John Stillwell is professor of mathematics at the University of San Francisco. He is the author of Reverse Mathematics: Proofs from the Inside Out (Princeton).

"This fascinating book by John Stillwell, an Australian mathematician who won the prestigious Chauvenet Prize, is a carefully structured and clearly written overview of a variety of ‘elementary’ mathematical topics, from number theory, computability, algebra, geometry, calculus, combinatorics, probability, and logic. . . . Specialists will enjoy it, whilst the rest of us will learn a lot."---Forbes.com --- "This excellent book is definitely for mathematicians and fellow travelers. It filled several gaps in areas of my own purported expertise, and opened vistas in others."---George Hacken, Computing Reviews --- "Readers familiar with Stillwell's previous books . . . Will not be surprised that this beautifully produced book features crystal-clear prose which is mathematically accurate, historically aware, philosophically sensitive and rich with novel twists and refreshing insights. . . . I thoroughly enjoyed this thought-provoking and very readable book. It is notably strong (and notably clear) on foundational issues and the manner in which these now permeate the whole of mathematics and, by the end, I really warmed to the idea of trying sensitively to locate the boundary between elementary and advanced mathematics."---Nick Lord, Mathematical Gazette --- "[Elements of Mathematics] is a book that everybody should read. You will be the better for it."---Reuben Hersh, American Mathematical Monthly --- "[A] wonderful book . . . I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics."---Victor Katz, Bulletin of the American Mathematical Society --- "Stillwell uses his broad and impressive command of mathematics to transport a reader through each topic and to a higher level of understanding and questioning." --- "Elements of Mathematicsis a fine . . . overview of the field of mathematics. . . . The writing is clear, succinct, organized, and the diagrams [and] illustrations excellent. . . . While some of the discussion is introductory or elementary, it always leads to deeper, more challenging ideas. . . . [T]his will make a fine basic addition to most mathematicians' bookshelves." --- "[A] wonderful book. . . . I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics."---Victor Katz, Bulletin of the American Mathematical Society --- "From a lifetime of teaching, Stillwell has distilled some nice examples from the entire gamut of elementary mathematics." --- "[Elements of Mathematics] is quite a tour de force, organized by areas of mathematics--arithmetic, computation, algebra, geometry, calculus, and so on--and in each area Stillwell manages to distill down the big ideas and the connections with other areas. He is a master expositor, and the text manages to be engaging and accessible without watering down the mathematics. I definitely learned new things from the book!"---Brent Yorgey, Math Less Traveled --- "An accessible read. . . . Stillwell breaks down the basics, providing both historical and practical perspectives from arithmetic to infinity."---Gemma Tarlach, Discover --- "Stillwell is . . . One of the better current mathematical authors: he writes clearly and engagingly, and makes more of an effort than most to provide historical detail and a sense of how various mathematical ideas tie in with one another. . . . The features we have learned to expect from Stillwell (including, but not limited to, excellent writing) are present in [Elements of Mathematics] as well." --- "A great exploration of elementary mathematics, its limitations, how infinity complicates things, and how various branches of mathematics fit together."---Antonio Cangiano, Math-Blog --- "One of Forbes.com’s 10 Best Astronomy, Physics and Mathematics Books of 2017, chosen by GrrlScientist"