Book Talk: Visions of Infinity: The Great Mathematical Problems

by Sharon Kane

If 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

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