The Joy of Mathematics is based on an in-depth filmed conversation between Howard Burton and Ian Stewart, Emeritus Professor of Mathematics at the University of Warwick and bestselling science and science fiction writer. For Ian Stewart, mathematics is far more than dreary arithmetic, while mathematical thinking is one of the most important—and overlooked—aspects of contemporary society. This wide-ranging conversation explores what mathematics is and why it’s worth doing, symmetry, networks and ...
Nov 12, 2021•1 hr 26 min•Ep. 90
Students and their families face a consequential choice in whether to pursue a degree, and in what area. For those considering mathematics programs, the choice may be particularly fraught: A gulf separates the exploratory and experimental mathematics done by professionals from the computational training of most secondary schools, and this can obscure the meanings of program options. Meanwhile, cultural anxieties and stereotypes can dissuade students who would flourish in mathematical careers. Th...
Nov 05, 2021•55 min•Ep. 68
Our universe might appear chaotic, but deep down it's simply a myriad of rules working independently to create patterns of action, force, and consequence. In Ten Patterns That Explain the Universe (MIT Press, 2021), Brian Clegg explores the phenomena that make up the very fabric of our world by examining ten essential sequenced systems. From diagrams that show the deep relationships between space and time to the quantum behaviors that rule the way that matter and light interact, Clegg shows how ...
Sep 28, 2021•52 min•Ep. 82
As algorithms become ever more significant to and embedded in our everyday lives, ever more accessible introductions to them are needed. While several excellent technical and critical treatments have emerged in recent years, i had not come across a book for the general public that would provide a deep sense for the intuitions and motivations behind their development. Chris Bleakley's new book offers this and more: conceptual rigor woven into historical vignettes in a style that i believe general...
Sep 27, 2021•1 hr 24 min•Ep. 67
Alfred S. Posamentier's Math Tricks: The Surprising Wonders of Shapes and Numbers (Prometheus Books, 2021) has a lovely assortment of puzzles from all areas of mathematics. Some will be familiar to many readers, but there are plenty of ones I’d never seen before – and I’ve seen lots of them. Some are at just the right level to intrigue students who may be put off by the dry way a lot of math courses are taught – and this alone is enough to make any parent consider having the book available when ...
Aug 30, 2021•54 min•Ep. 66
Math Renaissance: Growing Math Circles, Changing Classrooms, and Creating Sustainable Math Education (Natural Math, 2018) couples two educational memoirs: Student Rachel Steinig brings her experience from diverse schooling models, surveys of teachers and fellow students, and selections of peer-reviewed scholarship to an examination of math instruction in the United States. Her chapters seek to locate root causes, transcend conventional advice, and inspire readers to imagine radical alternatives....
Aug 26, 2021•1 hr 2 min•Ep. 65
Sixteen of today's greatest unsolved mathematical puzzles in a story-driven, illustrated volume that invites readers to peek over the edge of the unknown. Most people think of mathematics as a set of useful tools designed to answer analytical questions, beginning with simple arithmetic and ending with advanced calculus. But, as Mage Merlin's Unsolved Mathematical Mysteries (MIT Press, 2020) shows, mathematics is filled with intriguing mysteries that take us to the edge of the unknown. This richl...
Aug 10, 2021•1 hr 9 min•Ep. 78
Cryptoreality is based on an in-depth filmed conversation between Howard Burton and Artur Ekert, Professor of Quantum Physics at the Mathematical Institute at the University of Oxford and Director of the Centre for Quantum Technologies and Lee Kong Chian Centennial Professor at the National University of Singapore. Artur Ekert is one of the pioneers of quantum cryptography. This wide-ranging conversation provides detailed insights into his research and covers many fascinating topics such as math...
Aug 09, 2021•3 hr 56 min•Ep. 21
Pushing the Boundaries is based on an in-depth filmed conversation between Howard Burton and former mathematical physicist and writer Freeman Dyson, who was one of the most celebrated polymaths of our age. Freeman Dyson had his academic home for more than 60 years at the Institute for Advanced Study in Princeton. He has reshaped thinking in fields from math to astrophysics to medicine, while pondering nuclear-propelled spaceships designed to transport human colonists to distant planets. Howard B...
Aug 06, 2021•2 hr 46 min•Ep. 20
While i find it pretty easy to recognize when i'm reading articles in complexity science, i've never been satisfied by definitions of complexity and related concepts. I'm not alone! Researchers' own attempts to define complex systems incorporate a mix of folk wisdom and fraught assumptions anchored to a menagerie of contested examples. The field was ripe for a 2013 article proposing a unified account of complexity, and it's no less ripe today for this book-length expansion. In What Is a Complex ...
Jul 30, 2021•1 hr 14 min•Ep. 64
Plato’s Heaven: A User’s Guide is based on an in-depth filmed conversation between Howard Burton and James Robert Brown, Emeritus Professor of Philosophy at the University of Toronto. This wide-ranging conversation addresses a central theme in current philosophy: Platonism vs. Naturalism and provides accounts of both approaches to mathematics. The Platonist-Naturalist debate over mathematics is explored in a comprehensive fashion and also sheds light on non-mathematical aspects of a dispute that...
Jul 22, 2021•1 hr 29 min•Ep. 9
To many mathematicians and math enthusiasts, the word "innumeracy" brings to mind popular writing like that of John Allen Paulos. But inequities in our quantitative reasoning skills have received considerable interest and attention from researchers lately, including in psychology, development, education, and public health. Innumeracy in the Wild: Misunderstanding and Misusing Numbers (Oxford University Press, 2020) is a unified treatment of these broad-ranging studies, from the ways more and les...
