FAST CLASS

By EMILY PETERS • Assistant professor, Department of Mathematics and Statistics

Math and the imagination

with a passion for math, and convey the texture of mathematical life—the thrill of discovery, the torment of an incomplete proof, and the pleasure in explaining things clearly (to others or to oneself).

A

PENROSE TILES, EXTRA DIMENSIONS, AND THE PYTHAGOREAN THEOREM

Anathem, by Neil Stephenson, is set in a post-apocalyptic future of a world that may or may not be ours. Anti- intellectual sentiments have led to the creation of math monastaries, where the unfettered pursuit of knowledge is divorced from the distribution of knowledge. As this story begins, the monks and nuns are obedient to this directive. Unlikely events, however, push them further and further into the outside world, and into situations that can’t be understood without reason, logic, and yes, math! As befits a book about the inseparability of math from life, the math contained in the book is as diverse as it is beautiful—includ- ing the zen of Penrose tiles, physi- cal reasons to consider dimensions beyond the usual three, and a special surprise appearance of the Pythago- rean theorem.

GODEL’S INCOMPLETENESS THEOREM

Donald Rumsfeld’s remark about “unknown unknowns” resonates through In the Light of What We Know, by Zia Haider Rahman, a book about the war in Afghanistan, the immigrant experience, the global financial crisis of 2008, and privilege and class. More accu- rately, though, this book is about “unknowable unknowns” and the limits of knowledge. The guiding metaphor of the story is Godel’s in- completeness theorem, which says that any system of logic will either be incomplete (unable to prove certain true statements) or incon- sistent (able to prove that certain statements are both true and false). In the contexts of politics, work, marriage, friendship, and even self, the characters experience the truth of this theorem.

CRYPTOGRAPHY AND CRYPTANALYSIS

In PopCo, by Scarlett Thomas, loner and crossword puzzle writer Alice Butler has ended up working for international toy company PopCo. At a marketing retreat, she begins receiving coded messages. This book tells two stories: one about clever people working for corpora- tions whose morals are at best am- biguous, and the other about pirate treasure. The pirate treasure plot has a more satisfying ending than the corporate plot, and readers are well prepared to appreciate its solution thanks to the inclusion of a history of cryptography and crypt- analysis ranging from its basics (alphabet substitution ciphers, and frequency analysis) through more modern developments (including a too-brief description of the Nazis’ Enigma machine and the British efforts to break it) and tangential relations such as Godel’s theorem.

s a mathematician, I am often asked, “What is math research?” The following works of fiction make a serious and satisfying attempt to answer this question. The stories below have taken a deep mathematical concept and made it central to their plot or structure. They also feature characters

Penrose tiling

PATTERNS, PRIME NUMBERS, AND MORE

In The Curious Incident of the Dog in the Night-Time, by Mark Haddon, a boy named Christopher decides to find out who killed his neighbor’s dog. Although the book never says so explicitly, Christo- pher, age 15, is autistic. He relies on order, patterns, and math to make sense of the world. The digressive narration is a pleasure for math lovers; Christopher understands his experiences by connecting them with mathematical concepts, in sometimes unexpected ways. After explaining how to find all the prime numbers in a given inter- val, Christopher observes “Prime numbers are what is left when you have taken all the patterns away. I think prime numbers are like life. They are very logical but you could never work out the rules, even if you spent all your time thinking about them.”

ALSO DON’T MISS Proof, by David Auburn. This play tackles thorny questions about authorship, madness, and gender, and tells a compelling story about a dead mathematician’s familial and academic legacy.

FALL 2014 11

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By EMILY PETERS • Assistant professor, Department of Mathematics and Statistics

Math and the imagination

with a passion for math, and convey the texture of mathematical life—the thrill of discovery, the torment of an incomplete proof, and the pleasure in explaining things clearly (to others or to oneself).

A

PENROSE TILES, EXTRA DIMENSIONS, AND THE PYTHAGOREAN THEOREM

Anathem, by Neil Stephenson, is set in a post-apocalyptic future of a world that may or may not be ours. Anti- intellectual sentiments have led to the creation of math monastaries, where the unfettered pursuit of knowledge is divorced from the distribution of knowledge. As this story begins, the monks and nuns are obedient to this directive. Unlikely events, however, push them further and further into the outside world, and into situations that can’t be understood without reason, logic, and yes, math! As befits a book about the inseparability of math from life, the math contained in the book is as diverse as it is beautiful—includ- ing the zen of Penrose tiles, physi- cal reasons to consider dimensions beyond the usual three, and a special surprise appearance of the Pythago- rean theorem.

GODEL’S INCOMPLETENESS THEOREM

Donald Rumsfeld’s remark about “unknown unknowns” resonates through In the Light of What We Know, by Zia Haider Rahman, a book about the war in Afghanistan, the immigrant experience, the global financial crisis of 2008, and privilege and class. More accu- rately, though, this book is about “unknowable unknowns” and the limits of knowledge. The guiding metaphor of the story is Godel’s in- completeness theorem, which says that any system of logic will either be incomplete (unable to prove certain true statements) or incon- sistent (able to prove that certain statements are both true and false). In the contexts of politics, work, marriage, friendship, and even self, the characters experience the truth of this theorem.

CRYPTOGRAPHY AND CRYPTANALYSIS

In PopCo, by Scarlett Thomas, loner and crossword puzzle writer Alice Butler has ended up working for international toy company PopCo. At a marketing retreat, she begins receiving coded messages. This book tells two stories: one about clever people working for corpora- tions whose morals are at best am- biguous, and the other about pirate treasure. The pirate treasure plot has a more satisfying ending than the corporate plot, and readers are well prepared to appreciate its solution thanks to the inclusion of a history of cryptography and crypt- analysis ranging from its basics (alphabet substitution ciphers, and frequency analysis) through more modern developments (including a too-brief description of the Nazis’ Enigma machine and the British efforts to break it) and tangential relations such as Godel’s theorem.

s a mathematician, I am often asked, “What is math research?” The following works of fiction make a serious and satisfying attempt to answer this question. The stories below have taken a deep mathematical concept and made it central to their plot or structure. They also feature characters

Penrose tiling

PATTERNS, PRIME NUMBERS, AND MORE

In The Curious Incident of the Dog in the Night-Time, by Mark Haddon, a boy named Christopher decides to find out who killed his neighbor’s dog. Although the book never says so explicitly, Christo- pher, age 15, is autistic. He relies on order, patterns, and math to make sense of the world. The digressive narration is a pleasure for math lovers; Christopher understands his experiences by connecting them with mathematical concepts, in sometimes unexpected ways. After explaining how to find all the prime numbers in a given inter- val, Christopher observes “Prime numbers are what is left when you have taken all the patterns away. I think prime numbers are like life. They are very logical but you could never work out the rules, even if you spent all your time thinking about them.”

ALSO DON’T MISS Proof, by David Auburn. This play tackles thorny questions about authorship, madness, and gender, and tells a compelling story about a dead mathematician’s familial and academic legacy.

FALL 2014 11

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