Mathematical “heat dreams” hit the road

Ingrid Daubechies, a mathematician at Duke University, is an expert on many problems. In particular, it is the baking of cookies in the form of Pi, the ratio of the circumference of a circle to its diameter, or about 3.14159. The sugar cookie recipe works fine, says Dr. Daubechies. However, she prefers the flavorful version with cheese (Parmigiano-Reggiano) and herbs (thyme and marjoram).

In the summer of 2023, Dr. Daubechies created a Pi-shaped cookie cutter that tiles the plane. As a rule, if this shape cuts cookies from a large dough, it will not generate any wasted scraps in the row from one cookie to the next one on the row. (The reality of breadcrumbs makes this ideal difficult to fully implement, Dr. Daubechies pointed out.

Dr. Daubechies is planning to bake Pi cookies to celebrate Pi Day, Friday, March 14th. That day is also an international day for mathematics. The themes for 2025 are mathematics, art and creativity.

Take this opportunity this year, Dr. Daubechies will visit the University of Quebec in Montreal and will offer a special tour of “Mathemalchemy,” a travel multimedia mathematics art installation that has been a constant passion for the past five years (some may be obsessed with) by travel multimedia mathematics mathematics. She will also give a public lecture on “Mathematics for the Rescue of Art Curators.”

This exhibition – a 360 degree diorama of 20 feet long, 10 feet wide and 9 and a half feet high, was created in collaboration with Quebec textile sculptor Dominique Aleman and a team of 24 artists and mathematics artists. He made his debut at the National Academy of Sciences in Washington, DC in 2022 and has since created several stops.

“Mathematics” is said to be “a dream of mathematics fever that has become an artistic playground for all mathematicians (and hated).”

It is a fantasia made from beadwork, ceramics, crocheting, embroidery, knitting, leatherwork, leatherwork, folding, origami, painting, polymer clay, 3D printing, quilting, sewing, stained glass, steel welding, light, temari, weaving, wire bending, woodwork. Last year I stayed at the National Museum of Mathematics on Fifth Avenue in New York City. There, visitors to the opening night felt the atmosphere of the “Grimm” fairy tale. The official catchphrase for the project is “Mathematics where Mathematics is Changing.”

In 2023, hosted by the Junior College Museum of Art in Huntingdon, Pennsylvania, the project produced comic books translated into several languages. In May, the exhibition will be sent to the Navajo National Museum in Arizona. The “Mathematics” group ran funders to fund the installation, achieving its $25,000 target. Donors receive their own Pi-Cookie cutter as a thank you.

At the opening reception, PI cookies are always offered, often washed away with champagne.

This is a “math” Marvel sampling, both at the exhibition and ongoing. A virtual tour with detailed stories is available at mathemalchemy.org.

On the left, a cat named Arnold serves hot pike cookies from the oven.

The artwork is a nod from Vladimir Arnold, a mathematician known in part for his geometric surgery called “Arnold's Cat Map.” The map is a rough depiction of a cat's head. With many iterations, the image is stretched, sheared and scrambled. Along the way, it becomes a seemingly random yet uniform pixel mix, but eventually the original image reappears.

Arnold's maps used for image encryption and information security are examples of how simple systems can generate complex, chaotic dynamics. Another geometric operation, “baker map,” is a process similar to that of a baker's method of making inflated pastries, achieving similar effects through repeated layering, cutting, stacking and compression.

Nearby, Tess the Turtle walks along Zeno's path with Cielpinski Kite, a tetrahedral with a triangular self-repeating fractal pattern.

“For Tess to reach the end of the pass, she must do so in the middle,” the exhibit text explains. “But she has to go to the middle of the rest of the length and then to the infinites more midpoints. In theory, this will take forever!”

In “mathematics”, all roads ultimately lead to infinite.

Two infinite ball arches – one converges the sky, the other forks and dives into the bay – passing through “mathematics”. This is a complete turn at the National Academy of Sciences in 2022.

The balls are made in the Japanese traditions of Temari. The embroidery adorned with the embroidery represents the prime numbers of twins separated by two values. Balls 3 and 5, 5 and 7, 11 and 13 are the twin primes of the first three pairs. Mathematicians have speculated that the number of prime numbers in twins is infinite, but this has not been proven yet.

The mural depicts an octopus named Octpi, a graffiti artist. With one tentacle, Octopi draws the equation of waves. This is a way to explain how waves such as water, light, and other ripple over and change. The exhibit states, “This equation explains the ripples created by the green paint dripping from Octopi's bucket!”

As part of the “notical” theme, the crocheted octopus – Octopian daughter Kaylee – is a lounge in the bay, where her tentacles sometimes tangle elegantly.

The cattail is a cnot tail.

Helicoid beadwork evokes DNA strands and primitive soup.

The beads also reincarnate the starfish galaxy, which belongs to the phylum of animals, with echinodermata, which is five times more radial symmetry.

Recreating the remains of the anti-kittera mechanism, the oldest example of analog computers. The artifact, which was recovered from the shipwreck in 1901, dates back to the ancient times of Greece. It was used for astronomical calculations.

At one end of the exhibition, the quilt of encryption explores the history of encryption – “Secret Writing.” The central padlock is surrounded by depictions of Morse Code, Blockchain, carrier pigeons and letterlocks, fingerprints, enigma machines, Quipu and more.

Trained Quebec computer scientist Jills Brotherard (who describes himself as a mathematician and amateur physicist), first discovered “mathematics” in 2022. (He took office as an international member.) He visited several times over the course of several days and spent hours studying it up close. But after peering into the fantastic cryptographic quilt, he realized that quantum cryptography was not represented.

With this inspiration, Dr. Daubechies and Ehrmann created a mini quilt (“quantum cryptographic quiltlet”). Dr. Brassard developed the protocol in 1984 with physicist Charles H. Bennett. This is called the Quantum Key Indecivelism Scheme Bennett-Brassard-84 or BB84.

Quiltlett demonstrates how to best use fireflies, calcite crystals, and natural components of frogs (fibres, calcite crystals, frogs) to implement the BB84 scheme. This is Dr. Bennett's concept, and he sketched with a marker decades ago.

The Great Doodle Page, located behind the quilt, celebrates female mathematicians with stitched reproductions of pictures and doodles. One cluster was by Maryam Mirzakhani, becoming the first woman to win the most coveted award in mathematics, Fields Medal in 2014. The other is by 19th century mathematician Ada Lovelace, who wrote the first algorithms of computers.

A towering lighthouse secures the other end of the display. The beacon is housed within a stained glass decahedron, a normal polyhedron with 12 faces.

Mathematicians Jayadev Athreya, David Aulicino and Patrick Hooper recently proved that Dodecahedron has an infinite straight path, starting at one vertex, proceeding to a straight path around the polyhedron and returning to the starting vertex without passing through the other vertices.

Above the lighthouse, a sphere with an engraved pattern casts a three-dimensional schema on the ceiling. The projected pattern retains the angle rather than the length.

In November, at the opening in Montreal, Dr. Daubechies and Ehrmann spoke to an audience of about 250 people, unpacking the intervened contributions of two dozen “mathematicians.” “We consider it a strange collaboration,” Dr. Dovecheese said.