New Books in Mathematics

Brian Greene is a Professor of Mathematics and Physics at Columbia University in the City of New York, where he is the Director of the Institute for Strings, Cosmology, and Astroparticle Physics, and co-founder and chair of the World Science Festival. He is well known for his TV mini-series about string theory and the nature of reality, including the Elegant Universe, which tied in with his best-selling 2000 book of the same name. In this episode, we talk about his latest popular book Until the End of Time: Mind, Matter, and Our Search for Meaning in an Evolving Universe (Random House, 2020)

Until the End of Time gives the reader a theory of everything, both in the sense of a “state of the academic union”, covering cosmology and evolution, consciousness and computation, and art and religion, and in the sense of showing us a way to apprehend the often existentially challenging subject matter. Greene uses evocative autobiographical vignettes in the book to personalize his famously lucid and accessible explanations, and we discuss these episodes further in the interview. Greene also reiterates his arguments for embedding a form of spiritual reverie within the multiple naturalistic descriptions of reality that different areas of human knowledge have so far produced.

John Weston is a University Teacher of English in the Language Centre at Aalto University, Finland. His research focuses on academic communication. He can be reached at [email protected] and @johnwphd.

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Introductory courses in discrete mathematics cover a variety of distinctive but interconnected topics, from the underpinnings of logic and set theory through overviews of combinatorics and graph theory, which lend themselves to equally diverse presentation styles. In Discrete Mathematics with Ducks (Second Edition; CRC Press, 2018), dr. sarah-marie belcastro has reimagined both course and text. The book is written in an accessible and lighthearted style yet covers the full breadth of conventional topics and several more besides: Early chapters include much valuable advice on how to read, do, and write mathematics—essential points of reference for the mathematically inexperienced or disinclined. Meanwhile, the book includes an introductory chapter on algorithms and several bonus chapters, for example on number theory and on complexity, which instructors and interested students can subset as they please. Each chapter is arranged to support a week of gentle prep reading and discovery-based classroom activity. This makes the book a solid resource for active learning in the mathematics curriculum as well as for independent and group study.

Suggested companion work: Daniel Pinkwater, Ducks!

Cory Brunson (he/him) is a Postdoctoral Fellow at the Center for Quantitative Medicine at UConn Health.

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Slavery and the University: Histories and Legacies (University of Georgia Press, 2019), edited by Leslie M. Harris, James T. Campbell, and Alfred L. Brophy, is the first edited collection of scholarly essays devoted solely to the histories and legacies of this subject on North American campuses and in their Atlantic contexts. Gathering together contributions from scholars, activists, and administrators, the volume combines two broad bodies of work: (1) historically based interdisciplinary research on the presence of slavery at higher education institutions in terms of the development of proslavery and antislavery thought and the use of slave labor; and (2) analysis on the ways in which the legacies of slavery in institutions of higher education continued in the post–Civil War era to the present day.

The collection features broadly themed essays on issues of religion, economy, and the regional slave trade of the Caribbean. It also includes case studies of slavery’s influence on specific institutions, such as Princeton University, Harvard University, Oberlin College, Emory University, and the University of Alabama. Though the roots of Slavery and the University stem from a 2011 conference at Emory University, the collection extends outward to incorporate recent findings. As such, it offers a roadmap to one of the most exciting developments in the field of U.S. slavery studies and to ways of thinking about racial diversity in the history and current practices of higher education.

Today I spoke with Leslie Harris about the book. Dr. Harris is a professor of history at Northwestern University. She is the coeditor, with Ira Berlin, of Slavery in New York and the coeditor, with Daina Ramey Berry, of Slavery and Freedom in Savannah (Georgia).

Adam McNeil is a History PhD student at Rutgers University-New Brunswick.

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Alex Berke's Beautiful Symmetry (MIT Press, 2020) is both a fascinating book and a concept -- it's like no other book I’ve ever read. It's a coloring book about math, inviting us to engage with mathematical concepts visually through coloring challenges and visual puzzles. We can explore symmetry and the beauty of mathematics playfully, coloring through ideas usually reserved for advanced courses. The book is for children and adults, for math nerds and math avoiders, for educators, students, and coloring enthusiasts.

Through illustration, language that is visual, and words that are jargon-free, the book introduces group theory as the mathematical foundation for discussions of symmetry, covering symmetry groups that include the cyclic groups, frieze groups, and wallpaper groups. The illustrations are drawn by algorithms, following the symmetry rules for each given group. The coloring challenges can be completed and fully realized only on the page; solutions are provided. Online, in a complementary digital edition, the illustrations come to life with animated interactions that show the symmetries that generated them.

Traditional math curricula focus on arithmetic and the manipulation of numbers, and may make some learners feel that math is not for them. By offering a more visual and tactile approach, this book shows how math can be for everyone. Combining the playful and the pedagogical, Beautiful Symmetry offers both relaxing entertainment for recreational colorers and a resource for math-curious readers, students, and educators.

