Introduction -- A Citizen’s Dilemma -- The Structure of Mathematics -- A Danger Scale -- Public Key Encryption I -- Public Key Encryption II -- Fractals -- Graphs -- Military Math -- Statistics – A Rant -- Estimation -- Ramanujan -- Hardy -- It’s Obvious -- Chaos -- Recognition -- Map Coloring -- Groups -- Topology I -- Topology II -- Non-existence Proofs -- Existence Proofs -- Can’t Be Computed -- Can’t Be Proved -- Games -- The Greatest Three -- Sets -- Infinity -- The Largest Hotel Ever -- Tied Up in Knots -- Probably -- Rush Hour Traffic -- Fermat and His Last Theorem -- A Million Bucks -- Russia vs. America -- Cardano, Viète and Notation -- President James Garfield -- Error-Correcting Codes -- Mercator Maps -- Ball and Saddle Geometries -- The Spherical Earth -- Consistency -- Can Be Proved -- Cycloids -- C******* of Variations -- Amazing Waves -- How to Push a Pendulum -- Surprising Theorems -- Mathematical Aesthetics -- Katherine Johnson’s Math -- My Career as a Mathematician -- Afterword -- Further Reading -- Movies About Real Mathematicians.

This book answers, in the form of short and entertaining vignettes, the question: "What do mathematicians really do?" Readers will learn that mathematicians use numbers in the same way that novelists use letters. The individual letters are typed while the author thinks on a much grander scale, invisible to the observer. Requiring only familiarity with the multiplication table (and that for only one vignette), the book makes accessible a variety of mathematical concepts, such as game theory, chaos, and, as the author puts it, the c******* of variations. The author accomplishes this with a light, engaging style, and a range of real-world examples that includes everything from barbershops to President James Garfield. Mathematicians Don't Work With Numbers will be of interest to the large audience of people who have always assumed that mathematicians do, in fact, work with numbers.