The best books for mathematics enthusiasts

It is fair to say that many people—even those who loved mathematics as students—view mathematics as having always existed. The idea that definitions and theorems that fill our school textbooks were created or discovered by human beings is something that has never crossed their mind. In fact, mathematics has a long, fascinating, and rich history, and William Dunham’s Journey Through Genius is a perfect introduction to the topic. Dunham expertly writes about the history of topics like geometry, number theory, set theory, and calculus in a way that is entertaining, understandable, and rigorous. After finishing Journey Through Genius, readers will not think about mathematics in the same way, and they will be eager to learn about the history of other mathematical topics, people, and cultures.

Logicomix is as entertaining, beautiful, and informative as it is surprising; it is a graphic novel about the foundations of mathematics. The book follows the philosopher, logician, and mathematician Bertrand Russell and his contemporaries like Georg Cantor, Ludwig Wittgenstein, David Hilbert, Gottlob Frege, Kurt Gödel, and Alan Turing as they try to create a solid structure of logic and set theory on which all of mathematics can be built. Although Logicomix is, strictly speaking, a novel, it stays close to the historical and mathematical truth, and at the end of the book the authors say precisely what liberties they have taken with the true history.

It is no surprise that algorithms, statistics, and computation have changed our lives irrevocably. In many cases these are changes for the better. However, because we view mathematics as true and impartial, it is easy to view the output of algorithms as immune from the biases that affect human decision-making. In Weapons of Math Destruction Cathy O’Neil gives us many reasons to rethink this perception. Algorithms are written by humans and data is collected by humans. Thus, the output of these seemingly impartial algorithms may have the same biases that humans do, or even ones that are worse, and they may possess feedback loops that perpetuate injustice. O’Neil discusses examples like predictive policing, algorithmic judicial sentencing, college rankings, the screening of job applicants, and credit scores in this important and eye-opening book.

They say that Plato was not a mathematician but was a maker of mathematicians. The same could be said of Martin Gardner, a prolific author who wrote, among many other things, the “Mathematical Games” column for Scientific American for a quarter of a century. Although all his books are excellent, The Colossal Book of Mathematics is a great entry point to Gardner’s oeuvre. It consists of what Gardner viewed as his 50 best Scientific American columns along with addenda containing updated material on each topic. With topics like topology, geometry, recreational mathematics, the infinite, and probability, each article is an informative, playful, well-written gem. 

The idea of a fourth dimension grabbed the public’s attention in the late 19th and early 20th centuries. Before Minkowski and Einstein popularized time as the fourth dimension, people were enthralled by the mind-expanding idea of a possible fourth physical dimension perpendicular to our three. Edwin Abbott was one of the first authors to write about this idea for a popular audience. His 1884 novella Flatland beautifully illustrates by analogy how to view higher dimensions by telling the story of two-dimensional figures (polygons and circles) encountering a being who lives in the third dimension. Flatland is also a satirical take on certain aspects of Victorian society such as their view of women and the class structure among men.