The best books for mathematics enthusiasts

David S. Richeson Author Of Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity
By David S. Richeson

Who am I?

Although I loved studying mathematics in school, I have since learned that mathematics is so much more than school mathematics. My enthusiasm for all areas of mathematics has led me to conduct original mathematical research, to study the history of mathematics, to analyze puzzles and games, to create mathematical art, crafts, and activities, and to write about mathematics for general audiences. I am fortunate that my job—I am a professor of mathematics and the John J. & Ann Curley Faculty Chair in the Liberal Arts at Dickinson College—allows me the freedom to follow my passions, wherever they take me, and to share that passion with my students and with others. 

I wrote...

Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity

By David S. Richeson,

Book cover of Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity

What is my book about?

Tales of Impossibility is the story of the four most famous problems in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—served as ever-present muses for mathematicians for more than two millennia. The problems have inspired history’s greatest mathematical minds and amateurs alike. 

The book follows the trail of these problems to show that ultimately their proofs—demonstrating the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Although the problems were based on geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus.

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The books I picked & why

Book cover of Journey Through Genius: The Great Theorems of Mathematics

Why did I love this book?

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.

By William Dunham,

Why should I read it?

1 author picked Journey Through Genius as one of their favorite books, and they share why you should read it.

What is this book about?

Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve.

Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator - from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible…

Logicomix: An Epic Search for Truth

By Apostolos Doxiadis, Christos Papadimitriou,

Book cover of Logicomix: An Epic Search for Truth

Why did I love this book?

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.

By Apostolos Doxiadis, Christos Papadimitriou,

Why should I read it?

4 authors picked Logicomix as one of their favorite books, and they share why you should read it.

What is this book about?

This brilliantly illustrated tale of reason, insanity, love and truth recounts the story of Bertrand Russell's life. Raised by his paternal grandparents, young Russell was never told the whereabouts of his parents. Driven by a desire for knowledge of his own history, he attempted to force the world to yield to his yearnings: for truth, clarity and resolve. As he grew older, and increasingly sophisticated as a philosopher and mathematician, Russell strove to create an objective language with which to describe the world - one free of the biases and slippages of the written word. At the same time, he…

Book cover of Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy

Why did I love this book?

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.

By Cathy O’Neil,

Why should I read it?

10 authors picked Weapons of Math Destruction as one of their favorite books, and they share why you should read it.

What is this book about?

'A manual for the 21st-century citizen... accessible, refreshingly critical, relevant and urgent' - Financial Times

'Fascinating and deeply disturbing' - Yuval Noah Harari, Guardian Books of the Year

In this New York Times bestseller, Cathy O'Neil, one of the first champions of algorithmic accountability, sounds an alarm on the mathematical models that pervade modern life -- and threaten to rip apart our social fabric.

We live in the age of the algorithm. Increasingly, the decisions that affect our lives - where we go to school, whether we get a loan, how much we pay for insurance - are being made…

Book cover of The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems

Why did I love this 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. 

By Martin Gardner,

Why should I read it?

1 author picked The Colossal Book of Mathematics as one of their favorite books, and they share why you should read it.

What is this book about?

Whether discussing hexaflexagons or number theory, Klein bottles or the essence of "nothing," Martin Gardner has single-handedly created the field of "recreational mathematics." The Colossal Book of Mathematics collects together Gardner's most popular pieces from his legendary "Mathematical Games" column, which ran in Scientific American for twenty-five years. Gardner's array of absorbing puzzles and mind-twisting paradoxes opens mathematics up to the world at large, inspiring people to see past numbers and formulas and experience the application of mathematical principles to the mysterious world around them. With articles on topics ranging from simple algebra to the twisting surfaces of Mobius strips,…

Book cover of Flatland: A Romance of Many Dimensions

Why did I love this book?

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.

By Edwin A. Abbott,

Why should I read it?

3 authors picked Flatland as one of their favorite books, and they share why you should read it.

What is this book about?

This masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square, a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status.
Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland…

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