511: Mathematical Fallacies and Paradoxes by Bryan Bunch

511.3: Bunch, Bryan. Mathematical Fallacies and Paradoxes. Mineola, NY: Dover, 1997. 210 pp. ISBN 0-486-29664-4.

Dewey Breakdown:

• 500: Science
• 510: Mathematics
• 511: General principles of mathematics
• 511.3: Mathematical logic

About every month or so, diagrams go around social media proving various paradoxes. From proving 2 = 3, or that certain infinite series converge to -1/12, these proofs often use fallacious logic or hidden steps to achieve their ends. Bryan Bunch’s Mathematical Fallacies and Paradoxes collects eight such examples to help broaden our understanding of both logic and math. Be wary, though, this is not for the faint heart.

518: Principle of Numerical Analysis by Alston S. Householder

518: Householder, Alston S. Principles of Numerical Analysis. York, PA: The Maple Press Company, 1953. 246 pp.

Dewey Breakdown:

• 500: Science
• 510: Mathematics
• 518: Numerical analysis

Before I earned a degree in library science, and before became a major in English literature, I wanted to be a mathematician. I was even decently proficient at it. Integrals, differentials, infinite sets—these were all a lot of fun for me. So, for me, Alston Householder’s Principle of Numerical Analysis was a trip down memory lane. Here, he discusses the use and derivation of calculation errors, linear and nonlinear equations, matrix and vector mathematics, and yes, integrals and differentials.

512: A History of Pi by Petr Beckmann

512.924: Beckmann, Petr. A History of Pi. New York: Hippocrene Books, 1990. 189 pp. ISBN 0-8802-9418-3.

Dewey Breakdown:

• 500: Science
• 510: Mathematics
• 512: Algebra
• 512.9: Foundations of algebra
• 512.92: Algebraic operations
• 512.924: Approximation, ratio, and proportion

Pi is an amazing, irrational, and indispensable tool in the mathematical and scientific world. Nature loves a curve, and it takes pi to measure them. At its core, pi is the ratio of the circumference of a circle to its radius. It is a strange quirk of the universe that it takes a little more than three radii to completely measure the circumference. And it’s the “little more” part that has been vexing mathematicians for the last ten thousand years. Petr Beckmann’s A History of Pi (originally written in 1971) is a unique look at the social, scientific, and mathematical history of this strange constant.

516: Beautiful Geometry by Eli Maor and Eugen Jost

516: Maor, Eli and Eugen Jost. Beautiful Geometry. Princeton, NJ: Princeton University Press, 2013. 173 pp. ISBN 978-0-691-15099-4.

Dewey Breakdown:

• 500: Science
• 510: Mathematics
• 516: Geometry

If you want to love, or even like, geometry again, then this book might just do it. Beautiful Geometry pairs Maor’s elegant proofs with Jost’s vivid illustrations to help the layman understand geometry. They start with the basics—point, lines, and shapes—and work their way to Euclid, then prime geometry, infinite series, the golden ratio, experimentation with pi, parabolic geometry, and even fractals and epicycloids. There’s a fair amount of history on famous geometers and how they arrived at their discoveries. At the very least, if the proofs bore you, you can always marvel at the visuals. They’re worth the cost of admission. A quick and pretty book.

514: The Colours of Infinity by Nigel Lesmoir-Gordon

514.742: Lesmoir-Gordon, Nigel, ed. The Colours of Infinity: The Beautry and Power of Fractals. London: Springer, 2010. 172 pp. ISBN 978-1-84966-486-9.

Dewey Breakdown:

• 500: Science
• 510: Mathematics
• 514: Topology
• 514.7: Analytic topology
• 514.74: Global analysis
• 514.742: Fractals

Fractals are both recent and timeless. They have only existed in mathematical literature for the last hundred or so years, but nature has had them from its first day. Fractal patterns exist in snowflakes, in trees, in mountain ridges, in coastlines, and even in broccoli. Although the word “fractal” was coined in 1975 by the famed mathematician Benoit Mandelbrot, work was being done in fractional and recursive geometry around the time of the invention of calculus. Nigel Lesmoir-Gordon’s The Colours of Infinity is collection of essays that explores the mathematical, physical, and imaginative boundaries of fractals and what this means for our understanding of the world today.

510: Number Freak by Derrick Niederman

510: Niederman, Derrick. Number Freak: From 1 to 200 — The Hidden Language of Numbers Revealed. New York: Perigee, 2009. 284 pp. ISBN 978-0-399-53459-1.

Dewey Construction:

• 500: Science
• 510: Mathematics

Every number has a story to tell. And Derrick Niederman, in Number Freak, tells them from 1 to 200.

519: The Unfinished Game by Keith Devlin

519.2: Devlin, Keith. The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. New York: Basic Books, 2008. 181 pp. ISBN 978-0-465-00910-7.

Before you can understand science, you have to have a basic working relationship with mathematics, so books on mathematics are placed at the beginning of the 500s (in the 510s to be exact). Since new and exciting mathematical breakthroughs are made every day, this division keeps getting more and more packed with interesting subsections, but section 519 is reserved for probability and applied mathematics.

In 1654, Blaise Pascal, the precocious son of a French tax collector, sent famous mathematician Pierre de Fermat a letter with a proposed solution to an old but still lingering problem. The problem goes thusly: