Mathematics and Its History

John Stillwell

Get ready to embark on an extraordinary journey through undergraduate mathematics with Mathematics and its History by John Stillwell. Unlike traditional math textbooks, this book offers a captivating and concise exploration of the subject.

In order to truly appreciate the depth of this book, the author assumes readers have a solid understanding of basic calculus, algebra, geometry, set theory, and some advanced concepts like group theory, topology, and differential equations. This makes it the perfect companion for senior seminars or advanced students considering graduate school.

What sets Mathematics and Its History apart is its engaging and accessible writing style. I couldn’t put it down, even when it meant sacrificing my usual thrilling novels. Each chapter provides a preview section, setting the stage for what’s to come. The inclusion of exercises and brief biographies of influential mathematicians keeps readers engaged and adds depth to the topics discussed. Finally, the book fittingly concludes with a brief biography of the legendary mathematician Paul Erdos.

Stillwell masterfully weaves together the dominant themes of undergraduate mathematics, and the table of contents alone showcases the vast scope of the text. Let me highlight two chapters that particularly caught my attention.

The chapter on simple groups offers a fascinating history of the classification of finite simple groups, a major achievement in 20th-century mathematics. Simple groups, initially thought to be exhaustively represented by cyclic groups of prime order, were later joined by the alternating groups and the finite groups of “Lie type.” Further discoveries led to the identification of sporadic simple groups, and the tireless efforts of mathematicians ultimately resulted in the complete cataloging of 26 sporadic simple groups. Stillwell effortlessly brings this triumph to life, offering insights into the challenges this classification problem posed.

The chapter on polynomial equations is another standout. Starting with linear equations, the reader is taken on a carefully constructed journey through quadratic, cubic, and quartic equations. From quadratic irrationals to the impossibility of duplicating the cube using only straightedge and compass, this chapter reveals the fascinating interconnections between different mathematical concepts.

While Mathematics and its History brilliantly connects seemingly disparate areas of mathematics, each chapter can be read independently. I highly recommend this book to anyone with an interest in the history of mathematics. Mathematics and its History is also an invaluable resource for mathematics teachers, providing enriching material for undergraduate courses. If you’re looking for a gift for an outstanding math major or the president of a math club, look no further. But be warned – once you pick up Mathematics and its History, it’s hard to put down!