New Books in Mathematics

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 their child says that they hate math. Math is valuable not just because we can use it to balance our checking account or send rockets to the moon, but because it helps us think – and this book presents a lot of math in a very appealing fashion. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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. Teacher Rodi Steinig invites readers into the role of leading math circles with detailed play-by-plays from her own experience. These chapters evince the importance (and interplay) in this role of background knowledge, preparation, compassion, and improvisation—and, perhaps most saliently for beginning teachers, of resisting the urge to rescue.Taken together, the book critiques the existing systems that provide children's math education and drills down on an alternative model whose popularity continues to grow. Among my favorite parts of the book were Rodi's self-reflective thought bubbles on her performance facilitating math circles and Rachel's chapter on math instruction from a human rights perspective. The book is intended for teachers and parents of school-age children, though i think middle and high school students and even casual readers would find value in this forthright, thorough, and readable work. It was an absolute delight to discuss the book with both its authors!Suggested Companion Works:Rochelle Gutiérrez, Rehumanizing Mathematics: A Vision for the FutureFrancis Su, Mathematics for Human FlourishingDonald Finkel, Teaching with Your Mouth ShutRobert Kaplan and Ellen Kaplan, Out of the Labyrinth: Setting Mathematics FreeDave Auckly, Bob Klein, Amanda Serenevy, Tatiana Shubin, Inspiring Mathematics: Lessons from the Navajo Nation Math CirclesRodi Steinig is an educator, author, and teacher trainer who has educated K-12 students in an inquiry-based approach for over twenty years. She founded the Math Renaissance Math Circle in 2011 hoping to awaken children’s inner mathematicians, to shepherd the unfolding of their abstract reasoning, and to disabuse them of the notion that math is the study of memorizing a bunch of facts and algorithms.Rachel recently graduated from the University of Pennsylvania with a B.A. in Political Science. She is currently a Border Rights Project Fellow at the nonprofit Al Otro Lado, providing legal services to asylum-seekers at the border in Tijuana. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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 richly illustrated, story-driven volume presents sixteen of today's greatest unsolved mathematical puzzles, all understandable by anyone with elementary math skills. These intriguing mysteries are presented to readers as puzzles that have time-traveled from Camelot, preserved in the notebook of Merlin, the wise magician in King Arthur's court.Our guide is Mage Maryam (named in honor of the brilliant young mathematician, the late Maryam Mirzakhani), a distant descendant of Merlin. Maryam introduces the mysteries—each of which is presented across two beautifully illustrated pages—and provides mathematical and historical context afterward. We find Merlin confronting mathematical puzzles involving tinker toys (a present for Camelot's princesses from the sorceress Morgana), cake-slicing at a festival, Lancelot's labyrinth, a vault for the Holy Grail, and more. Each mystery is a sword awaiting removal from its stone, capturing the beauty and power of mathematics. Galina Limorenko is a doctoral candidate in Neuroscience with a focus on biochemistry and molecular biology of neurodegenerative diseases at EPFL in Switzerland. To discuss and propose the book for an interview you can reach her at galina.limorenko@epfl.ch. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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 mathematical and physical intuition, a detailed history of cryptography from antiquity to the present day and how it works in practice, the development of quantum information science, the nature of reality, and more.Howard Burton is the founder of the Ideas Roadshow, Ideas on Film and host of the Ideas Roadshow Podcast. He can be reached at howard@ideasroadshow.com. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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 Burton is the founder of the Ideas Roadshow, Ideas on Film and host of the Ideas Roadshow Podcast. He can be reached at howard@ideasroadshow.com. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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 System? (Yale UP, 2020), philosopher of science James Ladyman and physicist and mathematician Karoline Wiesner systematically interrogate popular definitions. They break the most commonly cited features into three bins: truisms on which there is universal agreement, the conditions necessary for complexity to arise, and various emergent products of complexity. A key insight of their account, for me, was to understand emergence as a relation between features rather than one feature among many.The book is compact, accessible, and at times profound. Indeed, James and Karoline bring the lessons of their account to some of the most consequential complex systems of our time, including Earth's climate and biosphere as well as our global social media ecosystem. I was honored to host them in conversation on this episode, and i encourage listeners to pick up the book itself for deeper dives into the topics we discussed.James Ladyman is professor of philosophy at the University of Bristol and works mainly in the philosophy of science. Karoline Wiesner is professor of physics at the University of Potsdam and uses information theory to understand complex systems.Cory Brunson is a Research Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. His research focuses on geometric and topological approaches to the analysis of medical and healthcare data. He welcomes book suggestions, listener feedback, and transparent supply chains. