant, for it shows a strength of character and a sense of judgement far advanced of Root's age. Despite such incidents, their time at the Professor's house strengthens the relationship between the Housekeeper and her son. It's the Professor who suggests—nay, practically orders—that the Housekeeper have her son come to his house after school so he doesn't have to be a latchkey kid. She cooks dinner for three now instead for one, and the arrangements are more domestic—like a family, but not quite. The Professor is always happy to show Root and his mother some new numerical notion. When she first meets the Professor, the Housekeeper is fascinated by his interest in math and his gift for teaching. However, it's Root's involvement that truly encourages her budding appreciation of mathematics. As she sees the Professor and Root explore math, both through Root's schoolwork and the problems posed by the Professor, she joins them in order to avoid feeling excluded—and in so doing, she becomes enchanted by math. The only other character of any importance is the Professor's sisterinlaw. She only appears when there's trouble, and she seems curiously intractable and eager it misunderstand. When never get a complete picture of how she feels about the Professor, other than that she feels compelled to care for him. I didn't enjoy the confrontation between her and the Housekeeper and didn't quite understand the significance of the Professor settling matters by scribbling down Euler's formula. Indeed, the inscrutability of this part of the plot is one of this book's few miscalculations. In almost every other respect, Ogawa manages to hit just the right notes. The depiction of the Professor's anterograde amnesia is realistic and harrowing. The poor man only has an eightyminute memory and walks around with notes clipped to his suit! Throughout the book, the Housekeeper has so many conversations with him, learns so much from him, even takes him to a baseball game . . . and he remembers none of it. For him, it's always 1975. Enatsu is still a famous pitcher for the Tigers. Ogawa shows us how the Professor's condition makes it difficult for him to live a fulfilling life. Oh, he enjoys himself when he's solving a math problem and constructing a proof . . . but he will never remember all of the proofs he's constructed prior to that, all of the contests he's won, or any of the great new developments in number theory since 1975. The thesis that the Housekeeper finds beneath the false bottom of a cookie tin containing baseball cards gives us a glimpse into the Professor's past life, one from which he is now irrevocably separated by his accident. He can experience transitory joy, but he no longer has the capability for lasting satisfaction or contentment. Then when the Professor's amnesia worsens toward the end of the book, it's just heartbreaking. Here is a man who is so kind and thoughtful, and he's already had so much taken from him. Now he's lost the rest, and his eightyminute memory becomes a zerominute memory. He lives entirely in the present, which is not as wonderful as it might sound. As a result, Ogawa reminds us that the past has immeasurable value. It helps form our personality and is full of a vast collection of experiences, both good and bad, that contribute to how we understand the universe. The Professor was always happy to meet Root and teach him mathematics. But he would never understand the joy of watching Root grow up over a number of years, never watch Root's love of mathematics blossom into a passion that would lead to teaching math in elementary school. This experience is forever lost to him. I wouldn't call the ending to The Housekeeper and the Professor sad, but it certainly wasn't happy. Although there is a little romantic tension between the two eponymous characters—and the Professor becomes a strong father figure for Root—this is not a romance, and there is no happilyeverafter. The Professor's anterograde amnesia becomes total, and he loses what small amount of independence he has managed to retain. The Housekeeper and Root must move on to other jobs, must continue on with their lives without the Professor, without his lectures or his mathematics or his notecovered clothing. It's a separation more profound than death, for they must go on with their separate lives, changing and growing even while the Professor continues to forget, and forget, and forget. . . . Memory is fragile and tenuous, yet oh so important to our conception of self. Yoko Ogawa reminds us of the importance of memory in a fascinating, unassuming way. The Housekeeper and the Professor is a whisper of a novel, something that will take root in your mind and blossom into a fond memory. ...more  Notes are private!
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1
 not set
 Dec 03, 2009

