New Books in Mathematics

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/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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 on to do after. For Part II, Neale gives the reader a deeper view into a selection of subfields and the work their practitioners do, including the technologically vital study of data compression and the (for now) more humanistic study of abstract networks known as Ramsey theory.Dr. Neale has exceptional experience and skill as a mentor that comes through as she addresses questions that, in my experience, often aren't: Are mathematics degrees mostly for mathematically adept students? Once in a program, whom should i get to know? Where are all the job postings for "mathematician"? It was a treat to hear her expound further on the book, and i would suggest that anyone at the beginning of their professional life, with interest, aptitude, or just curiosity about mathematics, seek out this resource (or recommend it to their mentors and guidance offices!) as they weigh their options.Suggested companion works: Maths Careers (UK) Numberphile YouTube channel Plus magazine Chalkdust magazine Vicky Neale is the Whitehead Lecturer at the Mathematical Institute, University of Oxford, and a Supernumerary Fellow at Balliol College. She teaches pure mathematics to undergraduates, and combines this with work on public engagement with mathematics: she gives public lectures, leads workshops with school students, and has appeared on numerous BBC radio and television programmes. One of her current interests is in using knitting and crochet to explore mathematical ideas. She is the author of Closing the Gap: The Quest to Understand Prime Numbers (Oxford University Press, 2017)—listen to her interview with Jim Stein about that book here.Cory Brunson is an 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. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/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 predict quantum behavior (and decorated Richard Feynman's van). Clegg explains how the periodic table reflects the underlying pattern of the configuration of atoms, discusses the power of the number line, demonstrates the explanatory uses of tree diagrams, and more.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

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, but each episode is a quick read, remarkable in their ability to convey depth and rigor in crisp, plain language. It was a delight to talk with Chris about these and other aspects of his book.Suggested companion works:--Simon Singh, The Code Book--George Dyson, Turing's Cathedral: The Origins of the Digital Universe--Greg Kohs (director), "AlphaGo"Chris Bleakley is Head of the School of Computer Science at University College Dublin. He graduated with a BSc (Hons) degree in Computer Science from Queen's University, Belfast, and a PhD degree in Electronic Engineering from Dublin City University. After college, he was employed as a software consultant by Accenture and, later, as a senior telecommunications researcher at Broadcom Eireann Research.Cory Brunson is an 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. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/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