You may well have seen “Numb3rs,” a TV show in which mathematicians help solve crimes. It’s fiction. But, as Leila Schneps and Coralie Colmez show in their eye-opening new book Math on Trial: How Numbers Get Used and Abused in the Court Room (Basic Books, 2013) math does play a role in criminal prosecution. Alas, it’s often bad math and, as such, often leads to bad outcomes: people get off who shouldn’t and others get convicted who shouldn’t. Schneps and Colmez show how math has been misused in ten interesting (and disturbing) cases. In some instances the errors are trivial; in others rather complex. But they all add up (excuse the pun) to injustice. Listen in and find out how and why.
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Leila Schneps and Coralie Colmez, “Math on Trial” (Basic Books, 2013)

Interviews with Mathematicians about their New Books
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Natural Sciences

Science & Medicine

Science

David S. Richeson's book Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (Princeton University Press, 2019) is the fascinating story of the 2000 year quest to solve four of the most perplexing problems of antiquity: squaring the circle, duplicating the cube, trisecting the angle, and constructing regular polygons. The eventual conclusion was that all four of these problems could not be solved under the conditions laid out millennia ago. But it's also an engaging tale of some of the greatest mathematicians, and some not-so-well known ones, who met the challenge and moved mathematics forward in ways that the Greek geometers could never have envisioned. Even if you never read a single proof through to its conclusion, you'll enjoy the many entertaining side trips into a geometry far beyond what you learned in high school.
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David S. Richeson, "Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity" (Princeton UP, 2019)

Graduate students in many programs besides mathematics will need to be familiar with the methods and results of a variety of mathematical topics. Just as importantly, these students will need to develop a level of mathematical maturity—how to think in broad strokes about the subject, how to study it, and even how to communicate their work. The gap between undergraduate training and graduate requirements can also give rise to misconceptions about how mathematics is done and what needs drive cutting-edge research.
Thomas A. Garrity's book All the Math You Missed (But Need to Know for Graduate School), now in its second edition (Cambridge UP, 2021), is a wide bridge across this gap—i do believe the material will bring any rising graduate student to readiness in the subject, whatever their needs. But it provides much more: Readers gain an intuition about the results and how they cohere that may be years coming through coursework alone; and an exposure to the culture of the mathematics community through historical vignettes, folklore, and prevailing beliefs (e.g. on the Riemann Hypothesis and whether P = NP). For such a broad introduction, the book is also surprisingly self-contained, and the chapters chart a uniformly continuous path through its topics.
In our interview, Dr. Garrity recounted the origins of the book, described his outlook on undergraduate and graduate mathematics, and elaborated on the style(s) he adopted across its topics. We also got into the choices of content and depth he made and what role both editions have played over 23 years. The discussion resonated with several of my own experiences, and in any event i plan to keep my copy of the book handy for any (undergraduate or graduate) students i teach or mentor in future.
Suggested companion works:
• Saunders MacLane, Mathematics Form and Function
• Timothy Gowers, June Barrow-Green, and Imre Leader (ed.), The Princeton Companion to Mathematics
Thomas A. Garrity is the Webster Atwell Class of 1921 Professor of Mathematics at Williams College, Massachusetts, where he was the director of the Williams College Project for Effective Teaching for many years. Among his awards are Rice University's Nicolas Salgo Outstanding Teaching award and the Haimo award of the MAA. His other books include Algebraic Geometry: A Problem Solving Approach (2013, co-authored) and Electricity and Magnetism for Mathematicians (2015).
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Thomas A. Garrity, "All the Math You Missed (But Need to Know for Graduate School)" (Cambridge UP, 2021)

