Two, Three, Four, and More: The Mathematically Special Dimensions
Jun 2027 · Princeton University Press
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456
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About this ebook
A beautifully illustrated exploration of the remarkable world of mathematics in low dimensions
Highly valued results in mathematics are often general: proofs in all dimensions, solutions for all degrees of polynomials. Yet great richness can be found in particular cases. John Stillwell presents a visual panorama of the multitudes that live in dimensions 2, 3, and 4—and a few higher dimensions—through the interplay of geometry, topology, and algebra.
We tend to think of the dimensions 2, 3, and 4 as the dimensions of our physical experience in space and time, but they are also of exceptional mathematical interest. Together with the degrees 2, 3, and 4 of equations, they cover some of the most remarkable mathematical objects and pose problems ranging from easy, to hard, to unsolvable. Each chapter of this engaging book focuses on a dimension or degree, starting at 2 dimensions and ascending to 4 dimensions and then beyond to objects such as the Leech lattice in 24 dimensions. The gradual increase in dimension reveals what is gained and what is lost with a bit more space to work in. Along the way, Stillwell brings the mathematics to life through rich examples, engaging historical context, and vivid anecdotes about the mathematicians who uncovered surprising solutions—or revealed why some problems can’t be solved.
With hundreds of illustrations, Two, Three, Four, and More is an illuminating mathematical tour by one of the discipline’s leading expositors, revealing how these intriguing special cases underpin some of the deepest ideas in mathematics.
Highly valued results in mathematics are often general: proofs in all dimensions, solutions for all degrees of polynomials. Yet great richness can be found in particular cases. John Stillwell presents a visual panorama of the multitudes that live in dimensions 2, 3, and 4—and a few higher dimensions—through the interplay of geometry, topology, and algebra.
We tend to think of the dimensions 2, 3, and 4 as the dimensions of our physical experience in space and time, but they are also of exceptional mathematical interest. Together with the degrees 2, 3, and 4 of equations, they cover some of the most remarkable mathematical objects and pose problems ranging from easy, to hard, to unsolvable. Each chapter of this engaging book focuses on a dimension or degree, starting at 2 dimensions and ascending to 4 dimensions and then beyond to objects such as the Leech lattice in 24 dimensions. The gradual increase in dimension reveals what is gained and what is lost with a bit more space to work in. Along the way, Stillwell brings the mathematics to life through rich examples, engaging historical context, and vivid anecdotes about the mathematicians who uncovered surprising solutions—or revealed why some problems can’t be solved.
With hundreds of illustrations, Two, Three, Four, and More is an illuminating mathematical tour by one of the discipline’s leading expositors, revealing how these intriguing special cases underpin some of the deepest ideas in mathematics.
A beautifully illustrated exploration of the remarkable world of mathematics in low dimensions
Highly valued results in mathematics are often general: proofs in all dimensions, solutions for all degrees of polynomials. Yet great richness can be found in particular cases. John Stillwell presents ...
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About the author
John Stillwell is emeritus professor of mathematics at the University of San Francisco and an affiliate of the School of Mathematics at Monash University in Melbourne. His many books include The Story of Proof: Logic and the History of Mathematics; Reverse Mathematics: Proofs from the Inside Out; and Elements of Mathematics: From Euclid to Gödel (all Princeton).
John Stillwell is emeritus professor of mathematics at the University of San Francisco and an affiliate of the School of Mathematics at Monash University in Melbourne. His many books include The Story of Proof: Logic and the History of Mathematics; Reverse Mathematics: Proofs from the Inside Out;...
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