Book Talk: Visions of Infinity: The Great Mathematical Problems

by Sharon Kane

visions-of-infinityIf you hear a student complain that a math problem is taking too long to solve, you can encourage her with this sentence from Ian Stewart’s Visions of Infinity: The Great Mathematical Problems (2013, Basic Books): “Fermat’s last theorem was an enigma for 350 years until Andrew Wiles dispatched it after seven years of toil” (ix). If someone asks what math has to do with life outside of school, or if this person thinks math is something static and unchanging, you can quote Stewart again: “At a rough estimate, the world’s research mathematicians number about a hundred thousand, and they produce more than two million pages of new mathematics every year (pp. ix–x).” And if students think math is done in solitude, or that it’s not important to show their work, you can offer this gem of a metaphor:

One recent piece of algebra, carried out by a team of some 25 mathematicians, was described as “a calculation the size of Manhattan.” That wasn’t quite true, but it erred on the side of conservatism. The answer was the size of Manhattan; the calculation was a lot bigger. (p. x)

I got all this from just the Preface, so you can imagine the richness of the material in the rest of the book as it describes the great mathematical problems. Ian Stewart is a mathematical storyteller, or a storytelling mathematician. (You can see a BookTalk on Professor Stewart’s Casebook of Mathematical Mysteries previously posted on this site.) In his final chapter, he offers twelve unsolved problems that mathematicians are working on, with intriguing names like “Odd Perfect Numbers,” “Lonely Runner Conjecture,” “Langton’s Ant,” and “Existence of Perfect Cuboids.” Who can resist?

I will never be famous for solving a math problem, but if I have Visions of Infinity in my classroom library maybe one of my students will be. I’ll end this BookTalk with another quote that I could offer to a student who thinks mathematics is boring or dry; notice how Stewart uses imagery to invite readers into his world:

Mathematics… is… like a natural landscape, where you can never really say where the valley ends and the foothills begin, where the forest merges into woodland, scrub, and grassy plains, where lakes insert regions of water into every other kind of terrain, where rivers link the snow-clad slopes of the mountains to the distant, low-lying oceans. But this ever-changing mathematical landscape consists not of rocks, water, and plants, but of ideas; it is tied together not by geography, but by logic. And it is a dynamic landscape, which changes as new ideas and methods are discovered or invented … Over time, some of the peaks and obstacles acquire iconic status. These are the great problems. (pp. 7–8)

Appropriate for high school

math, ELA


BookTalk: Do No Harm

by Sharon Kane

donoharmWe would like to think that brain surgeons are infallible, though of course that is an unrealistic expectation, as Henry Marsh’s Do No Harm: Stories of Life, Death, and Brain Surgery (2014, Thomas Dunne Books) demonstrates. Marsh shares his weaknesses, misjudgments, and anxieties as a neurosurgeon along with fascinating details of adventures he’s had in the operating room. We come to admire his talents in both his medical specialty and his writing as he “attempt[s] to give an honest account of what it is like to be a neurosurgeon” (p. x).

Most of the chapter titles indicate the conditions that lead to the need for Marsh’s services. The chapters include details of particular surgeries (most of which include a lot of blood), conversations with patients pre-and-post surgery, and explanations of how Marsh makes decisions in situations that are fraught with risk. Readers can feel his remorse and anguish when patients worsen after surgery, and his exhilaration when a seemingly hopeless scenario turns around due to his skill.

In one chapter, Marsh describes himself as a patient. He explains, “Most medical students go through a brief period when they develop all manner of imaginary illnesses . . . until they learn, as a matter of self-preservation, that illnesses happen to patients, not to doctors” (p. 215). He notes that doctors often dismiss their own initial symptoms and can be slow to diagnose themselves. But he could not ignore the effects of a vitreous detachment and thus had to place himself in the hands of a retinal surgeon. Another time, he broke his leg, and after that surgery his doctor “insisted on keeping me in hospital for five days on the grounds that I was a doctor and would not listen to his medical advice that I should rest my leg. . .” (p. 228). Some of his colleagues saw him in the hospital and “looked somewhat startled to see me disguised as a patient in a dressing gown with a leg in plaster” (p. 229).

Marsh manages to turn everything into a story, which is what makes this nonfiction account of his career so fascinating. He presents ethical dilemmas and then brings us along on his rounds as he deals with them. Marsh is an expert in his field and is someone I would trust.

Appropriate for high school and beyond

biology, ethics, careers, ELA

BookTalk: Dare to Disappoint: Growing Up in Turkey

by Sharon Kane

daretodisappointI visited Turkey a few years ago, and fell in love with the country. So when I began reading Özge Samanci’s memoir in graphic novel format, Dare to Disappoint: Growing Up in Turkey (2015, Farrar, Straus and Giroux), I was pleased to recognize some of the places and events mentioned, and I was eager to learn more about Turkish culture and history. Despite Özge’s childhood taking place in Turkey in the 1980s, the coming-of-age story is familiar, with what feels like a universal theme.

Panels and speech balloons take readers back and forth between school and home, where Özge works toward discovering, or constructing, her unique identity. A chapter on politics, called “Atatürk,” connects to her search for identity. The text of the Student Oath is included; it begins and ends with “I am a Turk.” In one panel, a bird says that “Students repeat this oath 800 times before they graduate from primary school” (p. 27). Özge’s uncle, a socialist, tells her she is being brainwashed. TV is censored. Her beloved teacher uses Özge’s pink ruler to beat her and her classmates. Figuring out her identity is complex, and so is figuring out her future.

Özge’s father insists she have a career in medicine or engineering. He only wants the best for her, which in his mind equates with security. Özge craves her father’s approval, yet the picture of Jacques Cousteau on her bedroom wall whispers to her, suggesting a different path. She boards at Istanbul Atatürk Science High School, where the principal insists there is no such thing as evolution, and teachers espouse the subservience of women. She does not fit in.

At college she majors in math, but isn’t passionate about it and doesn’t do well. Her father does not support her decision to add a drama major. Life after college brings more conflict. Özge fights with her father about his expectation that she should marry in addition to their never-ending arguments about a career. Will she ever truly find herself? I recommend this book for those who need hope and encouragement on their way to becoming themselves, no matter what their culture, family, or internal anxieties may be.


Appropriate for middle school and high school

art, careers, ELA, history, psychology