Oct 20, 2009
 Paperback
 
0307291170
 9780307291172
 4.26
 6,311
 Jan 01, 1996
 unknown

Welcome to our universe. We only get one (regardless of however many there are). The search for a more complete understanding of our universe, out int
Welcome to our universe. We only get one (regardless of however many there are). The search for a more complete understanding of our universe, out into the macroscopic and deep into the quantum foam, is a search for an understanding of who we are, why we're here . . . and where we might end up. This is a book of sublime thought that takes the ivory tower and turns it into an ivory ladder that anyone, given inclination and opportunity, can choose to ascend, one rung at a time. I cannot emphasize enough how important this book is to physics: it's a
Philosophiæ Naturalis Principia Mathematica
for the masses. Unlike Newton's groundbreaking scientific treatise, A Brief History of Time doesn't contain Hawking's own body of scientific work, but rather an overview of the development of theoretical physics, including relativity and quantum mechanics. Yet it's as important as the Principia, for in a single book we have a comprehensive look at a field of study often considered by the general populace to be obscure and esoteric. In a few hundred pages, Hawking demonstrates why we should be interested in the universe. He explains how relativity overturned the classical theory of Newtonian gravity, how quantum mechanics has exposed the flaws in relativity, and how physicists continue to search for a theory of quantum gravity to unify relativity and quantum mechanics in a Theory of Everything. Relativity and quantum mechanics are the foundations of physics, chemistry, and biology as we know them today. While A Brief History of Time cannot, obviously, serve as a detailed explanatory text of every phenomenon, it acquaints the reader with the two fields that underly all phenomena, from optics to cell division. Reading this book gives you understanding that will help you with future intellectual inquiries. Even if you're not interested in science, however, and have no intention of going further than this book, there's still something in here if you've ever wondered how the universe works. Hawking does not deliver a dry lecture consisting of complicated formulae and logicallyimplacable mathematical theorems. There are new terms, and some of the concepts might seem counterintuitive, but Hawking always has an analogy or concrete example at the ready. I won't claim that you'll understand everything he discusses—I know I didn't. And, as Hawking points out, even the most brilliant scientists still don't have a complete understanding. At the very least, you'll have a much better appreciation of what we don't understand, and why current scientific theories about the universe work but still have certain problems. I am immensely grateful to my grandparents, who gave me this book as a Christmas gift, for its illustrations make it superior to previous editions. Utility aside, let's be shallow for a moment: the illustrations make the book so beautiful. This is a true coffeetable book (and probably, for many people, that is all it will ever be, sadly). It's well worth reading, but it's also perfect for keeping in the living room—you can always open it up to an interesting illustration and show off your physics knowledge! In fact, I would go so far as to say that understanding these two concepts (that there may be more than four dimensions, and that curvature in three dimensions is a straight line in four or more) contributes to an understanding of the majority of this book. The barrier here is one of geometrical conception and not physics knowledge; i.e., you don't need to be able to solve its equations to understand relativity. Some of the illustrations are somewhat redundant or even confusing. Others are invaluable supplements. For example, both of the books hinge on the idea that the universe has more than three dimensions: there's at least four (spacetime), and probably more like 11 or 26. Now, when Hawking uses the existence of these extra dimensions to explain how relativity results in the curvature of spacetime or why gravity is weaker than it should be, it makes sense—but we can't visualize it, because it's impossible to visualize any more than three dimensions. The illustrations depict fourdimensional space as a threedimensional diagrams (with a spatial dimension removed and replaced by the time axis), which at least gives a better idea of what Hawking means by, "The mass of the sun curves spacetime in such a way that although the earth follows a straight path in fourdimensional spacetime, it appears to us to move along a circular orbit in threedimensional space." This book isn't perfect. Hawking's original treatment of time travel, for instance, leaves much to be desired. He rectifies this in The Universe in a Nutshell, providing a much more comprehensive look at how general relativity might allow time travel. Yet other parts of the second book heavily retread what Hawking discusses in A Brief History of Time, to the point of using similar or identical examples. This is not surprising, considering the two books were published separately. My advice is that if, like me, you read these books backtoback, then skip over any parts of The Universe in a Nutshell that you like. Even Hawking admits in the foreword that the book is designed to be less linear than A Brief History of Time; delve into those chapters that interest you and don't worry too much about reading every single word on every page. Regardless of how one reads it, A Brief History of Time should be required reading. As its track record indicates, it has well served its purpose as an accessible physics text. This is a book that presents theoretical physics as a comprehensible, cohesive conversation between Hawking and the reader. This edition, with its illustrations and the inclusion of a second book, The Universe in a Nutshell, is perhaps the best edition of the two books published to date. ...more  Notes are private!
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2
 Feb 13, 2010
 Feb 14, 2010

Mar 31, 2009
 
0345470214
 9780345470218
 3.14
 1,427
 Jan 01, 2008
 Aug 05, 2008

Overall, the word I'd use to describe this book is "shallow." Clarke and Pohl, two big names in SF, have managed to take two interesting concepts (Fer
Overall, the word I'd use to describe this book is "shallow." Clarke and Pohl, two big names in SF, have managed to take two interesting concepts (Fermat's Last Theorem and alien sterilization of Earth) and turn them into a boring book. It's as if they said one day, "Well, we've succeeded at everything else in literature; now we have to succeed at writing a bad book!" My major problem with the book is the lack of any consequences, or really, any conflict at all. At points the story threatens to inject a conflictsuch as when Ranjit becomes an unwitting accomplice to pirates and subsequently spends two years being tortured in prison. For a moment, I thought that might produce some genuine unhappiness that could mar this otherwise oppressively upbeat book. Unfortunately, that was not the case. Even toward the end, tragedy loomed on at least three separate occasions, yet somehow everything turned out all right. It's not that I have a problem with happy endings; I loves me a good happy ending. But happiness without struggle against adversity is hollow. I've read much better science fiction than thisthis book feels like it was written for a fourteenyearold as a "My first science fiction novel"it's patronizing. Our "protagonist", if indeed we can call him that, Ranjit, stumbles through his life without ever having to make any important decisions. Everything just sort of falls serendipitously into place. Oh, and along the way he discovers a miraculously short proof to Fermat's Last Theorem. Meanwhile, alien overlords have sent alien minions to sterilize Earth of dangerous humanity. But it's OK, because the overlords change their minds and then the minions befriend humanity. As with the possibilities of tragedy I mentioned above, the book tempts us with the prospect of a meaningful theme when it touches upon the dangerous nature of an EMPlike weapon controlled by "the Big Three"Russia, China, and the United States. Will this lead to an Orwellian future in which these Big Three control the only military forces on the planet? And will first contact with an alien species ironically lead to allout planetary war even as the countries of humanity approach global peace? Nah. It's much easier to just tell us in an epilogue that everything worked out fine, and thirteen thousand years everything was still going fine. I'd have to say that even The Da Vinci Code better integrated an esoteric academic subject than this book. I understand that not everyone loves math as much as me, so I tolerate the explanations of Fermat's Last Theorem. But it wasn't even interesting. It had no relevance to the plot, because there was no plot. And since this book had Arthur C. Clarke's name on the cover, this has been the cause of severe disappointment for me! ...more  Notes are private!
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1
 not set
 Dec 22, 2008

Dec 01, 2008
 Hardcover
 
0618784608
 9780618784608
 3.41
 1,100
 2008
 Aug 12, 2008

I agree with those reviewers who found this book somewhat less awesome than they initially anticipated. Coming from a math background, and as surround
I agree with those reviewers who found this book somewhat less awesome than they initially anticipated. Coming from a math background, and as surrounded by technology as I am, I think that the book would have had more of an impact with me if I knew less about these issues already. And that's why I'm giving it such a high rating: it does a good job educating, and I like that in a book. Stephen Baker's tone is conversational and analytical as he takes you through successive chapters that introduce us to the Numerati, the mathematicians, engineers, sociologists, and marketing gurus who are analyzing and modelling humanity. The Numerati's interests are varied, from the workplace to the bedroom. As a mathematician, I enjoy books that educate people about the realworld applications of math and remind them that it's not just a dry, dusty discipline full of formulas and equations. The medical chapter intrigued me the most. Baker interviews several people working with Intel on technology for modelling people's behaviour at home. These machines would alert doctors when a patient deviates from regular behaviour, thus allowing doctors to know if someone's weight dramatically decreases or if an elderly patient has fallen. The potential applications of our ability to model and predict human behaviour have immense implications for improving our medical industry, which is plagued with difficulties in both Canada (go universal healthcare!) and the U.S. (with its privatized healthcare). Baker does mention privacy concerns, but he mostly glosses over these, pointing out that there is a difference between disclosing one's "personal data" and one's "identity." I see his point. I also see why many people are concerned about the role of privacy in the Google age. I would have liked to see some more specific information on privacythe book in general feels short. In places, it could be much more specific, expansive. But I suppose that Baker wanted to keep it light enough to attract the curious reader, and I will forgive him for that, because it was interesting and informative. I'd read a sequel. ...more  Notes are private!
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1
 not set
 Oct 19, 2008

Sep 23, 2008
 Hardcover

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