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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 is central to contemporary philosophy. Thought experiments stand as a fascinating challenge to the necessity of data in the empirical sciences. Are these experiments, conducted uniquely in our imagination, simply rhetorical devices or communication tools or are they an essential part of scientific practice? This book also surveys the current state of this debate and explores new avenues of research into the epistemology of thought experiments.Howard Burton is the founder of the Ideas Roadshow, Ideas on Film and host of the Ideas Roadshow Podcast. He can be reached at howard@ideasroadshow.com. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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 less numerate people differ in our perceptions of risk and our number-based decisions to the roots of our numeric faculties and how we can make the best of them. Dr. Ellen Peters has made significant contributions to the subject and brings her expertise and an exceptional clarity to its presentation.Precious little of the research surveyed in her book could fit into this interview! We discussed the three components of numeric ability—objective numeracy, subjective numeracy, and the innate number sense—and how they vary within and across populations. We talked through some key lessons from this literature, such as the importance of calibrating our self-efficacy to our real ability and an awareness of how our cultural allegiances can drive even our mathematical reasoning. And we identified some of the essential personal habits and policy levers (early childhood education!!) available to us in our efforts to improve our individual numeracy and our collective numeric decision-making. For a firm grounding in the state of knowledge and urgent open questions, there may be no better resource for many years to come.Suggested companion works: Contributions from the labs of Isaac Lipkus, Angela Fagerlin, John Opfer, Edward Cokely, Rocio Garcia-Retamero, Jakub Traczyk, Agata Sobków, Wändi Bruine de Bruin, Keith Stanovich, and Valerie Reyna.Ellen Peters, Ph.D., is the Philip H. Knight Chair, and Director of the Center for Science Communication Research, in the University of Oregon’s School of Journalism and Communication. As a decision psychologist, she studies the basic building blocks of human judgment and decision making and their links with effective communication techniques and has published more than 150 peer-reviewed papers on these topics. She is former President of the Society for Judgment and Decision Making and a fellow of the American Association for the Advancement of Science, Association for Psychological Science, the American Psychological Association, and the Society for Experimental Social Psychology. She also works with federal agencies to advance decision and communication sciences in health and health policy, including having been Chair of FDA’s Risk Communication Advisory Committee and member of the NAS’s Science of Science Communication committee. She has been awarded the Jane Beattie Scientific Recognition Award and an NIH Group Merit Award. Finally, she has received extensive funding from the National Science Foundation and National Institutes of Health. Cory Brunson is a Research Assistant Professor at the Laboratory for Systems Medicine at the University of Florida. His research focuses on geometric and topological approaches to the analysis of medical and healthcare data. He welcomes book suggestions, listener feedback, and transparent supply chains. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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 14th year of publication by the AMS.I was excited to talk with three editors and contributors to a recent volume in the series, Inspiring Mathematics: Lessons from the Navajo Nation Math Circles (American Mathematical, 2019). Drs. Dave Auckly, Amanda Serenevy, and Henry Fowler have been instrumental to the Navajo Nation Math Circles Project, along with co-editors Tatiana Shubin and Bob Klein and a broader contact and support network. Their book showcases scripts developed and facilitated in Navajo Nation, including an introduction to modular arithmetic through bean bag tossing, prefix sorting in the guise of pancake flipping, and a tactile use of limiting behavior to folding a necktie. We discussed the origin and expansion of math circles, their potential to indigenous mathematics educators and students, and the content of and stories behind a selection of the scripts.Dr. Fowler's foreword and the editors' introduction situate the math circles movement and the Navajo Nation Math Circles Project in history, geography, and culture. Each script begins with a (minimal!) list of the necessary materials and a student handout that invites explorations with them. A short survey of connections to deeper mathematics precedes each handout, and each is followed by an extensive teacher's guide with (illustrative) solutions and presentation suggestions. The scripts vary in complexity and are suitable for student- and teacher-focused math circles. I hope the text becomes widely adopted for science-based and culturally conscious mathematics education and helps introduce others like myself to the greater math circles project.Suggested companion works:-James Tanton-The Julia Robinson Mathematics Festival-Gordon Hamilton and Lora Saarnio, MathPickle-Robert Kaplan and Ellen Kaplan, Out of the Labyrinth: Setting Mathematics Free-Rachel and Rodi Steinig, Math RenaissanceDave Auckly is a research mathematician at Kansas State University and Co-founder and Director of the Navajo Nation Math Circles Project. Amanda Serenevy is Co-founder and Director of the Riverbend Community Math Center. Henry Fowler is Associate Professor of Mathematics at Navajo Technical University and Co-director of the Navajo Nation Math Circles Project. Cory Brunson is a Research Assistant Professor at 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

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 can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high school-level math, to experience the joy of mathematical discovery. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics