Archive for the 'mathematics' category

Reading Diary: Genius At Play The Curious Mind of John Horton Conway by Siobhan Roberts

Jan 04 2016 Published by under book review, mathematics, reading diary, science books

John Horton Conway is a great mathematician, certainly one of the greatest living mathematicians. Polymathematical in his mathematical interests (game theory, geometry, group theory, topology and more, not to mention the Game of Life), he's also one of the most eccentric, and that's saying a lot in a field where Cedric Villani is prime eccentricity competition.

As one can imagine, the biographer of an oddball character like Conway faces certain ... challenges ... that most biographers don't face. Memory, obstinacy, whimsy, the whole nine yards.

So it pleases me to say that Siobhan Roberts' recent biography, Genius At Play The Curious Mind of John Horton Conway, rises to the occasion and gives a wonderful and quirky portrayal of a wonderful and quirky figure in the history of mathematics.

But it must be said. If the author of a book about such an unconventional

unusual, irregular, unorthodox, unfamiliar, uncommon, unwonted, out of the ordinary, atypical, singular, alternative, different; new, novel, innovative, groundbreaking, pioneering, original, unprecedented; eccentric, idiosyncratic, quirky, odd, strange, bizarre, weird, outlandish, curious; abnormal, anomalous, aberrant, extraordinary; nonconformist, Bohemian, avant-garde; informalfar out, offbeat, off the wall, wacky, madcap, oddball, zany, hippie, kooky, wacko (here)

figure faces some challenges, so does the reviewer of such a book. How to convey both the book subject's personality and how that personality is reflected in the book itself? Because make no mistake, Roberts does a great job of mirroring Conway's personality

the combination of characteristics or qualities that form an individual's distinctive character.

"she had a sunny personality that was very engaging"

synonyms: character, nature, disposition, temperament, makeup, persona, psyche

"her cheerful personality"

qualities that make someone interesting or popular.

"she's always had loads of personality"

synonyms: charisma, magnetism, strength/force of personality, character, charm, presence
"she had loads of personality" (here)

in the way she tells the story -- fresh, fun, whimsical, a bit wild and offbeat. But not purposefully difficult or obtuse or overly wilful or inventively fanciful with details (like Conway also can be), I guess leaving those aspects out of the direct telling of the tales.

What I'm going to do is leave it to the book itself to tell it's own tale. Here's a bunch of quotes, I won't tell you who from, from Roberts or Conway or one of the other people quoted in the book. 'Cause where would the fun be in that.

  • p. 20: There goes somebody looking strange. Ergo it must [be] a friend of Dad's!
  • p. 25: You know, it's hard to think what message to send your tongue to get it to do this thing.
  • p. 51: I'm a Platonist at heart, although I know there are very great difficulties with that view.
  • p. 57: Mercifully, the hiring process for the Cambridge mathematics faculty was then loosey-goosey, somewhere between anarchic and irrational.
  • p. 64: "Had the baby?" / Yes. / "Boy or girl?" / Yes.
  • p. 74: Were my lectures anywhere near that coherent?
  • p. 75: The smitten students loved him as much for his mind as his silly high jinks, and maybe most of all for his singular hybrid of sophistication, sincerity, and lascivious showmanship.
  • p. 82: Cue the tremolo whistle that presage a duel in "The Good, The Bad, and the Ugly." It's a mathematicians shootout. Who's the fastest to draw to draw a stellated icosahedron.
  • p. 97: During a trip to Montreal there was 8 inches of snow. Conway, as per usual, was wearing only his sandals.
  • p. 107: Are there any determinists present?
  • p. 124: I like to think of a huge abandoned warehouse equipped with logical devices such as AND, OR, and NOT gates.
  • p. 128: It terrifies him that another of his worst nightmares might come true, that his life will in the end be reduced to Life.
  • p. 133: You know, when you play a game, if you learn to be good at it, you find what it is you should be thinking about. That is really rather subtle. And that's what we do in mathematics.
  • p. 139: Come again? (As the actress said to the bishop.)
  • p. 145: Which is to say, Life could calculate pi. It could calculate anything. In the broadest logical sense, Life was a metaphor for all of mathematics; it contained all of mathematics.
  • p. 181: No. Yes. I'm not sure, to tell you the truth.
  • p. 186: Conway carries the Shannon philosophy to its extreme, often forced by his lack of system to rediscover his own results.
  • p. 213: Suppose surreal numbers had been invented first and real numbers second -- suppose it had gone the other way and we had all grown up learning surreal numbers.
  • p. 224: Conway's philosophy of study, which has served him well, is to always take his investigations several steps beyond what any reasonable human being would do.
  • p. 224: No no no no no! You're being far too REASONABLE.
  • p. 237: I arrived at the alcove armed with the "Monstrous Moonshine" hopes of getting, if not an answer, at least some elaboration about what exactly he and Norton had accomplished.
  • p. 242: Conway employs an entomologically inspired algorithm in explaining his own mating patterns.
  • p. 244: How, pray tell, does an unkempt nerdy mathematician get so lucky?
  • p. 275: It's one of the surest signs of senility in a scientist -- or a mathematician, for that matter -- when after having made a reputation in one subject, he somehow feels he can make a contribution to something else.
  • p. 364: We are parasites, we mathematicians, on the proper function of the brain.
  • p. 379: But my view is we are trying to find the truth, and there are other ways of finding the truth than proofs. And this is unsettling to mathematicians.
  • p. 390: Gareth, it must be said, is as psyched about having a nerd for a father as any boy could be.

