New Books in Mathematics

Machine learning systems are making life-altering decisions for us: approving mortgage loans, determining whether a tumor is cancerous, or deciding if someone gets bail. They now influence developments and discoveries in chemistry, biology, and physics—the study of genomes, extrasolar planets, even the intricacies of quantum systems. And all this before large language models such as ChatGPT came on the scene.
We are living through a revolution in machine learning-powered AI that shows no signs of slowing down. This technology is based on relatively simple mathematical ideas, some of which go back centuries, including linear algebra and calculus, the stuff of seventeenth- and eighteenth-century mathematics. It took the birth and advancement of computer science and the kindling of 1990s computer chips designed for video games to ignite the explosion of AI that we see today. In this enlightening book, Anil Ananthaswamy explains the fundamental math behind machine learning, while suggesting intriguing links between artificial and natural intelligence. Might the same math underpin them both?
As Ananthaswamy resonantly concludes, to make safe and effective use of artificial intelligence, we need to understand its profound capabilities and limitations, the clues to which lie in the math that makes machine learning possible.

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A celebration of the seemingly simple idea that allowed us to imagine the world in new dimensions--sparking both controversy and discovery.

The stars of this book, vectors and tensors, are unlikely celebrities. If you ever took a physics course, the word "vector" might remind you of the mathematics needed to determine forces on an amusement park ride, a turbine, or a projectile. You might also remember that a vector is a quantity that has magnitude and (this is the key) direction. In fact, vectors are examples of tensors, which can represent even more data. It sounds simple enough--and yet, as award-winning science writer Robyn Arianrhod shows in this riveting story, the idea of a single symbol expressing more than one thing at once was millennia in the making. And without that idea, we wouldn't have such a deep understanding of our world.

Vector and tensor calculus offers an elegant language for expressing the way things behave in space and time, and Arianrhod shows how this enabled physicists and mathematicians to think in a brand-new way. These include James Clerk Maxwell when he ushered in the wireless electromagnetic age; Einstein when he predicted the curving of space-time and the existence of gravitational waves; Paul Dirac, when he created quantum field theory; and Emmy Noether, when she connected mathematical symmetry and the conservation of energy. For it turned out that it's not just physical quantities and dimensions that vectors and tensors can represent, but other dimensions and other kinds of information, too. This is why physicists and mathematicians can speak of four-dimensional space-time and other higher-dimensional "spaces," and why you're likely relying on vectors or tensors whenever you use digital applications such as search engines, GPS, or your mobile phone.

In exploring the evolution of vectors and tensors--and introducing the fascinating people who gave them to us--Arianrhod takes readers on an extraordinary, five-thousand-year journey through the human imagination. She shows the genius required to reimagine the world--and how a clever mathematical construct can dramatically change discovery's direction.

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Most of us know something about the grand theories of physics that transformed our views of the universe at the start of the twentieth century: quantum mechanics and general relativity. But we are much less familiar with the brilliant theories that make up the backbone of the digital revolution. In Beautiful Math: The Surprisingly Simple Ideas behind the Digital Revolution in How We Live, Work, and Communicate (MIT Press, 2024) Chris Bernhardt explores the mathematics at the very heart of the information age. He asks questions such as: What is information? What advantages does digital information have over analog? How do we convert analog signals into digital ones? What is an algorithm? What is a universal computer? And how can a machine learn?
The four major themes of Beautiful Math are information, communication, computation, and learning. Bernhardt typically starts with a simple mathematical model of an important concept, then reveals a deep underlying structure connecting concepts from what, at first, appear to be unrelated areas. His goal is to present the concepts using the least amount of mathematics, but nothing is oversimplified. Along the way, Bernhardt also discusses alphabets, the telegraph, and the analog revolution; information theory; redundancy and compression; errors and noise; encryption; how analog information is converted into digital information; algorithms; and, finally, neural networks. Historical anecdotes are included to give a sense of the technology at that time, its impact, and the problems that needed to be solved.

Taking its readers by the hand, regardless of their math background, Beautiful Math is a fascinating journey through the mathematical ideas that undergird our everyday digital interactions.

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Back in 2021, John and Elizabeth sat down with Brandeis string theorist Albion Lawrence to discuss cooperation versus solitary study across disciplines. They sink their teeth into the question, “Why do scientists seem to do collaboration and teamwork better than other kinds of scholars and academics?”

The conversation ranges from the merits of collective biography to the influence of place and geographic location in scientific collaboration to mountaineering traditions in the sciences. As a Recallable Book, Elizabeth champions The People of Puerto Rico, an experiment in ethnography of a nation (in this case under colonial rule) from 1956, including a chapter by Robert Manners, founding chair of the Brandeis Department of Anthropology. Albion sings the praises of a collective biography of the Art Ensemble of Chicago, A Message to Our Folks. But John stays true to his Victorianist roots by praising the contrasting images of the withered humanist Casaubon and the dashing young scientist Lydgate in George Eliot’s own take on collective biography, Middlemarch.

