Mathematics books by women

It’s International Women’s Day, and The Aperiodical has a new piece up on “Books about Maths by Women”. One of my own projects for the last few weeks has been to create Wikipedia articles on noteworthy mathematics books, and so far roughly half of the creations have included at least one woman among their authors. They are (alphabetical by title):

• The Calculating Machines (1992), by Ernst Martin, translated and edited by Peggy A. Kidwell and Michael R. Williams. A history of pre-World-War-II mechanical calculators.

• Closing the Gap: The Quest to Understand Prime Numbers (2017), by Vicky Neale. History and recent developments in the twin prime conjecture.

• Combinatorics of Finite Geometries (1986; 2nd ed. 1997), by Lynn Batten. An undergraduate textbook on finite projective planes, finite affine planes, and other finite geometries.

• Complexities: Women in Mathematics (2005), edited by Bettye Anne Case and Anne M. Leggett. A celebration of women in mathematics featuring the stories of over 80 women.

• Crocheting Adventures with Hyperbolic Planes (2009; 2nd ed. 2018), by Daina Taimina. How to make hyperbolic surfaces out of crochet, and what we can learn mathematically from tactile interactions with these surfaces.

• Difference Equations: From Rabbits to Chaos (2005), by Paul Cull, Mary Flahive, and Robby Robson, an undergraduate textbook on finite difference equations, population dynamics, and related topics.

• A Guide to the Classification Theorem for Compact Surfaces (2013), by Jean Gallier and Dianna Xu. An exposition of the result that the topology of a two-dimensional surface can be completely described by its orientability, Euler characteristic, and number of punctures.

• Introduction to Tropical Geometry (2015) by Diane Maclagan and Bernd Sturmfels. What happens if you do algebraic geometry in an arithmetic where the two basic operations are addition and minimization, instead of multiplication and addition?

• Mathematics in Ancient Egypt: A Contextual History (2016), by Annette Imhausen. The length of time covered by this history is greater than the length of time since it happened. Its focus is on putting Egyptian mathematics into the context of the society of the times, rather than (as in earlier studies) trying to translate it into modern mathematical concepts and analyze the mathematical foundations of Egyptian calculational methods.

• Pearls in Graph Theory: A Comprehensive Introduction (1990), by Gerhard Ringel and Nora Hartsfield. A collection of the authors’ favorite topics in graph theory, although not as comprehensive as the title makes out.

• Poincaré and the Three-Body Problem (1997), by June Barrow-Green. The history surrounding Poincaré’s work on the the three-body problem, which led to chaos theory, began a long dispute between mathematicians and astronomers over the convergence of series, and was a big part of Poincaré’s own fame.

• Proofs That Really Count: the Art of Combinatorial Proof (2003), by Arthur Benjamin and Jennifer Quinn. An exposition of the concept of bijective proofs, in which one proves the equality of two integer formulas by showing that both count the same set of mathematical objects.

• Quasicrystals and Geometry (1995), by Marjorie Senechal. An investigation of the relation between the mathematical properties of aperiodic tilings like the Penrose tiling, and physical quasicrystals whose X-ray diffraction patterns show systems of Bragg peaks with five-way symmetry.

• Symmetry in Mechanics: A Gentle, Modern Introduction (2001), by Stephanie Singer. How to use symplectic geometry to reduce the solution of the two-body problem from twelve dimensions (three for the position and momentum of each body) to two, leading to an elegant derivation of Kepler’s laws of planetary motion.

• Taking Sudoku Seriously: The math behind the world’s most popular pencil puzzle (2011), by Jason Rosenhouse and Laura Taalman. An exploration of various topics in mathematics related to Sudoku puzzles and their solution, including Latin squares, graph coloring, algorithms for solving systems of polynomials, and extremal combinatorics.

• Thomas Harriot’s Doctrine of Triangular Numbers (2009), by Thomas Harriot, edited and translated by Janet Beery and Jackie Stedall. An important precursor to the invention of calculus by Newton, using finite differences instead of infinitesimal differences.

• Treks into Intuitive Geometry: The World of Polygons and Polyhedra (2015), by Jin Akiyama and Kiyoko Matsunaga. A Socratic dialogue on tessellations, polyhedra, polygonal dissections, and polyhedral unfoldings.

• Viewpoints: Mathematical Perspective and Fractal Geometry in Art (2011), by Marc Frantz and Annalisa Crannell. An undergraduate general-education textbook on perspective geometry and fractal structure in art.

There are many more I could include, but haven’t yet (including most of the Aperiodical list). Many of these books are award-winners, but to a large extent inclusion in this list is driven by my personal taste in books, so many of these are somewhat specialized rather than being general-audience books. But the main criterion for inclusion on Wikipedia is that everything must have multiple in-depth sources, and everything in the article must come from those sources. For books those sources are not the book itself, but (typically) published book reviews. The bare minimum is two reviews, but I’ve been aiming for books with at least four. So for instance I would have liked to include Geometry: The Line and the Circle (2019), by Maureen T. Carroll and Elyn Rykken, but I could find only one review of it, and that’s not enough. To all the book reviewers out there: your efforts are appreciated, and helpful.

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