You get the idea. And you'll have to get a hold of the book itself to figure out the context of the odder of the quotes above. Parasites. *snort*

Needless to say, this is an excellent book, one that belongs in every library's mathematics collection, academic or public. It is also indispensable for collections in the history of science or math. It would also make an excellent addition to the personal collection of any lover of math or personality.

(Review copy provided by publisher.)

Roberts, Siobhan. Genius At Play: The Curious Mind of John Horton Conway. New York: Bloomsbury, 2015. 480pp. ISBN-13: 978-1620405932

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Reading Diary: Birth of a Theorem: A Mathematical Adventure by Cédric Villani

Aug 04 2015 Published by under book review, mathematics, reading diary, science books

Cédric Villani's Birth of a Theorem: A Mathematical Adventure has risen to the top of my Best Science Book of 2015 list. It'll be tough for another book to kick it off that summit before the end of the year, that's for sure.

The name Cédric Villani probably sounds a bit familiar to most who follow the science world reasonably closely. That's because he's the spider-pendant wearing, cravat and three-piece suit porting, Fields Medal winning French mathematician who's currently the director of the Institut Henri Poincaré in Paris. He's known in math circles for his work on nonlinear Landau damping with Clément Mouhot.

Birth of a Theorem is his memoir of how he and Mouhot made their breakthrough in nonlinear Landau damping. Curiously, the book really isn't about nonlinear Landau damping itself, barely including any kind of non-specialist description of it all all. Rather BoaT is about how they made their discoveries. It's about process, not product.

So the book includes copious email discussions between the two, some barely comprehensible to non-specialists, including TeX code and equations. It includes digressions and discussions, explanations of illuminations about the famous figures in their field, side trips into the music Villani likes to listen to while working. It's about the importance of collaborators and mentors in the scientific enterprise. It's about needing time to think deeply, away from pedestrian concerns, to get to the heart of the math. The serendipity and randomness of learning new things and making unexpected connections. It's about the challenge of finding good bread and cheese in New Jersey.

And lots and lots of rumination about work/life balance, juggling spending time with his small children, balancing his wife's career and his own, and the challenges of relocating to Princeton and the Institute for Advanced Study for six months and throwing all those balls up into the air, working in the shadow of Einstein. Mostly it's about balancing total immersion into the world of pure math with the demands of the very real and impure world of people and institutional politics and collaborators and family and life and death. Is Villani rather self-absorbed? Do we feel for his poor wife and kids at times? Sure, but we also root for him fiercely, hoping that he and Mouhot will slay their dragon.

And as incomprehensible as some of the math is, the process is vibrant and alive like in few other books I've read. Something like Wrinkles in Time: Witness to the Birth of the Universe by George Smoot and Keay Davidson comes to mind as a similar example from what I've read before.

I would recommend this book without hesitation. Malcolm DeBevoise's translation is smooth and seamless. BoaT would make a great gift to any science- or math- loving member of your extended circle. In particular, for anyone contemplating a research career, this book would provide an amazing insight into how research actually happens, especially in the more abstract areas of math and science. This book should find an eager audience for any library that collects popular science.

In many ways, Villani has only whetted my appetite for learning about the processes of mathematical discovery. Michael Harris's Mathematics without Apologies: Portrait of a Problematic Vocation seems like an interesting second step in this adventure. It's much longer and from the reviews and descriptive material, it looks like it just might pick up from where Villani left off, taking us from the unraveling of one discovery into a more generalized discussion of how the mathematical mindset works.

I have also recently reviewed the graphic novel Les Rêveurs lunaires: Quatre génies qui ont changé l'Histoire by Cédric Villani and Baudoin.

Villani, Cédric. Translated from the French by Malcolm DeBevoise. Birth of a Theorem: A Mathematical Adventure. New York: Farrar, Straus and Giroux, 2015. 272pp. ISBN-13: 978-0865477674

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Reading Diary: Zombies & Calculus by Colin Adams

Colin Adams's Zombies & Calculus is one of the coolest, funniest, most creative science books I've read in a very long time.

What's interesting about that statement is that we're not talking a non-fiction book here. We're talking a novel. Yes, a novel. Zombies & Calculus is pure fiction. Fortunately. Now I'm a big fan of the Walking Dead tv show and the comics too (though I'm a bit behind on the trade paperback collections) so I"m quite glad it's fiction. Basically, the premise of this novel is, "What if Rick Grimes had been a university math prof instead of a police officer."

The opening scene is a college math lecture hall where a couple of zombies wander in and start chowing down on the students. Chaos ensues but our hero Professor Williams, rallies the students and escapes. The rest of the novel is Williams using his math abilities to figure out what is happening to them all -- growth rates, zombie wandering trajectories, how hard you have to smack a zombie to kill it, predator-prey oscillation curves -- and hopefully increase their odds of survival because of that knowledge.

The story itself is pretty amusing, with quite a few of the bizarre and grotesque touches you would expect of any zombie novel. The body count is pretty high. The author isn't a brilliant novelist but easily has enough facility with both prose and narrative storytelling to make the book very entertaining. The characterization is a bit basic and one-dimensional but serviceable. The novel part is only about 150 pages and the relative brevity of the story definitely contributes to the success. Adams also manages to put in a few humourous jabs at academic life and campus politics, from the checked-out senior prof to the incompetent administrator, to give the story some satirical sting. There's even a touch of romance, if you can believe it. Not to mention, extended calculus lectures delivered in deadpan style while holed-up and hiding during the zombie apocalypse is in-and-of-itself flat out hilarious. (Some of the conversations with fellow survivors can be a bit laboured, especially in the appendices.)

As for the hard-core math part, there is quite a bit of very real calculus both embedded in the novel itself and in some rather more detailed appendices. If you're not comfortable with at least some level of equations and graphs, then this probably isn't a book for you. However, Adams does do a decent job of keeping the story flowing without too much digression into long info-dumps. One of the most interesting math parts was about the growth rates of the zombie population and how potential equilibrium of zombies and humans might be reached. Colin Adams definitely needs to be a math consultant on The Walking Dead, especially as the show gets further into the time scale of their apocalypse.

Overall, I can't recommend this book enough; it was one of my favourite science books of 2014. The more math you know, the more you will enjoy this book. The main audience is probably university math students and professors, so if you know one of those, this would make a great gift. As for library collections, this would be a great addition to any undergraduate math collection and could even be used as a teaching tool in first year calculus. Large public library systems would probably also find an audience for this book.

Adams, Colin. Zombies & Calculus. Princeton: Princeton University Press, 2014. 240pp. ISBN-13: 978-0691161907

(Review copy provided by publisher.)

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Mathematician and activist Lee Lorch, 1915-2014

Mar 17 2014 Published by under Canada, mathematics, Politics, yorku

York University mathematician and civil rights activist Lee Lorch died February 28, 2014 at the age of 98.

A few years ago I posted on the 2007 Joint Mathematics Meetings in New Orleans Lee Lorch where Lee was awarded the Yueh-Gin Gung and Charles Y. Hu Award for Distinguished Service to Mathematics.

The citation read:

Lee Lorch's mathematical research has been in the areas of analysis, differential equations, and special functions. His teaching positions have included the City College of New York, Pennsylvania State University, Fisk University, Philander Smith College, the University of Alberta, Howard University, Royal Institute of Technology (Stockholm) and Aarhus University. He was at York from 1968 until retirement in 1985 and remains active in the mathematical community.

His scholarship has been recognized by election to Fellowship in the Royal Society of Canada; appointment to committees of the Research Council of Canada; election to the Councils of the American Mathematical Society, the Canadian Mathematical Society, and the Royal Society of Canada; and by many invitations to lecture.

Lee Lorch is a remarkable teacher of mathematics and an inspiration to his students. Among those he guided were Etta Falconer, Gloria Hewitt, Vivienne Malone Mayes, and Charles Costley. He has recruited into graduate work and mathematical careers many students who would not have otherwise considered such a path. [See V. Mayes, American Mathematical Monthly, 1976, pp708-711; and P. Kenschaft, Change Is Possible, American Mathematical Society, 2005.]

During the early organization of the Association for Women in Mathematics, Lee gave sage advice about the value of inclusiveness in supporting effective advocacy. He is responsible for the appearance of the preposition "for" in place of the initially proposed "of" in the name of the AWM.

Throughout his career he has been a vocal advocate and energetic worker for human rights and educational opportunities. His interventions, especially in the 1950's, led to changes in the policies and practices of the AMS and the MAA that ensured that all mathematicians could participate in the official events of these organizations. While his actions have not solved all the problems he addressed, surely his energy has contributed to much progress.

As an example, we cite events surrounding a meeting in 1951 held in Nashville. Lee Lorch, the chair of the mathematics department at Fisk University, and three Black colleagues, Evelyn Boyd (now Granville), Walter Brown, and H. M. Holloway came to the meeting and were able to attend the scientific sessions. However, the organizer for the closing banquet refused to honor the reservations of these four mathematicians. (Letters in Science, August 10, 1951, pp. 161-162 spell out the details). Lorch and his colleagues wrote to the governing bodies of the AMS and MAA seeking bylaws against discrimination. Bylaws were not changed, but non-discriminatory policies were established and have been strictly observed since then.

For his life-long contributions to mathematics, his continued dedication to inclusiveness, equity, and human rights for mathematicians, and especially his profound influence on the lives of minority and women mathematicians who have benefited from his efforts, the MAA presents this Yueh-Gin Gung and Charles Y. Hu Award for Distinguished Service to Mathematics to Lee Lorch.

