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 jobâI am a professor of mathematics and the John J. & Ann Curley Faculty Chair in the Liberal Arts at Dickinson Collegeâallows 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
It is fair to say that many peopleâeven those who loved mathematics as studentsâview 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 Dunhamâs Journey Through Geniusis 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.
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 accessibleâŚ
Logicomixis 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 GĂśdel, 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 Logicomixis, 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.
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, heâŚ
Social Security for Future Generations
by
John A. Turner,
This book provides new options for reform of the Social Security (OASI) program. Some options are inspired by the U.S. pension system, while others are inspired by the literature on financial literacy or the social security systems in other countries.
An example of our proposals inspired by the U.S. pensionâŚ
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 OâNeil 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. OâNeil 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.
'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 madeâŚ
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 âMathematical Gamesâ column forScientific American for a quarter of a century. Although all his books are excellent, The Colossal Book of Mathematics is a great entry point to Gardnerâs oeuvre. It consists of what Gardner viewed as his 50 best Scientific Americancolumns 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.Â
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,âŚ
Social Security for Future Generations
by
John A. Turner,
This book provides new options for reform of the Social Security (OASI) program. Some options are inspired by the U.S. pension system, while others are inspired by the literature on financial literacy or the social security systems in other countries.
An example of our proposals inspired by the U.S. pensionâŚ
The idea of a fourth dimension grabbed the publicâs 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 Flatlandbeautifully 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. Flatlandis also a satirical take on certain aspects of Victorian society such as their view of women and the class structure among men.
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 PointlandâŚ
Tales of Impossibilityis the story of the four most famous problems in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problemsâsquaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circleâserved as ever-present muses for mathematicians for more than two millennia. The problems have inspired historyâs greatest mathematical minds and amateurs alike.
The book follows the trail of these problems to show that ultimately their proofsâdemonstrating the impossibility of solving them using only a compass and straightedgeâdepended 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.