May 31, 2021•1 hr 9 min•Ep. 63
Math circles defy simple narratives. The model was introduced a century ago, and is taking off in the present day thanks in part to its congruence with cutting-edge research in mathematics education. It is a modern approach to teaching—or facilitation—that resonates and finds mutual reinforcement with traditional practices and cultural preservation efforts. A wide range of math circle resources have become available for interested instructors, including the MSRI Math Circles Library, now in its ...
Apr 27, 2021•1 hr 13 min•Ep. 62
Games have been of interest to mathematicians almost since mathematics became a subject. In fact, entire branches of mathematics have arisen simply to analyze certain games. The Raven's Hat: Fallen Pictures, Rising Sequences, and Other Mathematical Games (MIT Press, 2021) does something very different, and something that I think listeners will find intriguing – it uses games in order to explain mathematical concepts. The Raven's Hat presents a series of engaging games that seem unsolvable--but c...
Apr 02, 2021•57 min•Ep. 61
From its more mainstream, business-focused and business-friendly “Lean In” variants, to more radical, critical and intersectional understandings of feminism, the past decade has seen a flourishing of discussion from those proposing and critiquing different schools of thought for the way we think about gender in society. Dr. Eugenia Cheng’s addition to this conversation is x+y: A Mathematician's Manifesto for Rethinking Gender (Basic Books, 2020). She applies insights gained from her mathematical...
Apr 01, 2021•43 min•Ep. 24
Jason Rosenhouse's Games for Your Mind: The History and Future of Logic Puzzles (Princeton UP, 2020) is about a panoply of logic puzzles. You’ll find Mastermind and sudoku discussed early on, and then you’ll be hit with an incredible array of some of the most intriguing logic puzzles that have ever been devised. Some will be familiar to you, but some will almost certainly be brain-teasers you have never heard of. It’s absolutely amazing what a truly deep field grew from recreational pastimes – a...
Jan 25, 2021•56 min•Ep. 59
It would be simple enough to say that mathematics is being done, and that those who do it are mathematicians. Yet, the history and culture of the mathematical community immediately complicate these statements. In her book A New Year's Present from a Mathematician (CRC Press, 2020), Snezana Lawrence guides a tour of European mathematical history that broadens conventional ideas of who mathematicians are and what we do. Framed as journey across the desert out from Alexandria, the book recounts a v...
Jan 08, 2021•56 min•Ep. 58
Math has a complicated relationship with the counterintuitive: Rigorous logic, calculation, and simulation can both help us wrap our minds around phenomena that defy our intuition, and thrust upon us whole new worlds of counterintuitive results. In his new book, Jim Stein introduces readers to several unexpected and sometimes astonishing examples, while demanding a minimal mathematical background. The Fate of Schrodinger's Cat: Using Math and Computers to Explore the Counterintuitive (World Scie...
Dec 07, 2020•1 hr 16 min•Ep. 57
Mathematics as a subject is distinctive in its symbolic abstraction and its potential for logical and computational rigor. But mathematicians tend to impute other qualities to our subject that set it apart, such as impartiality, universality, and elegance. Far from incidental, these ideas prime mathematicians and the public to see in mathematics the answers—for example, an impartial arbiter, or a meritocratic equalizer—to many urgent societal questions. Anna Weltman's new book, Supermath: The Po...
Dec 01, 2020•2 hr 47 min•Ep. 65
Alfred S. Posamentier's The Joy of Geometry (Prometheus, 2020) is a book for someone who has taken geometry but wants to go further. This book, as one might expect, is heavy on diagrams and it is sometimes hard to discuss some of the ideas without reference to a diagram. Also, to be fair, this is not a book intended to be read casually. To fully appreciate this book, it is necessary to sit down, preferably in a comfortable chair with a beverage of one’s choosing, and prepare to give the diagrams...
Nov 11, 2020•57 min•Ep. 55
Doing mathematics can be stimulating, deep, and sometimes fantastic. It can also be frustrating, impenetrable, and at times dispiriting. In her new collection of essays, writer and mathematician Susan D'Agostino shows how math itself can be a useful guide through these experiences. How to Free Your Inner Mathematician: Notes on Mathematics and Life (Oxford University Press) draws upon the theorems, applications, and history of mathematics to inspire lessons and advice for us along our mathematic...
Sep 29, 2020•1 hr 5 min•Ep. 54
The book being discussed is Mathematics Entertainment for the Millions (World Scientific Publishing Co.), by Alfred Posamentier. In reading this book, it occurred to me that it might equally well have been entitled Millions of Mathematical Entertainments. There may not be millions of entertainments, but there’s an incredible amount – most of it easily accessible to a middle-school or high-school student, and that’s exactly the audience that we want to show how enticing mathematics can be. Anyone...
Sep 09, 2020•58 min•Ep. 53
Calculus Reordered: A History of the Big Ideas (Princeton UP, 2019) takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today. David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus re...
Aug 24, 2020•1 hr 27 min•Ep. 77
There are very few math books that merit the adjective ‘charming’ but Mage Merlin's Unsolved Mathematical Mysteries (MIT Press, 2020) is one of them. Satyan Devadoss and Matt Harvey have chosen a truly unique, creative and charming way to acquaint readers with some of the unsolved problems of mathematics. Some are classic, such as the Goldbach Conjecture, some are fairly well known, such as the Collatz Conjecture. Others are less well known but no less fascinating – and all are intriguing and bo...
Aug 13, 2020•58 min•Ep. 51
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 explai...
Jul 10, 2020•1 hr 7 min•Ep. 223
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...
Jul 08, 2020•2 hr 1 min•Ep. 50
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 random...
Jun 25, 2020•43 min•Ep. 164
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 ...
Jun 02, 2020•2 hr 1 min•Ep. 20
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 conventiona...
May 29, 2020•33 min•Ep. 49
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 resear...
Apr 28, 2020•1 hr•Ep. 193