A picture of a beaming Lee Lorch is here. There's also a nice article in the daily YorkU email newsletter about the award.

On paper, Lorch retired in 1985. But, as he likes to say, "I’m not retired. Unfortunately my salary is." At 91, he still uses an office at York and is collaborating on a research paper about Bessel functions with Prof. Martin Muldoon, a former grad student under Lorch in Edmonton and himself recently retired from York’s Mathematics Department. He’s given up teaching but travels to campus regularly and participates in meetings and other activities. Not as mobile as he once was, he uses a walker and relies on Wheel-Trans to get around. However, e-mail and the Internet have only fuelled his activism.

What’s remarkable, says Muldoon, is that Lorch still takes great interest in the mathematical community, especially its treatment of women and minorities. From his tiny home office, he reads five newspapers a day, including the New York Times. He sends flurries of e-mails daily about peace and justice issues – these days he focuses on Cuban-Canadian friendship – to friends and acquaintances in and out of the mathematical community. Only five years ago, he raised a fuss with the newly formed Fields Institute, a math organization in Toronto, over its first list of 33 fellows, all of whom were white men. Within two years, several women became fellows and the institute appointed a woman director.

It’s impossible not to admire Lorch’s persistence and courage. Does he feel he’s made headway in his struggles against racism, inequality and injustice? "Yes," he says, "but there’s a long way to go. These issues are still very much with us."

At the time, it was a great pleasure to note the award. Lee was an ardent library supporter and a very welcome visitor to my library, always willing to stop & chat, to share a story or two from his vast experience. I already miss seeing him around campus, usually with his friend Martin Muldoon.

He also donated many rare and unique books from his collection to the library, many of which I've had the pleasure of processing, making our collection a much better research-level collection. When Lee gave up his office a while back I went through many of the books in his office and added a bunch to the collection here at Steacie. In particular he had a lot of Russian books, both mathematical and of interest for the history of math in Russia and the Soviet Union. He even had a some communist children's books, as I recall. I remember fondly as we were going through the math books he'd often point to the Russian one we were looking at and remark on how rare it was outside Russia and thus important to have in a research collection. I think he got a lot of them via personal relationships with Russian mathematicians, especially while visiting them.

Lee was an active researcher up into his 80s and 90s. His most recent publication was from 2008, with his friend and former student Martin Muldoon: Monotonic sequences related to zeros of Bessel functions (OA version). His most recent sole author paper was from 2005: The First Positive Zeros of Cylinder Functions and of Their Derivatives. His earliest is from 1944: The Lebesgue constants for Borel summability.

Lee Lorch will be missed.

As is my habit, I'm listing some other items about Lee's life and work both in mathematics and advocacy.

Obituaries & Remembrances


General & Biographical


Other Material

If you knew Lee, please feel free to share a story or remembrance in the comments. As usual, If I've missed anything, add a link in the comments.

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Reading Diary: The Boy who Loved Math: The Improbable Life of Paul Erdős by Deborah Heiligman and LeUyen Pham

There are two kinds of children's books: those that are aimed primarily at the kids themselves and those that are aimed at the adults that actually shell out the cash to pay for the books. There's certainly a lot of overlap -- books that kids love but that also catch the eyes, hearts & minds and wallets of the adults doing the shopping. But wander the aisles of your local bookstore and you'll see what I mean. Often beautifully illustrated, with a sophisticated artistic touch and a mature and serious topic, you can tell the books that are aimed at the parents and uncles and cousins and aunts and friends and neighbours and grandparents. Next to them are the fun, silly and truly childish books that appeal to the actual kids themselves. And the reverse, too, silly books that are aimed at what adults thinks of as childish concerns but that miss the mark. There are plenty of serious books that perfectly frame the real issues in kids' lives but are perhaps too "gritty" or "realistic" for adults to think that the kids in their lives would be ready or mature enough to understand them.

And now we come to the notion of a biographical kids book about a mathematician. It seems kind of counter-intuitive, of course, at first glance but then you remember that perhaps there are a few interesting oddballs among the mathematical ranks. Even among the oddballs, perhaps most wouldn't make for great stories for kids -- think Paul Dirac or Grigori Perelman for example. And then you remember Paul Erdős. And yeah, perfect.

And that brings us to the book at hand, The Boy Who Loved Math: The Improbable Life of Paul Erdos by Deborah Heiligman and LeUyen Pham (ages 3-8).

A kids book about Paul Erdős actually kind of makes sense. Certainly he had his quirks and oddities, in fact his whole life was a bit of an oddity. Basically, he spent most of his adult life couch surfing from city to city, from the home of one mathematician to another, sleeping on their beds, eating their food and most of all, collaborating with them and producing scholarly papers by the ream. He's actually kind of famous for that habit of collaboration -- it's even spawned the famous Erdős Number (and variants like the Erdős-Bacon number), which calculates the degrees of collaborative separation between mathematicians and Erdős himself.

But, to once again somehow circle around to the main reason for this review, this bizarre idea of a kid's book about this eccentric mathematician. Does it work? Yes, actually it does. Not surprising, it's quirky and playful and a little nutty, and definitely plays up the more child-like aspects of Erdős's life and personality like his obsession of numbers and his playful disdain for everyday life and habits (and not the more adult sides, like his drug use). The book is actually quite light-hearted. LeUyen Pham's artwork very nicely picks up on the mathematical themes with lots of numbers and equations and visual hat-tips to math embedded in the various scenes. It's also clean and a bit retro even, not distracting at all from story.

The notes at the end explain a lot more about Erdős' life and math, something perhaps for the adults reading the book to pick up a bit more than the kids. Which cycles me even further back (recurses, maybe?) to the beginning of the review. Is this a kids book for kids or a kids book for adults? Eh, a little of both. Definitely not something just anybody would pick up for just any kid -- either the adult will likely have a math connection that they want to infect the kid with or perhaps some adult will recognize a kid with a math bug and research math-related kids books and find this one.

Which is kind of too bad. I think any kid would enjoy this book, as would any math-loving adult. It would make a great present for any family with a young kid or as a fun gift for any sciencey person in your life.

And to cycle even further back in time, I first heard about this book at the end of January, at the Ontatio Library Association SuperConference, in the exhibits room. The distributor for the book had a few copies on display and I tweeted a picture of the cover:

Which at one point was the top tweet for the conference! And luckily, while expressing my excitement over the book to the staff at the distributor's both, they were kind enough to give me the copy to take home. A favour I'm returning with this review. Trust me, it was tough waiting until the book was actually released to review it!

Of course, the book is titled The Boy who Loved Math. And we don't all have boys. What about girls that love math? Or who could love math if they had a book with a female role model? What books could we buy for them?

I have some suggestions, although not many that would be for girls in the 3-8 age range that the Erdős appeals to.

Further suggestions of books appealing to girls (and boys) are, of course, welcome in the comments.

Heiligman, Deborah and LeUyen Pham. The Boy Who Loved Math: The Improbable Life of Paul Erdos. New York: Roaring Book Press, 2013. 37pp. ISBN-13: 978-1596433076 (for ages 3-8)

(Advanced Reading Copy provided by publisher/distributer)

(A more math-centric review here.)

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From the Archives: Super Crunchers: Why thinking-by-numbers is the new way to be smart by Ian Ayres

I have a whole pile of science-y book reviews on two of my older blogs, here and here. Both of those blogs have now been largely superseded by or merged into this one. So I'm going to be slowly moving the relevant reviews over here. I'll mostly be doing the posts one or two per weekend and I'll occasionally be merging two or more shorter reviews into one post here.

This one, of Super Crunchers: Why Thinking-By-Numbers is the New Way To Be Smart, is from April 12, 2008.


You know how I'm always complaining about business-y buzz/hype books & articles? How they're 1/3 repetition, 1/3 hype and 1/3 real ideas?

Like I commented to Michael not too long ago: "I find these tendencies very true of a lot of cases where I look to the business literature to understand something important about the way our culture is changing."

The book under consideration in this review, Super Crunchers: Why Thinking-By-Numbers is the New Way To Be Smart by Ian Ayres, is a business book. It says something important about the way our culture is changing. On the other hand, it is also very profoundly a popular science book about the mathematical and statistical analysis of large datasets. Yes, indeed -- this is a popular math book about data mining. And it is a very good to boot. Thankfully, not so much plagued by the repetition and hype of many of the pure business books. I suspect it may have originally been aimed at a popular science audience as much as a business audience, accounting for a slightly different emphasis.

So, what is super crunching? (p.10)

It is statistical analysis that impacts real-world decisions. Super Crunching decisions usually bring together some combination of size, speed and scale. the sizes of the datasets are really big -- both in the number of observations and in the number of variables...And the scale of the impact is sometimes truly huge. this isn't a bunch of egghead academics cranking out provocative journal articles. Super Crunching is done by or for decision makers who are looking for a better way to do things.

In other words, data mining. To it's credit the book doesn't really talk about the hows and whys of the actual mathematical analysis; it mostly concentrates on the applications and implications of these powerful tools. The core theme of the book is how do you make decisions in the data mining (I've decided to to not bother with Ayres's cutsie term and just say data mining) world: evidence or intuition? Evidence wins every time.

Some interesting points to consider: the rise of data mining tools is in large part to the drastic decrease in storage costs the last number of years, far more than any increase in processing power. On the other hand, the use of neural network technology has also contributed to better and better techniques.

The book basically goes through a bunch of applications areas and shows how each are affected by data mining -- basically showing that the evidence provided by statistical evidence beats out human intuition every time. It's an interesting examination of the nature of expertise: what does it really mean to be a human expert when math wizards can transform large data sets into much more accurate predictions about human behaviour. What's left for us to do? Of course, the human role is to decide what data to collect, what questions to ask in the analysis and how to apply the results.

Ayres looks at recommendation systems (like Amazon), data mining applications in the entertainment industry (yes, scripts and box office data are data mined, resulting in, apparently, Will Farrell), economics and government policy and evidence-based medicine (perhaps the best chapter).

To his credit, Ayres doesn't duck the hard questions all this brings up. He deals with privacy concerns, the dangers of over-reliance on programmed creativity and other interesting areas. It's a powerful technology, and while balance is needed in some respects, understanding is a far preferable reaction to change.

Instead of a Luddite rejection of this powerful new technology, it is better to become a knowledgeable participant in the revolution. Instead of sticking your head in the sands of innumeracy, I recommend filling your head with the basic tools of Super Crunching. (p.191)

A good reaction to any new technology. And I like the way he ties it in with the general innumeracy of our times, especially the media and chattering classes. A tool can be used for many purposes. Let's all be

Passionate about the need to inculcate a basic understanding of statistics in the general public. "We have to get students to learn this stuff...We have to get over this phobia and we have to get over this view that somehow statistics is illiberal. There is this crazy view out there that statistics are right-wing"...One can crunch numbers and still have a passionate and caring soul. You can still be creative. You just have to be willing to put your creativity and your passions to the test to see if they really work. (p. 215)

I recommend this book without reservation. Any library that collects math or popular math books would find it a terrific addition to their collection. Business libraries would also find it appropriate. Collections that are looking at the way technology is changing our culture would find that Super Crunchers belongs alongside books like Wikinomics or Everything is Miscellaneous.

Ayres, Ian.Super Crunchers: Why Thinking-By-Numbers is the New Way To Be Smart. New York: Bantan, 2007. 260pp. ISBN-13: 978-0553384734

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The house that calculus built

Feb 07 2011 Published by under mathematics, science books

Or make that the house that the house that Calculus: Early Transcendentals and Calculus: Concepts and Contexts built. And more books too, all in multiple editions!

A few days ago The Toronto Star's Katie Daubs published an article on the home of James Stewart, the Toronto resident who wrote all those calculus textbooks.

James Stewart is a calculus rock star.

When he goes on book tours in China, they ask for his autograph. In Toronto, the city's movers and shakers gather at his home for concerts. People have drunkenly stumbled into his infinity pool.

Stewart's 18,000-square-foot home, named Integral House, is an architectural marvel. It has five floors, a concert space and a stairwell ensconced in handblown blue glass, his favourite colour. The house is filled with gadgets. Stewart delights in showing them off, including the wall to wall blinds that block out the sun with a push of a button in his treetop bedroom.

Check it out. The article has a lot more detail on Stewart's house as well as a bunch of really cool pictures.

Equally interesting are the (as of this moment) 45 comments on the piece. A lot of discussion about math, textbooks, money, ostentatious houses and more.

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From the Archives: King of infinite space: Donald Coxeter, the man who saved geometry by Siobhan Roberts

Dec 12 2010 Published by under book review, mathematics, science books

I have a whole pile of science-y book reviews on two of my older blogs, here and here. Both of those blogs have now been largely superseded by or merged into this one. So I'm going to be slowly moving the relevant reviews over here. I'll mostly be doing the posts one or two per weekend and I'll occasionally be merging two or more shorter reviews into one post here.

This one, of King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry, is from December 11, 2006.


I'm reading a lot of science auto/biography these days, and generally enjoying it a lot. While generally not much of a fan of the "great man" theory of science history, I also tend to like a really good story. Siobhan Roberts's biography of mathematician Harold Scott MacDonald "Donald" Coxeter is a little more heavily weighted on the "great man" side of the equation a perhaps a little light on the "good story" but I enjoyed it tremendously nevertheless. Not least because I have a rather interesting personal connection to this book, but more on that later.

So, who was Donald Coxeter? In a sense, he was the Einstein of geometry in the 20th century, in the sense that Einstein demonstrated that science wasn't exhausted in the 19th century, Coxeter demonstrated that classical geometry wasn't exhausted either, that there was a lot of interesting avenues for important research and applications, both in science and the arts.

A nice quote from page 4, giving a sense of the man and his life's passion.

Coxeter was also known to be both instructive and entertaining in revealing the hidden symmetry of an apple. Around the dinner table with colleagues gathered for the American Math Society conference in 1981, he asked: " Did you know t hat apples do not have cores?" They thought he was pulling their legs, until the hostess, Marjorie Senechal, a mathematics professor at Smith College, procured an apple and placed it before him with a knife, as requested. He filleted the fruit into thin horizontal sections, demonstrating that there was no stem-to-stern core, but rather elongated pods of seeds within. The piece de resistence occurred when he reached the center of the apple and sliced through the equator. There lay it's secret symmetry -- not nature's sloppy attempt at spherical symmetry, as suggested by an apple's exterior, but rather perfect fivefold symmetry, hidden at the apple's heart: the apple seeds were arranged in a five-point star. Everyone around the table gasped when they saw it. "It just shows," said Senechal, "that he was looking everywhere, and looking deeply. Coxeter delighted in the geometry of everyday objects, and, because he was so curious and astute, he found symmetries and regularities in these objects that the rest of us never suspected."