Discussed in this episode:

Listen to and Read the episode here.

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Models of the Mind: How Physics, Engineering and Mathematics Have Shaped Our Understanding of the Brain (Bloomsbury, 2021) provides a multifaceted and approachable introduction to theoretical neuroscience. It discusses some major topics of the field, including both the milestones from their history and the currently open questions.

It's accessible for a general audience, not expecting any previous knowledge of neuroscience or maths. At the same time, neuroscientists have described it as impressive. According to Gaute Einevoll, professor of brain physics, "this is a book that belongs on the bookshelf of any computational neuroscientist and lots of other people".

In our conversation, we covered some of the overarching themes of the book. The constant push and pull between mathematics and biology: mathematical models simplifying complex phenomena and biology pointing out the importance of a specific detail. What efficiency means for a biological system, like the brain. Whether and how much we can assume that an evolved system is efficient.

Dr. Grace Lindsay also talked about how science communication has helped her explore and discuss topics not directly related to her research. She started blogging and podcasting during her PhD, which has led to further writing opportunities, including this popular science book.

Similar to Models of the Mind, the Lindsay Lab is multidisciplinary: It uses artificial neural networks for psychology, neuroscience, and climate change. In the interview, Dr. Grace Lindsay talked about her decision about the lab's profile She explains the overlap in technologies used for studying visual systems and satellite images. We also hear about examples of how scientists in various fields have taken on research topics related to climate change.

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What are numbers, and where do they come from? Based on her groundbreaking study of material devices used for counting in the Ancient Near East, Karenleigh Overmann proposes a novel answer to these timeless questions.

Tune in as we talk with Karenleigh Overmann about her book, The Material Origin of Numbers: Insights from the Archaeology of the Ancient Near East (Gorgias Press, 2024).

Karenleigh Overmann earned a doctorate in archaeology from the University of Oxford, and is research fellow at the University of Bergen, Norway.

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Data has become a defining issue of current times. Our everyday lives are shaped by the data that is produced about us (and by us) through digital technologies. In Critical Data Literacies: Rethinking Data and Everyday Life (MIT Press, 2023), Luci Pangrazio and Neil Selwyn introduce readers to the central concepts, ideas, and arguments required to make sense of life in the data age. Bringing together cutting-edge thinking and discussion from across education, sociology, psychology, and media and communication studies, Critical Data Literacies develops a powerful argument for collectively rethinking the role that data plays in our everyday lives and re-establishing agency, free will, and the democratic public sphere.

In the episode, Luci Pangazio discusses how the tradition of critical literacies can offer a powerful foundation to address the big concerns of the data age, such as issues of data justice and privacy, algorithmic bias, dataveillance, and disinformation. We challenge the idea that datafication is an inevitable and inescapable condition.

This interview was conducted by Shreya Urvashi, a doctoral researcher of sociology and education based in Toronto, Canada.

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Across the humanities and social sciences, scholars increasingly use quantitative methods to study textual data. Considered together, this research represents an extraordinary event in the long history of textuality. More or less all at once, the corpus has emerged as a major genre of cultural and scientific knowledge. In Literary Mathematics: Quantitative Theory for Textual Studies (Stanford UP, 2022), Michael Gavin grapples with this development, describing how quantitative methods for the study of textual data offer powerful tools for historical inquiry and sometimes unexpected perspectives on theoretical issues of concern to literary studies.

Student-friendly and accessible, the book advances this argument through case studies drawn from the Early English Books Online corpus. Gavin shows how a copublication network of printers and authors reveals an uncannily accurate picture of historical periodization; that a vector-space semantic model parses historical concepts in incredibly fine detail; and that a geospatial analysis of early modern discourse offers a surprising panoramic glimpse into the period's notion of world geography. Across these case studies, Gavin challenges readers to consider why corpus-based methods work so effectively and asks whether the successes of formal modeling ought to inspire humanists to reconsider fundamental theoretical assumptions about textuality and meaning. As Gavin reveals, by embracing the expressive power of mathematics, scholars can add new dimensions to digital humanities research and find new connections with the social sciences.

Michael Gavin is Associate Professor of English at the University of South Carolina and author of The Invention of English Criticism, 1650-1760 (2015)

Morteza Hajizadeh is a Ph.D. graduate in English from the University of Auckland in New Zealand. His research interests are Cultural Studies; Critical Theory; Environmental History; Medieval (Intellectual) History; Gothic Studies; 18th and 19th Century British Literature. YouTube channel. Twitter.

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Today I talked to Al Posamentier about his books (co-authored with Christian Speitzer) The Mathematics of Everyday Life (Prometheus Books, 2018).  We all are told – practically from the moment we enter school – that mathematics is important because it permeates practically all aspects of our lives.  But, for the most part, we don’t really notice it except for those moments, such as when we balance a checkbook, that we know we’re doing mathematics.  This book, which requires nothing more than high-school math, is a wonderful way to see that mathematics really is all around us, in our home, in our workplace, in the entertainments we enjoy, and in the world we live in.

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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 [email protected].

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