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Hot Molecules, Cold Electrons: From the Mathematics of Heat to the Development of the Trans-Atlantic Telegraph Cable (Princeton University Press, 2020), by Paul Nahin, is a book that is meant for someone who is comfortable with calculus, but for those readers who are, it is a treat. It is a thorough study of the history and mathematics of the heat equation, which is not only important as an analysis of heat, its analysis marked the beginning of Fourier series. It came as a surprise to me that the heat equation was also instrumental in analyzing the problem of laying the transatlantic cable that was one of the great engineering feats of the nineteenth century. Although it isn’t necessary to work through the math to appreciate this book, I think that students studying this material would not only find Paul’s treatments easy to follow, but would benefit greatly by learning something of the history that surrounds the development of the analysis and applications of the heat equation.

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Paradox is a sophisticated kind of magic trick. A magician's purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn't require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind: 75 Ingenious Paradoxes in Mathematics, Physics, and Philosophy (MIT Press, 2020), Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts―and how reason can dispel the illusion of contradiction.

The journey begins with “a most ingenious paradox” from Gilbert and Sullivan's Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform “supertasks”; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world―and much more.

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From an undergraduate perspective, coming from the rigid proofs and concrete constructions of middle- or high-school courses, the broad discipline of geometry can be at once intimately familiar and menacingly exotic. For most of its history, and perhaps for many of the same reasons, geometers struggled to come to terms with the unsolved problems, unstated assumptions, and untapped generalizability contained in the "bible of mathematics", Euclid's Elements.

In their recent text, Geometry: The Line and the Circle (MAA Press, 2018), Maureen T. Carroll and Elyn Rykken have produced a unified survey of Euclidean and many significant non-Euclidean geometries, one that draws from the patterns of historical development to immerse students into progressively new territory. Their book is organized around the Elements but soon (and often) detours into spherical, finite, and other geometries that bring the limitations of the classic text—and the contributions of subsequent geometers—to the fore. Throughout, they examine the shifting roles and behaviors of two fundamental geometric concepts, the line and the circle—a narrative hook that might deserve more play in mathematics texts! In addition to their historical vignettes, Carroll and Rykken include rich selections of exercises and incorporate a variety of tactile and online tools, and their treatment is held together in an accessible and absorbing writing style. The book is tailored to an upper-level undergraduate course but could also support a history of mathematics or introduction to proofs course.

Suggested companion works:

Edwin A. Abbott, Flatland: A Romance of Many Dimensions (+ sequels & film adaptations)

Norton Juster, The Dot and the Line (+ film adaptation)

Cory Brunson (he/him) is a Postdoctoral Fellow at the Center for Quantitative Medicine at UConn Health.

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How does the world of book reviews work? In Inside the Critics’ Circle: Book Reviewing in Uncertain Times (Princeton University Press, 2020), Phillipa Chong, assistant professor in sociology at McMaster University, provides a unique sociological analysis of how critics confront the different types of uncertainty associated with their practice. The book explores how reviewers get matched to books, the ethics and etiquette of negative reviews and ‘punching up’, along with professional identities and the future of criticism. The book is packed with interview material, coupled with accessible and easy to follow theoretical interventions, creating a text that will be of interest to social sciences, humanities, and general readers alike.

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If you’re a grad student facing the ugly reality of finding a tenure-track job, you could easily be forgiven for thinking about a career change. However, if you’ve spent the last several years working on a PhD, or if you’re a faculty member whose career has basically consisted of higher ed, switching isn’t so easy. PhD holders are mostly trained to work as professors, and making easy connections to other careers is no mean feat. Because the people you know were generally trained to do the same sorts of things, an easy source of advice might not be there for you.

Thankfully, for anybody who wishes there was a guidebook that would just break all of this down, that book has now been written. Going Alt-Ac: A Guide to Alternative Academic Careers (Stylus Publishing, 2020) by Kathryn E. Linder, Kevin Kelly, and Thomas J. Tobin offers practical advice and step-by-step instructions on how to decide if you want to leave behind academia and how to start searching for a new career. If a lot of career advice is too vague or too ambiguous, this book corrects that by outlining not just how to figure out what you might want to do, but critically, how you might go about accomplishing that.

Zeb Larson is a recent graduate of The Ohio State University with a PhD in History. His research deals with the anti-apartheid movement in the United States. To suggest a recent title or to contact him, please send an e-mail to [email protected].

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The so-called Sabermetrics revolution in baseball that began in the 1970s, popularized by the book—and later Hollywood film—Moneyball, was supposed to represent a triumph of observation over intuition. Cash-strapped clubs need not compete for hyped-up prospects when undervalued players provide better price per run scored. Q.E.D., right?

In Scouting and Scoring: How We Know What We Know About Baseball (Princeton University Press, 2019), historian of science Christopher J. Phillips rejects his titular dualism. He shows us that baseball can be, in the words of seminal anthropologist and noted Tampa Bay Rays fan* Claude Lévi-Strauss, “good to think with.” Both traditional amateur scouts and statistically-savvy scorers rely on metrics and bureaucracy to make their judgments count, as it were. Some like to say that baseball is quantitative at its core, but by tracing the co-evolution of the sport’s competing data sciences—with episodes that bear witness to the development of the modern press and digital computers—Phillips crafts a compelling narrative sure to delight baseball fans and historians of the human sciences alike.

*kidding

Mikey McGovern is a PhD candidate in Princeton University’s Program in the History of Science. He is writing a dissertation on how people used discrimination statistics to argue about rights in 1970s America, and what this means for histories of bureaucracy, quantification, law, politics, and race.

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