New Books In Mathematics

There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations. Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objec

Students' success in mathematics at community colleges has been the subject of thorough quantitative research, which has reported poor overall results and described a range of explanations for them. Even as policies, course formats, and the composition of the student population have changed, success rates have remained dishearteningly low. The challenges confronted by community college students in developmental and higher-level math classes are historical, financial, social, and personal. Brian Cafarella's new book, which examines these challenges through the perspectives of the students themselves, is a welcome contribution to the topic. Breaking Barriers: Student Success in Community College Mathematics (CRC Press, 2021) is a qualitative study of the barriers faced, and the paths blazed through them, by more than 20 community college students who required developmental math at the starts of their programs and successfully completed college-level courses. From his interviews and exchanges with these students

Today I talked to Helga Nowotny about her new book In AI We Trust: Power, Illusion and Control of Predictive Algorithms (Polity, 2021). One of the most persistent concerns about the future is whether it will be dominated by the predictive algorithms of AI - and, if so, what this will mean for our behaviour, for our institutions and for what it means to be human. AI changes our experience of time and the future and challenges our identities, yet we are blinded by its efficiency and fail to understand how it affects us. At the heart of our trust in AI lies a paradox: we leverage AI to increase our control over the future and uncertainty, while at the same time the performativity of AI, the power it has to make us act in the ways it predicts, reduces our agency over the future. This happens when we forget that that we humans have created the digital technologies to which we attribute agency. These developments also challenge the narrative of progress, which played such a central role in modernity and is based on

A true understanding of the pervasive role of software in the world demands an awareness of the volume and variety of real-world software failures and their consequences. No more thorough survey of these events may be available than Thomas Huckle and Tobias Neckel's Bits and Bugs: A Scientific and Historical Review of Software Failures in Computational Science (SIAM, 2019). Their book organizing an extensive collection of episodes into eight chapters that expand on an array of flavors of failures, increasing in intricacy from precision and rounding errors to the software–hardware interface and problems that emerge from complexity. As I see it, this book serves three audiences: Instructors of computer engineering or numerical methods will find an educational text uniquely suited to a focus on software failures; software engineers will find an equally unique reference text; and students of the practice or the history of computational science will find a fully blazed trail through these complicated stories. Dr.

Why does a clarinet play at lower pitches than a flute? What does it mean for sounds to be in or out of tune? How are emotions carried by music? Do other animals perceive sound like we do? How might a musician use math to come up with new ideas? This book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music in a way that readers without scientific background can follow. David Sulzer, also known in the musical world as Dave Soldier, explains why the perception of music encompasses the physics of sound, the functions of the ear and deep-brain auditory pathways, and the physiology of emotion. He delves into topics such as the math by which musical scales, rhythms, tuning, and harmonies are derived, from the days of Pythagoras to technological manipulation of sound waves. Sulzer ranges from styles from around the world to canonical composers to hip-hop, the history of experimental music, and animal sound by songbirds, cetaceans, bats, and insects. He makes accessible a vas

One pervasive stereotype about mathematics is that it is objective, unbiased, or otherwise exempt from the influence of human passions. James Wynn and G. Mitchell Reyes's edited collection will be a revelation even to mathematics professionals who don't take this strict view. The essays in Arguing with Numbers: The Intersections of Rhetoric and Mathematics (The Pennsylvania State UP, 2021) explore the interplays between rhetoric and mathematics that have shaped scholarly and popular culture through to the present day. Opening the collection are both an historical sketch of scholarship at the intersection of these disciplines, from their division in ancient Greece to their hesitant reunion since the mid-twentieth century, and also a taxonomy of modern research into three distinct approaches, which we review in our discussion. The remaining essays use these approaches to probe the impact of mathematical rhetoric on the sciences (including Hantaro Nakaoka's analogical "Saturnian" model of atomic spectra), on cul

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 patterns, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, linking mathematical oscillations to animal gaits, how to deal with the peculiarities of the mathematical community, and much 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

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. This despite mathematical professionals being among the most satisfied and well-compensated in their careers. In Why Study Mathematics? (2020), Vicky Neale provides a compact guide to this juncture, which i expect students and their families and teachers will find hugely valuable. As part of the London Publishing Partnership's "Why Study" series, her book in Part I explores in detail the substance and varieties of math degrees, how students can shape them to their needs and interests, and what those who complete them go

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