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The Boy Who Loved Math: The Improbable Life of Paul Erdős
By Deborah Heiligman
Illustrated by LeUyen Pham
Roaring Brook (an imprint of Macmillan)
ISBN: 978-1-59643-307-6
Ages 6 and up
On shelves June 25th

Make a beeline for your local library’s children’s biography section and learn firsthand the shocking truth about picture book bios of mathematical geniuses. Apparently there was only one and his name was Einstein. End of story. The world as we know it is not overflowing with picture book encapsulations of the lives of Sir Isaac Newton or Archimedes (though admittedly you could probably drum up a Leonardo da Vinci book or two if you were keen to try). But when it comes to folks alive in the 20th century, Einstein is the beginning and the end of the story. You might be so foolish as to think there was a good reason for that fact. Maybe all the other mathematicians were dull. I mean, Einstein was a pretty interesting fella, what with his world-shattering theories and crazed mane. And true, the wild-haired physicist was fascinating in his own right, but if we’re talking out-and-out interesting people, few can compare with the patron saint of contemporary mathematics, Paul Erdős. Prior to reading this book I would have doubted a person could conceivably make an engaging biography chock full to overflowing with mathematical concepts. Now I can only stare in amazement at a story that could conceivably make a kid wonder about how neat everything from Euler’s map of Konigsburg to the Szekeres Snark is. This is one bio you do NOT want to miss. A stunner from start to finish.

For you see, there once was a boy who loved math. His name was Paul and he lived in Budapest, Hungary in 1913. As a child, Paul adored numbers, and theorems, and patterns, and tricky ideas like prime numbers. As he got older he grew to be the kind of guy who wanted to do math all the time! Paul was a great guy and a genius and folks loved having him over, but he was utterly incapable of taking care of himself. Fortunately, he didn’t have to. Folks would take care of Paul and in exchange he would bring mathematicians together. The result of these meetings was great strides in number theory, combinatorics, the probabilistic method, set theory, and more! Until the end of this days (when he died in a math meeting) Paul loved what he did and he loved the people he worked with. “Numbers and people were his best friends. Paul Erdős had no problem with that.”

There are two kinds of picture book biographies in this world. The first attempts to select just a single moment or personality quirk from a person’s life, letting it stand in as an example of the whole. Good examples of this kind of book might include Me…Jane by Patrick McDonnell about the childhood of Jane Goodall or Lincoln Tells a Joke: How Laughter Saved the President And the Country by Kathleen Krull. It’s hard to pinpoint the perfect way to convey any subject, but it can sometimes be even harder to tell an entire life in the span of a mere 40 pages or so. Still, that tends to be the second and more common kind of picture book biography out there. Generally speaking they don’t tend to be terribly interesting. Just a series of rote facts, incapable of making it clear to a kind why a person mattered aside from the standard “because I said so” defense. The Boy Who Loved Math is different because it really takes the nature of biography seriously. If the purpose of a bio is to make it clear that a person was important, how important was a guy who loved math puzzles? Well, consider what the story can do. In a scant number of pages author Deborah Heiligman gives us an entire life synthesized down to just a couple key moments, giving the man’s life form and function and purpose, all while remaining lighthearted and fun to read. Who does that?

Did you know that there are kids out there who like math? I mean, reeeeeeally like math? The kinds that beg their parents for math problems to solve? They exist (heck, Ms. Heiligman gave birth to one) and for those kids this book will come like a present from on high. Because not only does the author highlight a fellow who took his passion for numbers and turned it into a fulfilling and fun life, but thanks to illustrator LeUyen Pham the illustrations are overflowing with math equations and puzzles and problems, just waiting to be interpreted and dissected. I have followed the career of Ms. Pham for many years. There is no book that she touches that she does not improve with her unique style. Whether it’s zeroing in on a child’s neuroses in Alvin Ho or bringing lush life to a work of poetry as in A Stick Is an Excellent Thing, Pham’s art can run the gamut from perfect interstitial pen-and-inks to lush watercolor paints. I say that, but I have never, but ever, seen anything like what she’s done in The Boy Who Loved Math.

It would not be overstating the matter to call this book Pham’s masterpiece. The common story behind its creation is that there was some difficulty finding the perfect artist for it because whosoever put pen to paper here would have to be comfortable on some level with incorporating math into the art. Many is the artist who would shy away from that demand. Not Ms. Pham. She takes to the medium like a duck to water, seemingly effortlessly weaving equations, charts, diagrams, numbers, and theorems into pictures that also have to complement the story, feature the faces of real people, capture a sense of time (often through clothing) and place (often through architecture), and hardest of all, be fun to look at.

But that’s just for starters. The final product is MUCH more complex. I’m not entirely certain what the medium is at work here but if I had to guess I’d go with watercolors. Whatever it is, Pham’s design on each page layout is extraordinary. Sometimes she’ll do a full page, border to border, chock full of illustrations of a single moment. That might pair with a page of interstitial scenes, giving a feel to Paul’s life. Or consider the page where you see a group of diners at a restaurant, their worlds carefully separated into dotted squares (a hat tip to one of Paul’s puzzles) while Paul sits in his very own dotted pentagon. It’s these little touches that make it clear that Paul isn’t like other folks. All this culminates in Pham’s remarkable Erdős number graph, where she outdoes herself showing how Paul intersected with the great mathematicians of the day. Absolutely stunning.

Both Heiligman and Pham take a great deal of care to tell this tale as honestly as possible. The extensive “Note From the Author” and “Note From the Illustrator” sections in the back are an eye-opening glimpse into what it takes to present a person honestly to a child audience. In Pham’s notes she concedes when she had to illustrate without a guide at hand. For example, Paul’s babysitter (“the dreaded Faulein”) had to be conjured from scratch. She is the rare exception, however. Almost every face in this book is a real person, and it’s remarkable to look and see Pham’s page by page notes on who each one is.

Heiligman’s author’s note speaks less to what she included and more to what she had to leave out. She doesn’t mention the fact that Paul was addicted to amphetamines and honestly that sort of detail wouldn’t have served the story much at all. Similarly I had no problem with Paul’s father’s absence. Heiligman mentions in her note what the man went through and why his absences would make Paul’s mother the “central person in his life emotionally”. The book never denies his existence, it just focuses on Paul’s mother as a guiding force that was perhaps in some way responsible for the man’s more quirky qualities. The only part of the book that I would have changed wasn’t what Heiligman left out but what she put in. At one point the story is in the midst of telling some of Paul’s more peculiar acts as a guest (stabbing tomato juice cartons with knives, waking friends up at 4 a.m. to talk math, etc.). Then, out of the blue, we see a very brief mention of Paul getting caught by the police when he tried to look at a radio tower. That section is almost immediately forgotten when the text jumps back to Paul and his hosts, asking why they put up with his oddities. I can see why placing Paul in the midst of the Red Scare puts the tale into context, but I might argue that there’s no real reason to include it. Though the Note for the Author at the end mentions that because of this act he wasn’t allowed back in the States for a decade, it doesn’t have a real bearing on the thrust of the book. As they say in the biz, it comes right out.

I have mentioned that this book is a boon for the math-lovers of the world, but what about the kids who couldn’t care diddly over squat about mathy malarkey? Well, as far as I’m concerned the whole reason this book works is because it’s fun. A little bit silly too, come to that. Even if a kid couldn’t care less about prime numbers, there’s interest to be had in watching someone else get excited about them. We don’t read biographies of people exactly like ourselves all the time, because what would be the point of that? Part of the reason biographies even exist is to grant us glimpses into the lives of the folks we would otherwise never have the chance to meet. Your kid may never become a mathematician, but with the book they can at least hang out with one.

One problem teachers have when they teach math is that they cannot come up with a way to make it clear that for some people mathematics is a game. A wonderful game full of surprises and puzzles and queries. What The Boy Who Loved Math does so well is to not only show how much fun math can be on your own, it makes it clear that the contribution Paul Erdős gave to the world above and beyond his own genius was that he encouraged people to work together to solve their problems. Heiligman’s biography isn’t simply the rote facts about a man’s life. It places that life in context, gives meaning to what he did, and makes it clear that above and beyond his eccentricities (which admittedly make for wonderful picture book bio fare) this was a guy who made the world a better place through mathematics. What’s more, he lived his life exactly the way he wanted to. How many of us can say as much? So applause for Heiligman and Pham for not only presenting a little known life for all the world to see, but for giving that life such a magnificent package as this book. A must purchase.

