Mircea Pitici (Editor)
PRINCETON UNIVERSITY PRESS 2022, 320 PAGES
PRICE (PAPERBACK) £20.00 ISBN 978-0-691-22570-8
This book contains articles written in 2020. The editor speaks of the difficulties accessing libraries and resources, something we are all a bit too familiar with. Here I will comment on each of the twenty-six articles selected as the ‘best’ and draw an overall conclusion at the end.
Appropriately enough, the opening article to this volume Lockdown Mathematics: A Historical Perspective accounts for historical cases where mathematics was produced in isolation, such as lockdowns or imprisonments (even for noble causes). The article on Cryptocurrencies: Protocols for Consensus is very illuminating on permissionless protocols to create cryptocurrencies in a decentralised manner.
The article Logical Accidents and the Problem of the Inside Corner discusses how much of the design is now with software and the difficulties that arise. In Cosmatesque Design and Complex Analysis, the author discusses how to construct this cosmatesque type of tiling using a branch of complex analysis.
A variety (or algebraic set) is the shape produced by an algebraic equation. The authors of Nullstellenfont were looking to create a font where a polynomial equation would create an entire phrase. The Hyperbolic Flowers crocheted by the author herself aim to illustrate how hyperbolic planes are formed once the curvature of a construct becomes negative. Embodied Geometry in Early Modern Theatre comments on an early modern theatrical play starring 2D shapes, discussing Euclidean definitions of abstract concepts and some torture-related practices.
Modeling Dynamical Systems for 3D Printing provides examples on printing chaotic attractors, which are harder to describe and produce than multivariate calculus and geometry. Scientists Uncover the Universal Geometry of Geology discusses the amazement the analysis of the shattered rock pieces caused when it was found they average to six faces and eight vertices – almost as if Plato knew earth was made of cubes!
Bouncing Balls and Quantum Computing discusses how calculations about idealised billiard balls reveal numbers that increasingly approach an approximation of π in a surprising way. Landmark Computer Science Proof Cascades through Physics and Math discusses computers becoming more prevalent in mathematical proofs.
The article on Dark Data, discusses missing data. Data one does not have is not ignorable. The serious implications of drawing statistical and other conclusions when data is missing are discussed. Analysis in an Imperfect World discusses the impact of measurement errors, the repercussions of which are often more serious than one would expect.
A Headache-Causing Problem presents a problem where N men (original thesis in 1977 hence the exclusive nature of the crowd, possibly) are called to guess the number on their forehead, following certain rules; is this problem solvable in finite steps or not?
A Zeroth-Power Is Often a Logarithm Yearning to Be Free investigates integrating powers of x and discusses the exception when n=-1. The Bicycle Paradox discusses the disparity between a pedal in the lowest position, moving seemingly backwards when the bicycle is moving forwards. Tricolor Pyramids discusses triangular formations made with regular hexagons. The challenge is to use three colours to colour all hexagons following certain rules of how to create such puzzles.
Does Time Really Flow? New Clues Come from a Century-Old Approach to Math considers how mathematical equations do not make use of the present moment in time but at quantum level, the moment a particle is measured essentially adopts its status, making the present moment a defining moment. The article on The Role of History in the Study of Mathematics could come across as slightly opinionated and judgmental of mega-figures in mathematics. Some readers may find this rather surprising. The historical evolution of the Notices of the American Mathematical Society is explored under the lens of anticommunism and racism with some vivid examples, in “All of These Political Questions”: Anticommunism, Racism, and the Origin of the Notices of the American Mathematics Society.
A piece on mathematics education Reasoning as a Mathematical Habit of Mind discusses how reasoning is rarely the focus of teaching. Knowing and Teaching Elementary Mathematics – How Are We Doing? compares aspects of teaching and learning mathematics between US and China. Tips for Undergraduate Research Supervisors provides an extensive list of very tangible advice on how to approach the tricky area of supervision. “The Infinite Is the Chasm in Which Our Thoughts Are Lost”: Reflections on Sophie Germain’s Essays pays tribute to Sophie Germain’s legacy with some very extensive direct quotes (both in French and English).
The penultimate piece Who Owns the Theorem? poses some critical questions about what it means for one to ‘own’ a theorem. The last article is a personal account, entitled A Close Call: How a Near Failure Propelled Me to Succeed. It reads almost like a diary entry about what to avoid when preparing for exams, yet how almost failing can sharpen the focus.
Collating twenty-six articles on a variety of maths topics is an achievement in itself. Additionally, under Notable Writings at the end of the book is an impressively extended list of references also from 2020. Did the editor go through a couple of hundred articles before deciding on the twenty-six that made the final cut? One would need to go to great lengths to collate such an eclectic selection of topics. Regardless, the collection is wonderfully varied and for all mathematical tastes. I find it highly unlikely that a single individual will find all these articles relevant or ‘best’. The pitch and complexity are most certainly not consistent, but this is not necessarily a criticism as the reader can pick and choose what to read. Will I be buying the next compilations for future years? Possibly, yes!
Ioanna Georgiou CMathTeach FIMA
Book review published directly onto IMA website