The stereotype of the solitary mathematician is widespread, but practicing users and producers of mathematics know well that our work depends heavily on our historical and contemporary fellow travelers. Yet we may not appreciate how our work also extends beyond us into our physical and societal environments.
Kevin Lambert takes what might be a first crack at this perspective in his book Symbols and Things: Material Mathematics in the Eighteenth and Nineteenth Centuries (University of Pittsburgh Press, 2021). An historian of science, Dr. Lambert has shifted in his view of mathematics as a language of science to one as a material practice. Expanding on ideas from historians, archeologists, philosophers, and other scholars of human activity, and through several interweaving vignettes of mathematical work during a technologically dynamic period in British history, he argues that mathematical practice, communication, and even thought occur to a large degree outside the bodies of the persons performing them.
In this interview, we explore Kevin's journal to and through this book project. We discuss how such ideas as Andy Clark's extended mind informed his approach, and we review several of the lively stories—the co-creation of the long-distance mathematical community with the research journal, Peacock's museological argument for the adoption of symbolic algebra, and the foundational entanglement of electromagnetism, quaternions, and the philosophy of space, among others—he drew out of historical and archival sources. (Here i cannot resist mentioning Tait's collection of his intensive correspondence with Hamilton that transformed how quaternions were applied in physics and even conceptualized as mathematical objects.) We close with some thoughts on our own materially extended cognitive work and where Kevin's interests are currently driving him.
Suggested companion works:
• ChatGPT, as a cutting-edge extension of human thought
• work by Courtney Ann Roby, including the forthcoming The Mechanical Tradition of Hero of Alexandria: Strategies of Reading from Antiquity to the Early Modern Period
• Algorithmic Modernity: Mechanizing Thought and Action, 1500-2000, edited by Morgan G. Ames and Massimo Mazzotti
• work by Emily Miller Bonney, for example "A Reconsideration of Depositional Practices in Early Bronze Age Crete"
Kevin Lambert is a historian of science and mathematics in the early modern and modern periods and professor in the liberal studies department at California State University, Fullerton. His recent book Symbols and Things explores mathematics as a way of thinking outside the body and through the material environment. He also recently published a chapter in the volume Algorithmic Modernity that traces the genealogy of algorithmic practices. He is now working on the problem of writing longue durée histories of science. He is close to completing a paper called “Malthus in the Landscape” that investigates the temporalities of global histories. He is also exploring the problem of writing a global history of the early modern sciences without the prism of the so called “Scientific Revolution.” His work can be found on ResearchGate.
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Kevin Lambert, "Symbols and Things: Material Mathematics in the Eighteenth and Nineteenth Centuries" (U Pittsburgh Press, 2021)

What's the best way to determine what most voters want when multiple candidates are running? What's the fairest way to allocate legislative seats to different constituencies? What's the least distorted way to draw voting districts? Not the way we do things now. Democracy is mathematical to its very foundations. Yet most of the methods in use are a historical grab bag of the shortsighted, the cynical, the innumerate, and the outright discriminatory. Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation (Princeton UP, 2024) sheds new light on our electoral systems, revealing how a deeper understanding of their mathematics is the key to creating civic infrastructure that works for everyone.
In this timely guide, Ismar Volic empowers us to use mathematical thinking as an objective, nonpartisan framework that rises above the noise and rancor of today's divided public square. Examining our representative democracy using powerful clarifying concepts, Volic shows why our current voting system stifles political diversity, why the size of the House of Representatives contributes to its paralysis, why gerrymandering is a sinister instrument that entrenches partisanship and disenfranchisement, why the Electoral College must be rethought, and what can work better and why. Volic also discusses the legal and constitutional practicalities involved and proposes a road map for repairing the mathematical structures that undergird representative government.
Making Democracy Count gives us the concrete knowledge and the confidence to advocate for a more just, equitable, and inclusive democracy.
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Ismar Volić, "Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation" (Princeton UP, 2024)

Bookshop.org is an online book retailer that donates more than 80% of its profits to independent bookstores. Launched in 2020, Bookshop.org has already raised more than $27,000,000. In this interview, Andy Hunter, founder and CEO discusses his journey to creating one of the most revolutionary new organizations in the book world. Bookshop has found a way to retain the convenience of online book shopping while also supporting independent bookstores that are the backbones of many local communities. 
Andy Hunter is CEO and Founder of Bookshop.org. He also co-created Literary Hub.
Caleb Zakarin is the Assistant Editor of the New Books Network.
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Leila Schneps and Coralie Colmez, “Math on Trial” (Basic Books, 2013)

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