On shelves June 25th

Source: Advanced readers galley sent from publisher for review.

Like This? Then Try:

• On a Beam of Light: The Story of Albert Einstein by Jennifer Berne, illustrated by Vladimir Radunsky

• Play, Mozart, Play by Peter Sis

• Me . . . Jane by Patrick McDonnell

• Odd Boy Out: Young Albert Einstein by Don Brown

Misc:

• Read what Ms. Heiligman had to say about the book on a recent NYPL panel Ethics in Nonfiction for Kids.

By Lara Alcock

Two contrasting experiences stick in mind from my first year at university.

First, I spent a lot of time in lectures that I did not understand. I don’t mean lectures in which I got the general gist but didn’t quite follow the technical details. I mean lectures in which I understood not one thing from the beginning to the end. I still went to all the lectures and wrote everything down – I was a dutiful sort of student – but this was hardly the ideal learning experience.

Second, at the end of the year, I was awarded first class marks. The best thing about this was that later that evening, a friend came up to me in the bar and said, “Hey Lara, I hear you got a first!” and I was rapidly surrounded by other friends offering enthusiastic congratulations. This was a revelation. I had attended the kind of school at which students who did well were derided rather than congratulated. I was delighted to find myself in a place where success was celebrated.

Looking back, I think that the interesting thing about these two experiences is the relationship between the two. How could I have done so well when I understood so little of so many lectures?

I don’t think that there was a problem with me. I didn’t come out at the very top, but obviously I had the ability and dedication to get to grips with the mathematics. Nor do I think that there was a problem with the lecturers. Like the vast majority of the mathematicians I have met since, my lecturers cared about their courses and put considerable effort into giving a logically coherent presentation. Not all were natural entertainers, but there was nothing fundamentally wrong with their teaching.

I now think that the problems were more subtle, and related to two issues in particular.

First, there was a communication gap: the lecturers and I did not understand mathematics in the same way. Mathematicians understand mathematics as a network of axioms, definitions, examples, algorithms, theorems, proofs, and applications.  They present and explain these, hoping that students will appreciate the logic of the ideas and will think about the ways in which they can be combined. I didn’t really know how to learn effectively from lectures on abstract material, and research indicates that I was pretty typical in this respect.

Students arrive at university with a set of expectations about what it means to ‘do mathematics’ – about what kind of information teachers will provide and about what students are supposed to do with it. Some of these expectations work well at school but not at university. Many students need to learn, for instance, to treat definitions as stipulative rather than descriptive, to generate and check their own examples, to interpret logical language in a strict, mathematical way rather than a more flexible, context-influenced way, and to infer logical relationships within and across mathematical proofs. These things are expected, but often they are not explicitly taught.

My second problem was that I didn’t have very good study skills. I wasn’t terrible – I wasn’t lazy, or arrogant, or easily distracted, or unwilling to put in the hours. But I wasn’t very effective in deciding how to spend my study time. In fact, I don’t remember making many conscious decisions about it at all. I would try a question, find it difficult, stare out of the window, become worried, attempt to study some section of my lecture notes instead, fail at that too, and end up discouraged. Again, many students are like this. I have met a few who probably should have postponed university until they were ready to exercise some self-discipline, but most do want to learn.

What they lack is a set of strategies for managing their learning – for deciding how to distribute their time when no-one is checking what they’ve done from one class to the next, and for maintaining momentum when things get difficult. Many could improve their effectiveness by doing simple things like systematically prioritizing study tasks, and developing a routine in which they study particular subjects in particular gaps between lectures.  Again, the responsibility for learning these skills lies primarily with the student.

Personally, I never got to a point where I understood every lecture. But I learned how to make sense of abstract material, I developed strategies for studying effectively, and I maintained my first class marks. What I would now say to current students is this: take charge. Find out what lecturers and tutors are expecting, and take opportunities to learn about good study habits. Students who do that should find, like I did, that undergraduate mathematics is challenging, but a pleasure to learn.

Lara Alcock is a Senior Lecturer in the Mathematics Education Centre at Loughborough University. She has taught both mathematics and mathematics education to undergraduates and postgraduates in the UK and the US. She conducts research on the ways in which undergraduates and mathematicians learn and think about mathematics, and she was recently awarded the Selden Prize for Research in Undergraduate Mathematics Education. She is the author of How to Study for a Mathematics Degree (2012, UK) and How to Study as a Mathematics Major (2013, US).

