Barry Mazur (Harvard University)

Barry Mazur is the author of books: Imagining Numbers, Prime Numbers and the Riemann Hypothesis, Kolyvagin Systems, Numeros Imaginados (En Especial La Raiz Cuadrada De-15), Universal Extensions And One Dimensional Crystalline Cohomology, Current Developments in Mathematics, P-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture: A Workshop on P-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture, August 12-16, 1991, Boston University, The Education of T.C. Mits: What modern mathematics means to you, Infinity: Beyond the Beyond the Beyond, Number: The Language of Science, The Masterpiece Science Edition

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Title

Description

01

Shows how the art of mathematical imagining is not as mysterious as it seems. This book reveals how anyone can begin to visualize the enigmatic 'imaginary numbers' that first baffled mathematicians in the 16th century.

02

Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann Hypothesis, which remains to be one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann Hypothesis. Students with minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann Hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann Hypothesis.

07

P-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture: A Workshop on P-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture, August 12-16, 1991, Boston University

Recent years have witnessed significant breakthroughs in the theory of $p$-adic Galois representations and $p$-adic periods of algebraic varieties. This book contains papers presented at the Workshop on $p$-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture, held at Boston University in August 1991. The workshop aimed to deepen understanding of the interdependence between $p$-adic Hodge theory, analogues of the conjecture of Birch and Swinnerton-Dyer, $p$-adic uniformization theory, $p$-adic differential equations, and deformations of Galois representations. Much of the workshop was devoted to exploring how the special values of ($p$-adic and classical'') $L$-functions and their derivatives are relevant to arithmetic issues, as envisioned in Birch-Swinnerton-Dyer-type conjectures'', Main Conjectures'', and Beilinson-type conjectures'' \a la Greenberg and Coates.

08

"A delightful book."—*New York Times*

"I have studied with pleasure [this] new book…Beautiful examples…Illuminating. I am convinced that [Lieber's] original enterprise will get the recognition it so richly deserves."—Albert Einstein

"The Liebers have written an ingenious, entertaining, and illuminating book."—*Saturday Review of Literature*

"The book should be 'required reading' especially for non-mathematicians."—E.T. Bell, author of*The Development of Mathematics*

First published in 1942, this whimsical exploration of how to think in a mathematical mood continues to delight math-lovers of all ages.

Do you know that two times two is not always four; that the sum of the angles in a triangle does not always equal 180°; that sometimes it is possible to draw two parallel lines through the same point? In*The Education of T. C. MITS*, Lillian Lieber opens the door to the wonder of mathematical thinking and its application to everyday life. Lieber uses simple language and fanciful illustrations drawn by her husband, Hugh, to present fundamental mathematical concepts with a deft touch.

The new foreword by Harvard University mathematics professor Barry Mazur is a tribute to the Liebers' influence on generations of mathematicians.

**Lillian Lieber** was the head of the Department of Mathematics at Long Island University. She wrote a series of lighthearted (and well-respected) math books in the 1940s, including *The Einstein Theory of Relativity*, *Infinity*, and *Mits, Wits & Logic*.

**Hugh Gray Lieber** was the head of the Department of Fine Arts at Long Island University. He illustrated many books written by his wife Lillian.

**Barry Mazur** Barry Mazur is a mathematician and is the Gerhard Gade University Professor at Harvard University. He is the author of *Imagining Numbers (particularly the square root of minus fifteen)*. He has won numerous honors in his field, including the Veblen Prize, Cole Prize, Steele Prize, and Chauvenet Prize.

"I have studied with pleasure [this] new book…Beautiful examples…Illuminating. I am convinced that [Lieber's] original enterprise will get the recognition it so richly deserves."—Albert Einstein

"The Liebers have written an ingenious, entertaining, and illuminating book."—

"The book should be 'required reading' especially for non-mathematicians."—E.T. Bell, author of

First published in 1942, this whimsical exploration of how to think in a mathematical mood continues to delight math-lovers of all ages.

Do you know that two times two is not always four; that the sum of the angles in a triangle does not always equal 180°; that sometimes it is possible to draw two parallel lines through the same point? In

The new foreword by Harvard University mathematics professor Barry Mazur is a tribute to the Liebers' influence on generations of mathematicians.

09

"The interpolations tying mathematics into human life and thought are brilliantly clear."—*Booklist*

"Her presentation…is conversational and humorous, and should help to simplify some complex concepts."—*Kirkus*

Infinity. It sounds simple…but is it? This elegant, accessible, and playful book artfully illuminates one of the most intriguing ideas in mathematics. Lillian Lieber presents an entertaining, yet thorough, explanation of the concept and cleverly connects mathematical reasoning to larger issues in society.*Infinity* includes a new foreword by Harvard professor Barry Mazur.

"Another excellent book for the lay reader of mathematics…In explaining [infinity], the author introduces the reader to a good many other mathematical terms and concepts that seem unintelligible in a formal text but are much less formidable when presented in the author's individual and very readable style."—*Library Journal*

"Mrs. Lieber, in this text illustrated by her husband, Hugh Gray Lieber, has tackled the formidable task of explaining infinity in simple terms, in short line, short sentence technique popularized by her in*The Education of T.C. MITS*."—*Chicago Sunday Tribune*

**Lillian Lieber** was the head of the Department of Mathematics at Long Island University. She wrote a series of lighthearted (and well-respected) math books in the 1940s, including *The Einstein Theory of Relativity* and *The Education of T.C. MITS* (also published by Paul Dry Books).

**Hugh Gray Lieber** was the head of the Department of Fine Arts at Long Island University. He illustrated many books written by his wife Lillian.

**Barry Mazur** is a mathematician and is the Gerhard Gade University Professor at Harvard University. He is the author of *Imagining Numbers (particularly the square root of minus fifteen)*. He has won numerous honors in his field, including the Veblen Prize, Cole Prize, Steele Prize, and Chauvenet Prize.

"Her presentation…is conversational and humorous, and should help to simplify some complex concepts."—

Infinity. It sounds simple…but is it? This elegant, accessible, and playful book artfully illuminates one of the most intriguing ideas in mathematics. Lillian Lieber presents an entertaining, yet thorough, explanation of the concept and cleverly connects mathematical reasoning to larger issues in society.

"Another excellent book for the lay reader of mathematics…In explaining [infinity], the author introduces the reader to a good many other mathematical terms and concepts that seem unintelligible in a formal text but are much less formidable when presented in the author's individual and very readable style."—

"Mrs. Lieber, in this text illustrated by her husband, Hugh Gray Lieber, has tackled the formidable task of explaining infinity in simple terms, in short line, short sentence technique popularized by her in