''Mathemalchemy'' (French: ''MathémAlchimie'') is a traveling art installation dedicated to a celebration of the intersection of art and mathematics. It is a collaborative work led by

Duke University Duke University is a Private university, private research university in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present-day city of Trinity, North Carolina, Trinity in 1838, the school moved to Durham in 1 ...

mathematician

Ingrid Daubechies Baroness Ingrid Daubechies ( ; ; born 17 August 1954) is a Belgian-American physicist and mathematician. She is best known for her work with wavelets in image compression. Daubechies is recognized for her study of the mathematical methods that ...

and

fiber artist Fiber (spelled fibre in British English; from ) is a natural or artificial substance that is significantly longer than it is wide. Fibers are often used in the manufacture of other materials. The strongest engineering materials often incorp ...

Dominique Ehrmann."Mathemalchemy: a mathematical and artistic adventure - Ingrid Daubechies"
Oxford Mathematical Institute, 2021. The cross-disciplinary team of 24 people, who collectively built the installation during the calendar years 2020 and 2021, includes artists, mathematicians, and craftspeople who employed a wide variety of materials to illustrate, amuse, and educate the public on the wonders, mystery, and beauty of mathematics. Including the core team of 24, about 70 people contributed in some way to the realization of ''Mathemalchemy''.Honaker, Andrea (July 8, 2021)
"Mercer professor part of team creating large-scale mathematical art piece at Duke"
Mercer University.

Description

The art installation occupies a footprint approximately , which extends up to in height (in addition, small custom-fabricated tables are arranged around the periphery to protect the more fragile elements). A map shows the 14 or so different zones or regions within the exhibit, which is filled with hundreds of detailed mathematical artifacts, some smaller than ; the entire exhibit comprises more than 1,000 parts which must be packed for shipment. Versions of some of the complex mathematical objects can be purchased through an associated "Mathemalchemy Boutique" website. The art installation contains

pun A pun, also known as a paronomasia in the context of linguistics, is a form of word play that exploits multiple meanings of a term, or of similar-sounding words, for an intended humorous or rhetorical effect. These ambiguities can arise from t ...

s (such as " Pi" in a bakery) and

Easter eggs Easter eggs, also called Paschal eggs, are eggs that are Egg decorating, decorated for the Christian holiday of Easter, which celebrates the resurrection of Jesus. As such, Easter eggs are commonly used during the season of Eastertide (Easter ...

, such as a miniature model of the

Antikythera mechanism The Antikythera mechanism ( , ) is an Ancient Greece, Ancient Greek hand-powered orrery (model of the Solar System). It is the oldest known example of an Analog computer, analogue computer. It could be used to predict astronomy, astronomical ...

hidden on the bottom of "Knotilus Bay". Mathematically sophisticated visitors may enjoy puzzling out and decoding the many mathematical allusions symbolized in the exhibit, while viewers of all levels are invited to enjoy the self-guided tours, detailed explanations, and videos available on the accompanying official websit

A downloadable

comic book A comic book, comic-magazine, or simply comic is a publication that consists of comics art in the form of sequential juxtaposed panel (comics), panels that represent individual scenes. Panels are often accompanied by descriptive prose and wri ...

was created to explore some of the themes of the exhibition, using an independent narrative set in the world of ''Mathemalchemy''.

Themes

The installation features or illustrates mathematical concepts at many different levels. All of the participants regard "

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research-and-application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

"—especially when it has a strong visual component—as having an important role in education and in culture in general. Jessica Sklar maintains that "mathematics is, at heart, a human endeavor" and feels compelled to make it accessible to those who don't regard themselves as "math people". Bronna Butler talks about the heritage of JH Conway, whose lectures were "almost magical in quality" because they used what looked like curios and tricks but in the end arrived at answers to "fundamental questions of mathematics".

Henry Segerman Henry Segerman (born 1979 in Manchester, UK) is an Associate Professor of mathematics at Oklahoma State University in Stillwater, Oklahoma who does research in three-dimensional geometry and topology, especially three-manifolds, triangulation ...

, who wrote the book ''Visualizing Mathematics With 3D Printing,''Visualizing Mathematics With 3D Printing by Henry Segerman
reviewed by Laura Taalman, The

American Mathematical Monthly ''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an exposi ...

, 22 Mar 2018, pp. 379-384 contributed 3D pieces that explore

stereographic projection In mathematics, a stereographic projection is a perspective transform, perspective projection of the sphere, through a specific point (geometry), point on the sphere (the ''pole'' or ''center of projection''), onto a plane (geometry), plane (th ...

and

polyhedra In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary su ...

. According to Susan Goldstine, "The interplay between mathematics and fiber arts is endlessly fascinating ndallows for a deeper understanding ways that these crafts can illuminate complex concepts in mathematics". Edmund Harriss says, "You don’t need a background in math to appreciate the installation, just like you can enjoy a concert without being a musician". The creators had the goal of illustrating as much of mathematics as possible. Thus the various exhibits touch on

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

fractal In mathematics, a fractal is a Shape, geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scale ...

tessellation A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety ...

probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

Zeno's paradoxes Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia. Zeno de ...

Venn diagram A Venn diagram is a widely used diagram style that shows the logical relation between set (mathematics), sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple ...

knot theory In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be und ...

calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

chaos theory Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sens ...

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

hyperbolic geometry In mathematics, hyperbolic geometry (also called Lobachevskian geometry or János Bolyai, Bolyai–Nikolai Lobachevsky, Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For a ...

symbolic logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

—and much else—all in a setting that is beautiful and fun. Mathematicians explicitly mentioned or alluded to include

Vladimir Arnold Vladimir Igorevich Arnold (or Arnol'd; , ; 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to s ...

, John H. Conway,

Felix Klein Felix Christian Klein (; ; 25 April 1849 – 22 June 1925) was a German mathematician and Mathematics education, mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations betwe ...

Sofya Kovalevskaya Sofya Vasilyevna Kovalevskaya (; born Korvin-Krukovskaya; – 10 February 1891) was a Russian mathematician who made noteworthy contributions to analysis, partial differential equations and mechanics. She was a pioneer for women in mathematics a ...

Henri Lebesgue Henri Léon Lebesgue (; ; June 28, 1875 – July 26, 1941) was a French mathematician known for his Lebesgue integration, theory of integration, which was a generalization of the 17th-century concept of integration—summing the area between an ...

Ada Lovelace Augusta Ada King, Countess of Lovelace (''née'' Byron; 10 December 1815 – 27 November 1852), also known as Ada Lovelace, was an English mathematician and writer chiefly known for her work on Charles Babbage's proposed mechanical general-pur ...

Benoit Mandelbrot Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of phy ...

Maryam Mirzakhani Maryam Mirzakhani (, ; 12 May 1977 – 14 July 2017) was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller space, Teichmüller theory, hyperbolic geometry, ergodic the ...

August Möbius August is the eighth month of the year in the Julian and Gregorian calendars. Its length is 31 days. In the Southern Hemisphere, August is the seasonal equivalent of February in the Northern Hemisphere. In the Northern Hemisphere, August ...

Emmy Noether Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's theorem, Noether's first and Noether's second theorem, second theorems, which ...

, Marjorie Rice,

Bernhard Riemann Georg Friedrich Bernhard Riemann (; ; 17September 182620July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the f ...

Caroline Series Caroline Mary Series (born 24 March 1951) is an English mathematician known for her work in hyperbolic geometry, Kleinian groups and dynamical systems. Early life and education Series was born on March 24, 1951, in Oxford to Annette and Georg ...

Wacław Sierpiński Wacław Franciszek Sierpiński (; 14 March 1882 – 21 October 1969) was a Polish mathematician. He was known for contributions to set theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions ...

Alicia Boole Stott Alicia Boole Stott (8 June 1860 – 17 December 1940) was a British mathematician. She made a number of contributions to the field and was awarded an honorary doctorate from the University of Groningen. She grasped four-dimensional geometry from ...

William Thurston William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thurst ...

Helge von Koch Niels Fabian Helge von Koch (25 January 1870 – 11 March 1924) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake, one of the earliest fractal curves to be described. He was born to Swedish nobil ...

Gladys West Gladys Mae West (née Brown; born October 27, 1930) is an American mathematician. She is known for her contributions to mathematical modeling of the shape of the Earth, and her work on the development of satellite geodesy models, that were lat ...

Zeno Zeno may refer to: People * Zeno (name), including a list of people and characters with the given name * Zeno (surname) Philosophers * Zeno of Elea (), philosopher, follower of Parmenides, known for his paradoxes * Zeno of Citium (333 – 264 B ...

, and many others. Twenty of the "mathemalchemists" are women, and the facility especially celebrates the contributions of women in mathematics, from amateur Marjorie Rice, who found new kinds of

pentagon tiling In geometry, a pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon. A regular tiling, regular pentagonal tiling on the Euclidean plane is impossible because the internal angle of a Pentagon#Regular ...

s, to

, the first woman to ever garner a

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...

