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Barry Mazur invites lovers of poetry to make a leap into mathematics. Through discussions of the role of the imagination and imagery in both poetry and mathematics, Mazur reviews the writings of the e

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 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 a 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 w

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 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 a 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 w

The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction

This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" i

Number is an eloquent, accessible tour de force that reveals how the concept of number evolved from prehistoric times through the twentieth century. Tobias Dantzig shows that the development of math

Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of t

“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

“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