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Image credit: Screenshot of Oxford English Dictionary definition of mathematics, n., via OED Online. All rights reserved.

The post Memories of undergraduate mathematics appeared first on OUPblog.

How many stars were in the sky? A million? A billion? Maybe the number was as big as infinity.  I started to feel very, very small.  How could I even think about something as big as infinity?

• An interview with author Kate Hosford may be found at Archimedes Notebook!
• Another review and related activity at Simply Science blog.

Pages: 32Trim Size: 9 1/4 x 11Dewey: [E]Reading Level: 3Interest Level: K-4Ages: 5-10ATOS Quiz #: 0.5ATOS AR Points: 3.40ATOS: 151611.00Lexile Level: 670

The Chicken Problem
By Jennifer Oxley and Billy Aronson
Random House
$16.99
ISBN: 978-0-375-86989-1
Ages 3-7
On shelves now.

I was once in Prospect Park in Brooklyn when I passed a very small child wearing a porkpie hat running as fast as his chubby legs could carry him. Behind him his father yelled out (to little avail), “Pontius! Pontius, slow down!” I mention this because there is a particular Brooklyn aesthetic to a picture book like The Chicken Problem. Consider, if you will, its heroine Peg. Here she is sporting a mighty trendy little outfit replete with striped tights and buckled red boots. Even her name, Peg, suggests that she was named after Peggy Lee or someone of equal caliber. Notice too that she’s playing a ukulele on the endpapers and that pretty much clinches it. Peg is trendy. Too trendy for your preschooler? Not in the least. Peg may be a specific type of heroine peculiar to a single geographical location but with her urbane Cat and her trouble with high-spirited chicks this is one of those memorable heroines and one-on-one readalouds that add a little bit of math to a little bit of story alongside a whole lot of fine and beautiful art to bring us one fine fine book.

It’s a bright and beautiful day when young Peg and her cat Cat go to the farm to have a perfect picnic with a pig. Peg is one of those girls who like everything to be just so, and when she discovers that she accidentally cut an extra slice of pie she feels it’s a dire problem. Cat solves the imbalance by removing a very small chick from a nearby coop and surely that would be the end of that . . . if he’d managed to remember to close the coop door. Suddenly one hundred chickens are free and roaming the farm. It’s up to Peg, Cat, and maybe that pig they picked up, to figure out a way to cajole these freedom loving fowl into returning from whence they came. When that mission is finally accomplished that leaves one final matter: Time for pie!

I’ve read the occasional professional review that snarked about the svelte story found here, but to be honest I was rather charmed by it. It’s not the most dire straits that Peg and Cat must escape but in the simplest sense it’s a story with a mistake, a solution, and a conclusion that feels satisfying. The language itself repeats in good ways and sounds pleasant on the tongue (“The pie was fresh and juicy and gooey”) while the plot appeals to the pint-sized obsessive compulsives out there that insist that everything be exactly right.

The art is particularly charming, though I found I couldn’t figure out the medium. If I was going to harbor a guess I’d say that it was digital art doing a stand-up and cheer imitation of mixed media. I might have figured it to be done by hand, were it not for the fact that on more than one occasion a chicken will repeat in a large crowd scene. No matter, since it’s the charm of the characters that ultimately pull this puppy through. Peg, noseless though she may be, is a likeable soul. Cat, a feline I initially considered lacking in smiles, turns out to have quite a bit of nuance to his rotund eggplant-like little body. The pig is always referred to as “a pig”, as if he were just some barnyard stray the duo stumbled over on their travels. He seems so content wherever he is, legs neatly crossed beneath him, that you suspect he’d follow Peg and Cat to the ends of the earth if they asked. As for the chickens themselves, they’re beautifully expressionless and yet you spend a lot of your time just trying to keep up with their antics.

