Ingrid Daubechies, a mathematician at Duke University, is an expert on many matters, not least the baking of cookies in the shape of pi, the mathematical constant that equals the ratio of a circle’s circumference to its diameter, or roughly 3.14159. A sugar cookie recipe works fine, Dr. Daubechies says. But she prefers a savory version with cheese (Parmigiano-Reggiano) and herbs (thyme and marjoram).
In the summer of 2023, Dr. Daubechies made a pi-shaped cookie cutter that tiles the plane: In principle, when this shape cuts cookies from a large sheet of dough, it generates absolutely no wasteful scraps from one cookie to the next, row upon row upon row. (The reality of crumbs makes it hard to execute this ideal perfectly, Dr. Daubechies noted.)
Dr. Daubechies plans to bake pi cookies to celebrate Pi Day, which is this Friday, March 14 — 3/14. That day is also the International Day of Mathematics; the theme in 2025 is mathematics, art and creativity.
For the occasion, this year Dr. Daubechies is visiting the University of Quebec in Montreal, where she will offer special tours of “Mathemalchemy,” a traveling multimedia math-meets-art installation that has been her constant passion (some might say obsession) for the last five years. She will also give a public talk on “Mathematics to the Rescue of Art Curators.”
The exhibition — a 360-degree diorama of sorts, 20 feet long, 10 feet wide and nine and a half feet high — was created in collaboration with Dominique Ehrmann, a fiber sculptor from Quebec, and a team of 24 artistic mathematicians and mathematical artists. It debuted in 2022 at the National Academy of Sciences in Washington, D.C., and has made several stops since.
“Mathemalchemy” has been described as “a mathematics fever dream turned artistic playground for all math lovers (and haters, too).”
It is a fantasia fabricated in beadwork, ceramics, crochet, embroidery, knitting, leatherwork, needle felting, origami, painting, polymer clay, 3-D printing, quilting, sewing, stained glass, steel welding, light, temari, weaving, wire bending and woodworking. Last year it had an extended stay at the National Museum of Mathematics on Fifth Avenue in New York City, where one visitor on opening night felt a “Grimms’ fairy tale vibe.” The project’s official catchphrase is: “Mathemalchemy, where math is transforming.”
In 2023, while hosted by the Juniata College Museum of Art in Huntingdon, Pa., the project spawned a comic book that has been translated into several languages. In May the exhibition goes to the Navajo Nation Museum in Arizona. The “Mathemalchemy” group ran a fund-raiser to finance this installation, and met the goal of $25,000; donors receive their very own pi-cookie cutter as thanks.
At opening receptions, pi cookies are always served, often washed down with champagne.
Here’s a sampling of “Mathemalchemy” marvels, both on exhibit and in progress. A virtual tour with a detailed narrative is available at mathemalchemy.org.
A cat named Arnold, left, offers pi cookies hot from the oven.
The artwork is a nod to Vladimir Arnold, a mathematician known in part for a geometric operation called “Arnold’s cat map.” The map is a crude depiction of a cat’s head. Over numerous iterations, the image is stretched, sheared and scrambled; along the way, it becomes a seemingly random yet uniform mix of pixels, but eventually the original image reappears.
Used for image encryption and information security, Arnold’s map is an example of how simple systems can generate complex, chaotic dynamics. A “baker’s map,” another geometric operation, achieves a similar effect through repeated layering, cutting, stacking and compressing, in a process akin to a baker’s method for making puffed pastry.
Nearby, Tess the Tortoise strolls along Zeno’s Path with her Sierpinski kite, a tetrahedron with a triangular self-repeating fractal pattern.
“In order for Tess to reach the end of the path, she must make it halfway,” the exhibit text explains. “But then she has to make it to the halfway point of the remaining length, and to infinitely more halfway points after that. In theory, this will take forever!”
In “Mathemalchemy,” every road eventually leads to infinity.
Two infinite ball arches — one converging skyward, the other diverging and diving into a bay — transit through “Mathemalchemy.” Here’s the full whirl at the National Academy of Sciences in 2022.
The balls are crafted in the Japanese tradition of temari. Those decorated with embroidery represent twin prime numbers that are separated by the value of two: Balls 3 and 5, 5 and 7, 11 and 13 are the first three pairs of twin primes. Mathematicians have conjectured that the number of twin primes is infinite, but this has yet to be proved.
A mural depicts an octopus, named OctPi, who is a graffiti artist. With one tentacle, OctoPi paints the wave equation, a way to describe how waves — of water, light and the like — ripple and change. The exhibit display notes, “The ripples created by the green paint dripping from OctoPi’s bucket are described by this equation!”
As part of the “knotical” theme, a crocheted octopus — OctoPi’s daughter, Cayley — lounges in the bay, her tentacles sometimes arranging in elegant tangles.
Cattails are knottails.
Helicoid beadwork evokes a strand of DNA and the primordial soup.
Beads also incarnate a galaxy of starfish, which belong to the only phylum of animals with fivefold radial symmetry, Echinodermata.
A reproduction of a remnant of the Antikythera mechanism, the oldest example of an analogue computer. Recovered from a shipwreck in 1901, the artifact dates to Greek antiquity; it was used for astronomical computation.
At one end of the exhibit, the Cryptography Quilt explores the history of cryptography — “secret writing.” The central padlock is surrounded by depictions of Morse code, blockchain, a carrier pigeon and letter locking, a fingerprint, the enigma machine, quipu and more.
Gilles Brassard, a Quebec computer scientist by training (he describes himself as a failed mathematician and an amateur physicist), first discovered “Mathemalchemy” in 2022, while at the National Academy of Sciences for an event. (He was inducted as an international member.) He made several visits over the course of a couple days and spent hours studying it up close. But, peering at the fabulous cryptographic quilt, he noticed that quantum cryptography was not represented.
Thus inspired, Dr. Daubechies and Ms. Ehrmann created a mini-quilt — the “Quantum Cryptography Quiltlet”— illustrating the first quantum cryptography protocol, a method of encryption using quantum mechanics. Dr. Brassard developed the protocol in 1984 with Charles H. Bennett, a physicist; it is called the quantum key establishment scheme Bennett-Brassard-84, or BB84.
The quiltlet illustrates how two parties could, rather fancifully, use natural components — fireflies, calcite crystals and frogs, optimally in a bath of ice cubes — to implement the BB84 scheme. This was Dr. Bennett’s notion, which he sketched out decades ago with markers.
“The Great Doodle Page,” on the flip side of the quilt, celebrates female mathematicians, using stitched reproductions of their drawings or doodles. One cluster is by Maryam Mirzakhani, who in 2014 became the first woman to win a Fields Medal, the most coveted prize in mathematics. Another is by the 19-century mathematician Ada Lovelace, who wrote the first algorithm for a computer.
A towering lighthouse anchors the other end of the exhibit. The beacon is housed within a stained-glass dodecahedron, a regular polyhedron with 12 faces, each a pentagon.
The mathematicians Jayadev Athreya, David Aulicino and Patrick Hooper recently proved that there are infinite straight paths on the dodecahedron that start at one vertex, proceed in a straight path around the polyhedron and return to the starting vertex without passing through any other vertexes.
Atop the lighthouse, a sphere with a carved-out pattern casts a stereographic projection on the ceiling — the projected pattern preserves angles but not lengths.
In November, at the opening in Montreal, Dr. Daubechies and Ms. Ehrmann addressed an audience of some 250 people and unpacked the intertwined contributions of two dozen “mathemalchemists.” “We consider it a curious collaboration,” Dr. Daubechies said.