New Books In Mathematics

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 these patterns provide a unique view of the physical world and its fundamental workings. Guiding readers on a tour of our world and the universe beyond, Clegg describes the cosmic microwave background, sometimes called the "echo of the big bang," and how it offers clues to the universe's beginnings; the diagrams that illustrate Einstein's revelation of the intertwined nature of space and time; the particle trail patterns revealed by the Large Hadron Collider and other accelerators; and the simple-looking patterns that

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 readers will find truly enjoyable to read. Poems that Solve Puzzles: The History and Science of Algorithms (Oxford UP, 2020) is itself a quite poetic book, in which echoes of ideas and variations on themes can be heard throughout. Its stories encompass the early hypothetical and mechanical computers, the charactered rise of weather forecasting, the origins (and lulls) of machine learning, and the sensational competitions between master game players and artificial intelligence. The book traverses a long historical arc,

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/adchoices Support 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

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 whi

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/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathem

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/adchoices Support 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, access

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

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 w

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

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

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 background to propose a new way to talk about gender and to propose an alternative: the terms “ingressive” and “congressive” behavior. In this interview, Dr. Cheng and I talk about what we gain from bringing a mathematical understanding to questions of social relations and structures. We talk about how she rethinks “gender”, and the new terms she proposes in her book. We end with a short discussion of whether these insights are applicable to conversations about other demographic and social identifiers. Dr. Eugenia Che

One of the questions I am often asked is exactly what do mathematicians do. The short answer is that they look at different mathematical structures, try to deduce their properties, and think about how they might apply to the real world. Math Without Numbers (Dutton, 2020) does a wonderful job of explaining what mathematical structures are, and does so in a fashion that even readers who are uncomfortable with the process of doing mathematics can appreciate and enjoy. There are courses in music and art appreciation, and if there ever are courses in math appreciation, this book would certainly be at or near the top of the reading list. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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 – and this book is an absolute treasure trove of stuff you can’t help thinking about. If you like logic, you’re certain to be sucked in – but you’ll enjoy the ride. Logic puzzles were first introduced to the public by Lewis Carroll in the late nineteenth century and have been popular ever since. Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history a

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 vignette from European mathematical history anchored to each month of the year, as drops of creativity and wisdom to sustain the trek. It is not unusual for books on the history of mathematics to tell very human stories about their often famous subjects. What is remarkable about Lawrence's collection is the breadth of these stories: Her subjects were idealists, pragmatists, mystics, skeptics, radicals, ascetics, and collectives. (Contrast, for example, the self-aware spite of Isaac Newton with the defiant good humor of

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 Scientific, 2020) takes the reader along a journey in three segments. The first, through only by-hand calculations, builds up to a variation on Schrödinger's notorious thought experiment in which an observer can use an unrelated random process to predict the outcome of a 50/50 trial more than half the time. The kernel of this setup is Blackwell's Bet, a simple yet extraordinary illustration of what Stein calls "probabilistic entanglement". The second section uses computer simulation to get a handle on several paradoxical e

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 Power of Numbers for Good and Evil (Johns Hopkins University Press, 2020), surveys a number of ways this conception of mathematics has informed scientific undertakings and public policies, not to mention our everyday behaviors, and makes a powerful case for reevaluating its assumptions. The book's five chapters contain stories of mathematical exploits from ancient to ongoing and across the spectrum from pure to applied. Many may be familiar, for example active research and journalism into the use and misuse of predictive

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 a close look. The effort will be well rewarded. Learn more about your ad choices. Visit megaphone.fm/adchoices

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 mathematical (and other) pursuits. While the math, some familiar and some less so, has clear scientific significance, the lessons help us also appreciate its humanistic value. Delightful illustrations and an (honestly) enjoyable exercise accompany each essay, and readers can jump around the text however they please. This book will appeal to aspiring mathematicians at any career stage, but its most important audience may be the latent mathematicians who have been discouraged from the discipline but are open to a fresh invitation.