Gallery

File:Mathemalchemy-Chipmunks.webp, Chipmunks learn about

prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

and

composite number A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime numb ...

s through a game involving acorns and Babylonian numeral tiles File:Polyhedra-in-garden-and-reef-with-Sieve-of-Eratosthenes.png, Mathematically-inspired flora and fauna fill the garden and reef as two squirrels discuss prime number algorithms in front of their

Sieve of Eratosthenes In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite number, composite (i.e., not prime) the multiples of each prime, starting with ...

File:Converging-ball-arch-detail.png, A

convergent series In mathematics, a series is the sum of the terms of an infinite sequence of numbers. More precisely, an infinite sequence (a_1, a_2, a_3, \ldots) defines a series that is denoted :S=a_1 + a_2 + a_3 + \cdots=\sum_^\infty a_k. The th partial ...

of ''mari'' (unembroidered) and '' temari'' (embroidered) balls rises above the installation File:Koch-snowflakes-and-cavalcade.png,

Koch snowflake The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Cur ...

s descend through the Cavalcade of mathematical pages onto Integral Hill in the exhibit File:Doodle-quilt-detail.png, Great Doodle Page celebrates jottings by seven notable

women in mathematics This is a timeline of women in mathematics. Timeline Classical Age * Before 350: Pandrosion, a Greeks, Greek mathematician known for an approximate solution to doubling the cube and a simplified exact solution to the construction of the geometr ...

File:Mandelbrot-Bakery.png, What does math taste like? Cat and mouse prepare treats in the math-infused Mandelbrot Bakery File:Cryptography-quilt.png,

Cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...

Quilt represents 27 ways to encode messages File:Zenos-Path.png, Tess the Tortoise ambles down Zeno's Path toward Integral Hill File:Cavalcade-detail.png, Detail from Cavalcade of mathematical pages File:Tamari ball arch with teenager.png, The silhouette of a teenager surfs above the Cavalcade and Ball Arches

History

Mathemalchemy_sendoff_party_projection_match_map

Daubechies and Ehrmann presented the project in a special session at the 2020

Joint Mathematics Meetings The Joint Mathematics Meetings (JMM) is a mathematics conference hosted annually in early January by the American Mathematical Society (AMS). Frequently, several other national mathematics organizations also participate. From 1998 to 2020, the JMM ...

(JMM) in

Denver, Colorado Denver ( ) is a List of municipalities in Colorado#Consolidated city and county, consolidated city and county, the List of capitals in the United States, capital and List of municipalities in Colorado, most populous city of the U.S. state of ...

.Mathemalchemy to Open at NAS
Cultural Programs of the National Academy of Sciences, Jan. 12, 2022 They soon had a core group of more than a dozen interested mathematicians and artists who in turn suggested other people not at JMM. Eventually the group would grow to 24 people.Mathemalchemy: A Playful Pandemic Project
, by Kimberly A. Roth and Jessica K. Sklar, MAA Focus, October/November 2021, pp. 20-23 Originally, the intent was to collectively design and fabricate in a series of workshops to be held at

Durham, North Carolina Durham ( ) is a city in the U.S. state of North Carolina and the county seat of Durham County, North Carolina, Durham County. Small portions of the city limits extend into Orange County, North Carolina, Orange County and Wake County, North Carol ...

, starting in March 2020. The COVID-19 pandemic disrupted these plans. Working instead over

Zoom Zoom may refer to: Arts, entertainment and media Film * ''Zoom'' (2006 film), starring Tim Allen * ''Zoom'' (2015 film), a Canada-Brazil film by Pedro Morelli * ''Zoom'' (2016 Kannada film), a Kannada film * ''Zoom'' (2016 Sinhala film), a Sr ...

, under the guidance of Dominique Ehrmann and various "team leaders" for different parts of the installation, the installation was collectively designed and discussed. In July 2021 the team could finally get together at Duke for the first in-person meeting, where the components that had been fabricated in various locations in the US and Canada were assembled for the first time, leading to the first complete full-scale construction. The 24 members of the team employed

ceramics A ceramic is any of the various hard, brittle, heat-resistant, and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porce ...

knitting Knitting is a method for production of textile Knitted fabric, fabrics by interlacing yarn loops with loops of the same or other yarns. It is used to create many types of garments. Knitting may be done Hand knitting, by hand or Knitting machi ...

crocheting Crochet (; ) is a process of creating textiles by using a crochet hook to interlock loops of yarn, thread, or strands of other materials. The name is derived from the French term ''crochet'', which means 'hook'. Hooks can be made from different ...

quilting Quilting is the process of joining a minimum of three layers of textile, fabric together either through stitching manually using a Sewing needle, needle and yarn, thread, or mechanically with a sewing machine or specialised longarm quilting ...

beadwork Beadwork is the art or craft of attaching beads to one another by stringing them onto a thread or thin wire with a sewing or beading needle or sewing them to cloth. Beads are produced in a diverse range of materials, shapes, and sizes, and vary ...

3D printing 3D printing, or additive manufacturing, is the construction of a three-dimensional object from a CAD model or a digital 3D model. It can be done in a variety of processes in which material is deposited, joined or solidified under computer ...

welding Welding is a fabrication (metal), fabrication process that joins materials, usually metals or thermoplastics, primarily by using high temperature to melting, melt the parts together and allow them to cool, causing Fusion welding, fusion. Co ...

woodworking Woodworking is the skill of making items from wood, and includes cabinetry, furniture making, wood carving, joinery, carpentry, and woodturning. History Along with stone, clay and animal parts, wood was one of the first materials worked b ...

textile Textile is an Hyponymy and hypernymy, umbrella term that includes various Fiber, fiber-based materials, including fibers, yarns, Staple (textiles)#Filament fiber, filaments, Thread (yarn), threads, and different types of #Fabric, fabric. ...

embellishment,

origami ) is the Japanese art of paper folding. In modern usage, the word "origami" is often used as an inclusive term for all folding practices, regardless of their culture of origin. The goal is to transform a flat square sheet of paper into a ...

, metal-folding, water-sculpted brick, and temari ballsArs Mathemalchemica: From Math to Art and Back Again
by S. Goldstine, E. Paley, and H. Segerman,

Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume was published in 1953. Each issue of the magazine ...

, Vol 69, No 7, 2022 to create the room-sized installation.Art Installation Celebrates the Beauty and Whimsy of Math
Duke Today, November 9, 2021

Venues

The finished installation was originally displayed at Duke University, then moving to the National Academy of Sciences (NAS) building in

Washington DC Washington, D.C., formally the District of Columbia and commonly known as Washington or D.C., is the capital city and Federal district of the United States, federal district of the United States. The city is on the Potomac River, across from ...

, where it was on display from December 4, 2021, until June 12, 2022. The installation next showed at

Juniata College Juniata College () is a private liberal arts college in Huntingdon, Pennsylvania. Founded in 1876 as a co-educational normal school, it was the first college started by members of the Church of the Brethren. It was originally founded as a cent ...

Huntingdon, Pennsylvania Huntingdon is a borough in and county seat of Huntingdon County, Pennsylvania, in the Middle Atlantic states region of the Northeastern United States. It lies along the Juniata River about east of larger Altoona and west of the state capita ...

before moving to

Boston University Boston University (BU) is a Private university, private research university in Boston, Massachusetts, United States. BU was founded in 1839 by a group of Boston Methodism, Methodists with its original campus in Newbury (town), Vermont, Newbur ...

from January to March 2023, partially overlapping with the 2023

in Boston. The exhibit then moved to Beaty Biodiversity Museum in

Vancouver, British Columbia Vancouver is a major city in Western Canada, located in the Lower Mainland region of British Columbia. As the List of cities in British Columbia, most populous city in the province, the 2021 Canadian census recorded 662,248 people in the cit ...

and then in November of that year it went to

Northern Kentucky University Northern Kentucky University is a public university in Highland Heights, Kentucky, United States. Established in 1968, it is the youngest of Kentucky's eight public universities. The university has seven constituent colleges in arts and science ...

where it remained until February 2024.Traveling multimedia project celebrates math at Mathematics
The Northerner, December 6, 2023 From May 22 to October 27, 2024 ''Mathemalchemy'' was at the

National Museum of Mathematics The National Museum of Mathematics or MoMath is a mathematics museum in Manhattan, New York City. It opened on December 15, 2012, with over thirty interactive exhibits. The mission of the museum is to "enhance public understanding and perceptio ...

(MoMath) in New York City. From November 6, 2024 to May 2, 2025, the

University of Quebec in Montreal A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Univ ...

(UQAM) hosted the exhibition. After successful fundraising, the exhibition is scheduled for the Navajo Nation Museum in

Window Rock, Arizona Window Rock, known in Navajo language, Navajo as Tségháhoodzání (), is a city and census-designated place that serves as the capital of the Navajo Nation, the largest List of federally recognized tribes in the contiguous United States, Nativ ...

from June 18, 2025 through October 31, 2025. The exhibit is planned to ultimately reside in the Duke University mathematics building, on permanent display.

References

External links

*
Mathemalchemy Art Installation on YouTube
{{mathematical art Installation art works Recreational mathematics Mathematics organizations Mathematics conferences Mathematics education Mathematics and art Traveling exhibits Mathematics education in the United States Organizations established in 2020 Artist groups and collectives 2020 establishments