Speaking of endpapers, I’ve seen inside jokes in my day. I’ve seen clever details and little pokes of fun. What I have never seen are endpapers that are SO o’erfilled with details and ideas that you could spend the better part of twenty minutes parsing them. It is important to know that the front endpapers are incredibly different from the back endpapers. I mention this in part because I know that libraries have a tendency to glue their bookflaps to their books’ front and back covers and the result is going to cover up quite a bit of content. At the front of the book you can find six scenes drawn from Peg and Cat’s adventures. Sometimes they might be rowing George Washington over the Delaware while other times they’re jamming with a band of bears. Quick flip to the back of the book and you’ve the strangest collection of one hundred chickens you ever did see. An explanation is provided in the special thanks section. It says, “And, for posing so patiently for the pictures, the one hundred chickens,” and then names each and every last one of them. It took a while for me to realize that the names correspond with the pictures on the opposite page. I had already looked at the pictures of the chicks before and noticed odd details about them (like the fact that one of them resembled President Obama on his HOPE poster) but didn’t realize that each one had a name (“Barawk Obama”). Look closely enough and you’ll find references to Lady Gaga, Mahatma Gandhi, Rumpelstiltskin, St. John, George Bernard Shaw, and many others. My personal favorite was the preppy turtleneck donning Cluck C. Cluck III. Even without reading his name I knew he was a 1% chicken, if you know what I mean.

As the bookflaps explain, Peg and Cat are well on their way to becoming a television series on PBS that teaches preschoolers math someday. And while that might account for some of the adventures on the endpapers, the story stands perfectly well on its own. I don’t need to see Peg on my TiVo to know she’s a special kind of kid. Whether or not the show occurs, I do hope that we’ll see more of Peg and her erstwhile purple companion on good old-fashioned paper and board in the future. I suspect folks will end up picking up the book more for the art and story than the math, and that’s okay. Fun pretty much sums it up.

On shelves now.

Source: Final copy sent from publisher for review.

Like This? Then Try:

• Chicken Dance by Tammi Sauer, ill. Dan Santat

• The Day the Babies Crawled Away by Peggy Rathmann

• Millions of Cats by Wanda Gag

• The Problem With Chickens by Bruce McMillan, ill. Gunnella

Interview: Nerdy Book Club

Video:

There was a cute little book trailer, of course:

And though its website is gone, you get a pretty clear sense of Peg, Cat and their world here.

I am now entertaining the ridiculous hope that when the show premiers they make Peg-with-ukelele YouTube videos like the millions already out there.  Just Peg, a ukelele, a blank wall, and one of her songs.  I mean, might as well at this point, right?

Each bug on these pages
Looks unique and rare,
Not like the insects
You see everywhere.

They're made up of numbers:
The ones that you count.
'Cause when you think bugs,
You think BIG amounts.

Now some smarties might notice
As the go through and look,
Not every creature is a bug in this book. 

Not all critters that fly or crawl  on the ground
Are technically bugs, but we both have found
Mos folks call them bugs, and since they do,
We figured, why not? We'd call them "bugs" too. 

Real bugs are insects, but not all insects are bugs
And spiders are neither (oh, please don't say, "Ugh").

Book: BUGS BY THE NUMBERS,

Author/Illustrator:  Sharon Werner and Sarah Forss
Publisher: Blue Apple Books
Publication Date: April 2011
Pages: 56 pages
Grades: 3-8
ISBN: 978-1609050610
Source of Book: Copy borrowed from my local public library

P.S. - Did I mention that their new book, Alphasaurs and Other Prehistoric Types, comes out in October?

This review was written for Nonfiction Monday. Head on over to The Swimmer Writer and check out all the great posts highlighting nonfiction this week.

 

Once upon a midnight rotten,

Cold, and rainy, I'd forgotten

All about the apple pie

Still cooling from the hour before.

I ignored the frightful stranger

Knocking, knocking . . . I, sleepwalking,

Pitter-pattered toward the pantry,

Took a knife from the kitchen drawer,

And screamed aloud, "How many cuts

Give me ten pieces?" through the door,

          The stranger bellowed, "Never four!"

My tightie whities look so sad.

My tightie whities look so sad.

Edward Lear's Elephant with Hot Dog

Inspired by "There Was An Old Man With a Beard" by Edward Lear 

When an elephant sat down to order

A half of a third of a quarter

     Of an eighty-foot bun

     And a frankfurter, son

Was it longer than three feet, or shorter?

New comic at Into the Thicklebit today, and it’s one of my personal favorites.

And I’ve got a review of kids’ math apps at GeekMom. Fun stuff!