New Books in Mathematics

• Anil Ananthaswamy, "Why Machines Learn: The Elegant Maths Behind Modern AI" (Dutton, 2024)

  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. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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• Robyn Arianrhod, "Vector: A Surprising Story of Space, Time, and Mathematical Transformation" (U of Chicago Press, 2024)

  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. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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• Chris Bernhardt, "Beautiful Math: The Surprisingly Simple Ideas behind the Digital Revolution in How We Live, Work, and Communicate" (MIT Press, 2024)

  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. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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• Scientists Cooperate while Humanists Ruminate (EF, JP)

  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: Richard Rhodes Making of the Atomic Bomb Ann Finkbeiner, The Jasons: The Secret History of Science’s Postwar Elite James Gleick, The Information Jon Gertner, The Idea Factory: Bell Labs and the Great Age of American Innovation Black Hole photographs win giant prize Adam Jaffe, “Geographic Localization of Knowledge Spillovers as Evidenced by Patent Citations“ Jamie Cohen-Cole, The Open Mind Julian Steward et al., The People of Puerto Rico Paul Steinbeck, Message to Our Folks Jenny Uglow, Lunar Men George Eliot, Middlemarch Listen to and Read the episode here. Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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• Grace Lindsay, "Models of the Mind: How Physics, Engineering and Mathematics Have Shaped Our Understanding of the Brain" (Bloomsbury, 2021)

  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. Links:  Dr. Grace Lindsay's homepage Lindsay Lab Dr. Grace Lindsay's blog post about Models of the Mind Learn more about your ad choices. Visit megaphone.fm/adchoices Support our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

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