And this is what Benoit Mandelbrot had to say about Coxeter style and place in history (p127):

"He was viewed as a throwback...He was a bit marginal...I remember feeling the strength of his style. The enjoyment Coxeter always had handling shapes, models, and letting models help him dream, is something I find very attractive and very important -- the spirit of loving shapes and the role of the eye and the hand, that what I found so marvellous in Coxeter."

"Most people are not strong enough to have a well-defined personal style...The should bend according to fashion or circumstance and he clearly did not bend. He kept with his classical tradition of geometry, wich had been totally flattened -- pulverized would be even closer -- by Bourbaki. to learn mathematics without pictures is criminal, a ridiculous enterprise."

So, what is it about Roberts' book that makes it worth reading? First of all, it's quite a good outline of Coxeter's life, if a little shallow on his non-mathematical life. We hit the high points, like birth, death & marriage, but we see his children on stage only peripherally until the end when his daughter Susan starts taking care of him. To me this is a bit of a weakness of the book, the lack of color and emotion in the tale of Coxeter's life. Maybe there wasn't much, perhaps the life of a mathematician is like the life of a novelist, where all the good stuff happens between their ears rather than on a grander stage. And there are hints that Coxeter was a bit cold and distant. But still, remarkably little seemed to have happened in a life of over 90 years.

On the other hand, the story of Coxeter's intellectual life is absolutely griping, entwined as it was with the history of mathematics in the 20th century, especially the place of geometry in that history. In a way, you can almost see the story of Coxeter's life as the intellectual history of geometry in the last century, rising from the doldrums to take it's place in as a driving force in physics, ecommerce, databases and even bioinformatics. The overriding theme of the book is the interrelationship of geometry and life, the visual elements that we interact with in film, in art, in science, in architecture, in virtually every aspect of our lives. Coxeter's lifelong battle was to bring the visual sense back into math and math education, rejecting the more algebra-based ideas of the French Bourbaki collective, making math more understandable and accessible. And it was very clear that Coxeter was passionately concerned with the teaching of math and geometry and that cared a great deal about this students. There's a great story about how one of his students, Asia Ivic Weiss, now of York University, was a bit leary of telling him about an error he'd made. When she did, he was actually delighted that she'd found the error and even gave her a wedding gift that commemorated the occasion (p129-130).

Yes, the more math, especially geometry, you know, the more you will enjoy this book. It doesn't shy away from challenging the reader to grasp subtle concepts, to make connections, to understand and enjoy geometry for it's own sake. But, we are rewarded by our efforts. We see how Coxeter's life intersects those of various notable personalities, both scientific and artistic and how Coxeter always takes something away to improve his own work. The artist M.C. Escher is a perfect example. He and Coxeter had a wonderfully odd, mutually beneficial relationship, a relationship well explored in the book as was Coxeter's relationship with Buckminster Fuller.

So, yes, this book is not perfect. I would have appreciated a bit more about Coxeter the man It's also a bit strange how much information was packed into 80+ pages of endnotes, almost like a parallel book actually more about Coxeter's life. I would have appreciated it if a lot of the material in the notes was expanded and pulled into the main narrative. Also, a couple of times a glossary would have been helpful.

But, overall this is a great book that tells a very important story. At the beginning I said I wasn't too fond of the "great man" theory of science history. That's certainly true, but at the same time I realize that so much of the intellectual history of an age can be seen through the works of individual scholars, that to ignore their stories is as great a error as to glorify them. And this book does strike a balance between the man, his work and the intellectual currents that surrounded him.

(A note to the math librarians out there reading this -- the bibliography is a wonderful source for collection development in the roots of classical geometry, in particular I guess we should all make sure our libraries are full of Coxeter!)

I guess I should elaborate on my personal connection to this fine book. In my capacity as Mathematics librarian at York University, I've obviously gotten to know many of the math profs at York and one of them is Asia Ivic Weiss, who happens to have been Coxeter's last grad student at the University of Toronto. Prof. Weiss was the graduate program director in the math department for a few years, including around when Coxeter passed away. As it happens, before he died Coxeter donated a significant amount of his mathematical papers to the Math Department at York, to be housed in their Coxeter Reading Room. Well, a few years ago, after Coxeter had passed away, Asia approached me for some advice on what to do with these papers. They were nice to have, and scholars certainly took advantage of them, but she was not sure if this was the best place. So, we met and discussed the situation. We quickly saw that the issue was larger in scope, that really we should come to terms with all of Coxeter's papers, most of whom were at his house in the Rosedale neighbourhood in Toronto. So, Asia, Coxeter's daughter Susan Thomas, Coxeter's mathematical executor Arthur Sherk and I all met at the Coxeter house where Susan was still living. I also consulted with one of York's archivists, Susanne Dubeau, to get her advice on the situation. After that meeting and subsequent conversations we all agreed that Coxeter's papers belonged at the University of Toronto Archives, including the ones that were currently at York. And so, that's where they are now. It was gratifying that everytime I checked a footnote in Robert's book and saw that the source was from the UofT archives that I played a small part in making sure that Coxeter's papers are accessible to scholars and journalists. It's also great to see the names of so many of the profs know from my work mentioned, like Lee Lorch, John Andraos from Chemistry and Walter Whiteley. Walter was probably the most interviewed person in the book, with many insights on the role of Coxeter's work in other areas of math and science and on the "geometry gap" -- the idea that if we don't teach geometry to scientists, they'll miss out spacial or geometric connections in their work.

Tomorrow, December 12, 2006, there's a book launch at the Fields Institute in Toronto. I hope to be there and report back my experiences.

Update 2006.12.16: I went to the book launch at the Fields institute on the 12th and it was a very nice event. Not a reading, more of a cocktail party with a short talk/film clips in the middle. The relaxed atmosphere was very congenial; it was nice to see my York colleagues Asia Ivic Weiss and Walter Whiteley as well as to meet Susan Thomas, Coxeter's daughter, again after a couple of years. As usual at such events, it's always a treat to shake the author's hand and say how much you enjoyed the book.

Roberts, Siobhan. King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry. Toronto: Anansi, 2006. 399pp.

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Logicomix: An Epic Search for Truth by Apostolos Doxiadis, Christos H. Papadimitriou, Alecos Papdatos and Annie Di Donna

Nov 09 2009 Published by under book review, mathematics, science books

As graphic novels go, Logicomix: An Epic Search for Truth is every bit as good as Maus or Watchmen, if not quite as game-changing. The only other things out there that I can think of that are similar are Chester Brown's Louis Riel or Ho Che Anderson's King: A Comics Biography of Martin Luther King, Jr.

That's high praise and it's well deserved.

So what's Logicomix all about? The core is the story of Bertrand Russell's and his work -- the search for the foundations of mathematics, the most basic kind of truth: logic. His search takes us through the history of mathematics and philosophy in the late 19th and early 20th centuries, both in terms of following the course of Russell's life and loves but also encountering many of the main figures in math and philosophy of the era: Frege, Hilbert, Godel and Wittgenstein all make appearances (the authors take some chronological and historical liberties to get Russell to meet all these people). Russell's relationship with Wittgenstein is explored in particular detail. Russell also deals quite a bit with the relationship between logic an madness both in his own family and in logicians in general.

But that's just the surface story.

Interestingly, Logicomix the story is structured like an onion, with different and distinct layers. Russell's personal and professional biography is the innermost layer, the core, but there are also two outer layers that add a real depth and resonance to the story. The layers interweave the history and philosphy of mathematics and logic, the rise of Nazism, Greek tragedy and the relationship between obsessive logic and insanity.

Next out from the centre is the internal framing story -- Russell giving a speech to a group of pacifists just as World War II is getting started. It is as part of this speech that he recounts his life story, the innermost layer. The point he is trying to make with his life story as it relate to pacifism is all about the relationship between rationality and irrationality, the core of the scientific world view and the place of logic in human affairs.

The next layer out from the core is the story of the authors and artists creating the comic. Yes, the comic is also about it's own creation, with the authors and artists as characters talking about what they hope to accomplish in telling Russell's story, ingeniously contrasting his search for truth and logic with one of the comic's creator's participation in staging a Greek tragedy.

The writing itself is crisp and assured. Each of the layers uses a different tone and voice, one that is suitable for the story it is telling. For example the outer layer, the story of the comics creation, uses a light-hearted, colloquial tone. The pacing is tight; there's no wasted words, no padding or flab for a fairly long book.

The art is perfect -- clear and clean yet very expressive. Light when needed, dark and moody when that is needed as well. There are several gorgeous set pieces sprinkled throughout, especially the scenes where the authors are strolling around Athens, talking about their project. The WWI scenes starting on page 245 are brutally dark and effective. My advanced reading copy only has 12 coloured pages so I can only comment on the colouring in a limited way but what I've seen is very good. On the other hand, reading the rest in black and white I didn't feel the least bit deprived. Even in b&w, it's gorgeous.

Buy this book. Buy one for yourself, buy one for your library. The holidays are coming, so buy a bunch of copies for all your comics-loving family & friends as well as all your science-loving family & friends. Most of all, if there's a precocious kid out there that just might be enthralled and inspired by Bertrand Russell's story, well, this book is perfect. Let's just say that my own reading of the book was delayed a bit when I told my older son about it -- he quickly kidnapped it and read it twice before I got my hands back on it.

I recommend this book without hesitation for academic libraries that collect biographies in science or philosophy; this would be a great first graphic novel for your history and philosophy of science collection. High school and middle school libraries are also a perfect and natural fit, as is pretty well any public library.

Doxiadis, Apostolos; Christos H. Papadimitriou; Alecos Papdatos and Annie Di Donna. Logicomix: An Epic Search for Truth. New York: Bloomsbury, 2009. 347pp. ISBN-13: 978-0747597209

(Advanced reading copy provided by publisher.)

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