New Books in Mathematics

The branch of mathematics called game theory – the Prisoners Dilemma is a particularly well-known example of a game – is used by philosophers, social scientists, and others to explore many types of social relations between humans and between nonhuman creatures.In Games in the Philosophy of Biology (Cambridge University Press, 2020), Cailin O’Connor introduces the basics of game theory and its particular branch, evolutionary game theory, and discusses how game theoretic models have helped explain the genesis of the meanings of linguistic and nonlinguistic signals, altruistic behavior, the spread of misinformation, and the origins of fair and unfair distributions of benefits in society.O’Connor, who is associate professor of logic and philosophy of science at the University of California–Irvine, also considers some of the drawbacks of game theoretic models. Her short introduction makes a major area of social scientific investigation accessible to readers without mathematical background.  Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Category theory is well-known for abstraction—concepts and tools from diverse fields being recognized as specific cases of more foundational structures—though the field has always been driven and shaped by the needs of applications. Moreover, category theory is rarely introduced even to undergraduate math majors, despite its unifying role in theory and its flexibility in application.Postdoctoral Associate Brendan Fong and Research Scientist David I. Spivak, both at MIT, have written a marvelous and timely new textbook that, as its title suggests, invites readers of all backgrounds to explore what it means to take a compositional approach and how it might serve their needs.An Invitation to Applied Category Theory: Seven Sketches in Compositionality (Cambridge University Press, 2019) has few mathematical prerequisites and is designed in part as a gateway to a wide range of more specialized fields. It also centers its treatment on applications, motivating several key developments in terms of real-world use cases.In this interview we discussed their views on the promise of category theory inside and outside mathematics, their motivations for writing this book, several of the accessible examples and remarkable payoffs included in its chapters, and their aspirations for the future of the field.Suggested companion works:--Tai-Danae Bradley, Math3ma--Eugenia Cheng, The Catsters--Saunders Mac Lane, Mathematics Form and Function--F. William Lawvere & Stephen H. Schanuel, Conceptual Mathematics: A First Introduction to Categories--Eugenia Cheng, x + y: A Mathematician's Manifesto for Rethinking GenderCory Brunson (he/him) is a Research Assistant Professor in the Laboratory for Systems Medicine at the University of Florida. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

For decades, statisticians, social scientists, psychologists, and economists (among them Nobel Prize winners) have spent massive amounts of precious time thinking about whether streaks actually exist.After all, a substantial number of decisions that we make in our everyday lives are quietly rooted in this one question: If something happened before, will it happen again? Is there such a thing as being in the zone? Can someone have a “hot hand”? Or is it simply a case of seeing patterns in randomness? Or, if streaks are possible, where can they be found?In The Hot Hand: The Mystery and Science of Streaks (Custom House, 2020), Wall Street Journal reporter Ben Cohen offers an unfailingly entertaining and provocative investigation into these questions.He begins with how a $35,000 fine and a wild night in New York revived a debate about the existence of streaks that was several generations in the making. We learn how the ability to recognize and then bet against streaks turned a business school dropout named David Booth into a billionaire, and how the subconscious nature of streak-related bias can make the difference between life and death for asylum seekers. We see how previously unrecognized streaks hidden amidst archival data helped solve one of the most haunting mysteries of the twentieth century, the disappearance of Raoul Wallenberg.Cohen also exposes how streak-related incentives can be manipulated, from the five-syllable word that helped break arcade profit records to an arc of black paint that allowed Stephen Curry to transform from future junior high coach into the greatest three-point shooter in NBA history.Crucially, Cohen also explores why false recognition of nonexistent streaks can have cataclysmic results, particularly if you are a sugar beet farmer or the sort of gambler who likes to switch to black on the ninth spin of the roulette wheel.Paul Knepper was born and raised in New York and currently resides in Austin. He used to cover basketball for Bleacher Report and his first book titled Knicks of the Nineties: Ewing, Oakley, Starks and the Brawlers Who Almost Won It All is due out this year. You can reach Paul at paulknepper@gmail.com and follow him on Twitter @paulieknep. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/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 john.weston@aalto.fi and @johnwphd. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Today I talked to Alfred S. Posamentier, a co-author (with Christian Spreitzer) of Math Makers: The Lives and Works of 50 Famous Mathematicians (Prometheus, 2020). This charming book is more than just mathematics, because mathematicians are not just makers of mathematics. They are human beings whose life stories are often not just entertaining, but are sometimes interwoven with important historical events. Of course you get the math in this book –but I would have read this book just for the fascinating anecdotes. Just for openers, how many other disciplines have people who made remarkable contributions but were arrested for revolutionary activities in their teens, and then killed in a duel at age 21? This is the story of Evariste Galois, just one of the 50 fascinating lives you'll read about in this book. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics