Four Math Museums Around the World: From Oldest to Newest

Readers of the Notices are likely already familiar with MoMath, the mathematics museum-cum-playground in the heart of New York City. MoMath has previously been profiled in these pages, thanks to receiving a well-deserved communication award AMS16. Readers may be less familiar with other mathematical tourism options available as you travel the world. The map of math museums continues to grow. Here we will take a look at a handful that readers might want to visit, including the oldest and newest, to discover the many faces of mathematics.

First let us consider the different, but overlapping, rationales for the creation of each of these physical, mathematics learning spaces. Doing so helps to understand the flavor of each museum. Math museums bring math into the wider culture, into people’s lives outside of the classroom, and into people’s identities. Participation in informal learning is strongly associated with educational success. The Harvard Family Research Project researched out-of-school learning and family involvement in learning across the curriculum. They found that “The dominant assumption behind much current educational policy and practice is that school is the only place where and when children learn. This assumption is wrong. Forty years of steadily accumulating research shows that out of school or ‘complementary learning’ opportunities are major predictors of children’s development, learning and educational achievement.” WLB$^{+}$09

Each math museum is a product of its country’s prevailing culture. The four museums we describe—in Germany, Turkey, the UK, and France—were all established by enthusiastic mathematicians and educators. In some cases, the museums were set up to satisfy the appetite for mathematics that already exists, and in others they were established to generate that appetite in response to anxiety about widespread, unhelpful attitudes to mathematics.

In the UK, the drive to set up a math museum is based on a desire to overcome local cultural barriers that exclude so many people from the world of mathematics. The Nuffield Foundation (who are large UK funders of research in education, justice, and welfare) found that three of four UK countries have less than 20% of students between 16 and 18 studying mathematics, with Scotland in the 21–50% range RHPS10. This is in contrast to neighbors France and Germany, who have participation rates of over 80%, due to compulsory mathematics courses for a large proportion of their students. In the UK no subjects are compulsory at this stage. This is why in the UK it is so pressing to make mathematics a prominent, popular choice for young people. This was the motivation to establish MathsCity described later in the article.

Turkey is home to a competitive and challenging education system, where every year three million people take an entrance exam to be able to attend university, but only 25% of participants qualify. With such a focus on exams, the Turkish education system is largely based on memorization and mastering multiple choice questions, without further exploration or questioning of the concepts that are being learned. The founder of the Thales Mathematics Museum, F. Alp Ayaydın, feels strongly that the museum is both an educational necessity and an obligation to address this weakness in the current education system.

Although educators in France and Germany are not complacent about attitudes to math among young people, the museums we discuss in France and Germany have emerged from more favorable mathematical backdrops.

The difference in motivation across these countries may account for different focuses and styles of the museums. In the museums in France and Germany we see a more adult, and purely mathematical focus. In Turkey and the UK, a younger audience is targeted. Applications of math to the world around us are included in the centers in Turkey, the UK, and France. In Germany, applied math is prominent in the many science and engineering museums, which leaves space for a pure mathematics museum.

Overall, the commonalities between the math museums are greater than their differences. Collaboration among the museums is facilitated by the international biannual conference MATRIX $\times$ IMAGINARY. Hands-on activities feature prominently in all four museums in this article. This form of engagement leads to a high level of communication and group work among visitors. Engagement is interest-led, and the exhibits promote both curiosity and the facility of asking interesting mathematical questions.

Mathematikum

If you know of an older math museum that is still in operation please let us know. We believe Mathematikum, which opened in 2002 in Giessen near Frankfurt, takes the prize. This is not a surprise given the strong culture around engineering and mathematics in Germany. Mathematikum came out of a successful touring exhibition run by the founder and director, Professor Albrecht Beutelspacher. Mathematikum is a successful math museum attracting over 150,000 visitors annually.

Coauthor Katie visited Mathematikum in September 2023, and this is her summary.

After my first, and blessedly straightforward, drive on the Autobahn, I arrived at Mathematikum, a stylish space inside the historic Giessen gaol building. It is beautifully spacious with exposed brickwork and beams (Figure 1). High ceilings and large windows give a light, airy, and relaxed feeling to the museum. It could be a section of IKEA, except it has an excellent selection of thoughtful, exciting mathematics exhibits.

Figure 1.

Inside the top floor of Mathematikum, which features a rolling ball sculpture.

There are over 170 exhibits to explore. These take a range of formats: demonstrations, puzzles, and exploratory pieces. The exhibits are made out of robust durable laminated beech. These are still in beautiful condition, more than 21 years after Mathematikum opened. It was a conscious decision to use wood because it was understood that visitors will be more inclined to handle wood than other materials. This is one of the many careful decisions that Mathematikum made along the way. The exhibits mostly cover pure mathematics topics with geometry and problem solving being the most common themes. Applications of math are largely absent. The newest exhibit is a monotile puzzle. Visitors fill in a fixed frame with the newly discovered tile, uncovering its properties along the way.

The impression of the exhibits overall is simplicity, with a touch of surprise and delight. A favorite exhibit, Lights On, is a challenge consisting of a circle of seven lights with a button per light. Each button toggles its light on/off and also the lights on either side of it. The goal is to get all seven lights on. The puzzle is a little fiendish, with the added bonus that the participant’s face literally glows while playing. This modular arithmetic puzzle lends itself to thinking about generalizations, such as different numbers and configurations of lights—an excellent first step into mathematical thinking.

I was drawn to the exhibit Eulerian lines where three graphs are marked on three boards and the visitor is challenged to make an Eulerian or Hamiltonian path around it with rope. This exhibit generates its own questions about when such a path can and can’t be achieved.

There are clever twists on commercially available mathematics materials. For example, a table was marked with the nets of Platonic and Archimedean solids; alongside this were magnetic polygon building sets. Pinch points were indicated on the net drawings. Picking up the magnets, using the pinch points indicated, caused your shape to pop into its 3d form instantly and satisfyingly.

Figure 2.

Self-supporting structures in Mathematikum: A catenary arch and the young children’s version of a Leonardo bridge.

On the top floor there is a young children’s area with simplified versions of a lot of the puzzles. There are bubbles and a kaleidoscope “den.” I think the way in which puzzles and challenges have been simplified is very thoughtful, with the interest and mathematical point kept, but the potential for frustration removed. For example a 3-d puzzle which involves building a tetrahedron out of four pieces has been simplified to two.

There were visitors of all ages when I arrived, from three year olds to those in their 80s. A large group of university students were just as engaged as the other age groups, which is a testament to the range of exhibits and the ideas covered.

I rounded off my visit with a coffee, with the letter $\pi$ decorating the cream on top, again simple and delightful.

Thales Mathematics Museum

Thales Mathematics Museum was established in 2015, and is the first and only mathematics museum in Turkey. Since its opening, the Thales Mathematics Museum has welcomed approximately 500,000 visitors aged 9 and above. The museum is named after the ancient Greek philosopher, astronomer and mathematician Thales (spelled Tales in Turkey), who lived in the ancient city of Miletus and who is known for Thales’s theorem. Co-author Mustafa Kayamaz is the Vice Manager of the museum, and here he describes what a visit to the museum is like and the impact his team is aiming for.

With Thales we set out to make the concepts of mathematics tangible for children, and to show that mathematics is connected to all aspects of life.

Figure 3.

Building a Leonardo Dome outside Thales Mathematics Museum.

When you enter the museum garden, you are welcomed by olive trees and birdsong, setting a warm and relaxed mood to experience mathematics. Before entering the museum, you pass through the science park (Figures 3 and 4). This is an outdoor space that contains 30 different learning stations, which are all focused on experiential science and mathematics. For example, one station allows you to discover, through play, that the Möbius strip has one side, while another station invites exploration of the relationship between the circumference and diameter of a circle.

Figure 4.

Thales Science Park.

When you walk toward the entrance of the mathematics museum, you are greeted by a modern building with large numbers and mathematical symbols on the facade.

Thales is an instructor/guide-led experience. Your instructor takes you on a deep exploration by asking questions and providing information according to your age and education level. Your instructor shows how mathematics is used in architecture, engineering, nature, astronomy, painting, music, etc. For example, a question about painting a city introduces Francis Guthrie’s four-color problem and its gamified applications. The question “Why are sewer covers circular?” shows that we are prone to overlook simple elements that surround us in our cities and shows how understanding the relationship between sides and diagonals makes our lives safer. Whilst exploring the relationship between mathematics and beauty we look at Da Vinci’s Vitruvian Man and explore the golden ratio in nature. By experimenting on an ancient, simple instrument called a monochord, visitors learn about the oldest musical scale, the Pythagorean scale, and see the proportional sequence of harmonic sounds.

Figure 5.

Tangrams at the Thinking Skills Station in Thales Mathematics Museum.

Figure 6.

Visitors to Thales Mathematics Museum engage with a weighing experiment (left) and the Towers of Hanoi (right).

We have exhibits on pure mathematics and problem solving, which are in common with those at Mathematikum, such as many wooden puzzles, curves of constant width, and catenary arches.

One difference with the other museums discussed is our optical illusion exhibition, which is extremely popular. A more striking difference is the role of instructors in our center. It is these instructors who bring out the power of mathematics in the world.

By focusing on interactive, experience-based learning, and by transforming mathematics from an abstract concept to something you can touch, we at the museum aim to create curiosity and excitement toward mathematics.

MathsCity

Coauthor Katie is the CEO of MathsWorldUK, a UK based charity which is working toward creating the UK’s first National Math Museum. In October 2021 MathsWorldUK launched a pop-up mathematics discovery center, MathsCity, in Leeds. Here Katie describes the center.

MathsCity is (probably) the second newest math discovery center/museum on the map. It is next to the food court in a busy mall, close to the city train station. MathsCity is a relatively small space, 120 m$^2$, and yet it contains over 40 exhibits on the themes of problem solving, geometry, code breaking, and fluid dynamics. You can easily spend two hours engaging with the inter-activities. To date MathsCity has welcomed over 32,000 visitors.

MathsCity’s design is quasi-industrial with surfaces and dividing walls made of scaffolding and funky colored panels. Care has been taken to be visually appealing to teenagers, as they are easily put off by a childish environment. Given that MathsCity’s aims are around opening access to mathematics, we use an informal, play-rich approach to exhibit selection with challenge and interest for all ages. Our goal is to get the right balance between challenges and demonstrations, i.e., a mix of hands-on and minds-on.

Figure 7.

Exhibits in MathsCity (left to right, top to bottom): Leonardo bridge, conic sections, giant bubble, and box of infinite patterns.

MathsWorldUK visited a number of math discovery centers around the world and sought exhibits from them to build up MathsCity’s experience. A good proportion of the pure mathematics exhibits here were manufactured by Mathematikum, and these have proven to be first class. A favorite from MMACA in Barcelona is the Leonardo Dome, a self-supporting structure which can be built with a number of different tessellations as in Figure 3. A favorite from MoMath is the Ring of Fire, a vertical circular frame which is inlaid with lasers. When objects are placed in the frame the cross-section is illuminated. The exhibit comes with transparent polyhedrons and challenges, such as finding the square cross-section in a tetrahedron or the hexagon cross-section in a cube.

Within the UK we collaborated with science discovery centers to make additional pure mathematics exhibits. Parabola Bounce is an example in which the visitor is challenged to find the focal point of a parabola with a bouncy ball and a bell. The bell is moved incrementally, visitors repeatedly drop a bouncy ball onto the parabola and see that it will always hit the bell when it is positioned at the parabola’s focal point. Alongside the pure mathematics exhibits described, MathsCity also incorporates giant versions of commercial games based on logic and spatial reasoning.

Figure 8.

Code-breaking exhibit in MathsCity. The Scytale is a coding method that was used by the Romans. The message is inscribed on a belt. This can only be read off when wrapped around a staff (tube in this case) of the right diameter.

Figure 9.

A member of Parliament plays with the Cipher Wall in MathsCity. The Cipher Wall has coded messages in three levels of difficulty. All are types of affine codes, with the simplest encoded using a Caesar wheel.

After the first year of operation we expanded the collection of exhibits to include applications of mathematics. Our goal is to show the true faces of mathematics in order to overcome the perception that math is pointless (a very common and unfortunate view). We aim to show the role of math in the areas of medical research, engineering, green technology, computing, big data, finance, space exploration, and more.

The first mathematical theme we added was code breaking. The Scytale and the Cipher Wall are code-breaking exhibits which are shown and described in Figures 8 and 9. Another favorite code-breaking exhibit is a Hamming error-correcting code which is presented as a mind-reading trick between two players. Player one thinks of a number and player two has to deduce it from the whether or not it appears on various cards. Player one can lie once. Alongside a regular Caesar wheel is an Enigma wheel, which is what one “cog” of the Engima machine could look like. Visitors have a message to decode using the wheel, while recalling that the cog changes position by one place after decoding each letter.

Figure 10.

Interactive sandbox showing contour lines of topography of the contained sand.

Work is under way on a collection of fluid dynamics exhibits under the heading “Our Chaotic Earth.” The most popular exhibit on this theme is the interactive sandbox (Figure 10). As the sand is moved, the depth of the sand is read and the projection onto the sand alters accordingly. In its pictured topographical setting, the height contours are shown and an intuitive understanding of this representation is gained by even small visitors. Soon to be installed are chaos demonstrations such as a chaotic double pendulum and an atmospheric turbulence demonstration. The turbulence demonstration is a spinnable hemisphere filled with pearlescent fluid, which allows the visitor to see and trace the often chaotic movement of the fluid inside. Within the theme of “Our Chaotic Earth” we will cover the effects of increasing the Earth’s average temperature by one degree, and include exhibits that show how mathematicians can help fight against the effects of a warming climate.

As we worked on expanding our collection of exhibits we also wanted to make sure we were achieving our goals. We commissioned an evaluation of MathsCity which showed positive results. Visitors described it as fun, cool, exciting, enjoyable, and interesting. Enjoyment of math increased, and interest in studying it at university increased. Pupils reported math “can be more than just a textbook” and saw how applicable mathematics is to everyday life. The visit provided an opportunity for pupils to collaborate and work in teams on math-based challenges, something that doesn’t ordinarily take place in school. The feedback also asked for more exhibits and more space, which of course we want too, and this has given us further motivation to work for a permanent center in the UK.

Maison Poincaré

Coauthor Joshua visited the Maison Poincaré one Saturday in December 2023; this is his description of the museum.

This compact museum, which opened to the public in September 2023, is located on two floors in a building across from the Institut Henri Poincaré (IHP), just off the Rue Pierre-et-Marie-Curie in Paris. Packed with mathematical gems, stories, and activities, it is well worth a visit for mathematical enthusiasts of all ages.

A tour of the Maison Poincaré reveals an emphasis on mathematics as embedded in individual lives and cultures. Several exhibits feature biographies of living mathematicians and people working in related fields. Others highlight stories of teams working together. Still others illustrate diverse locations around the world from which now-familiar ideas arose throughout history.

The permanent exhibits of the museum are organized around seven themes, each with its own space. Upon entering at street level, one simultaneously encounters the themes Connecter (“Connect”) on the left and Modéliser (“Model”) on the right. These are vibrant spaces, with most of the interactive exhibits in the museum.

Figure 11.

The mathematical metro. Du&Ma – Institut Henri Poincaré – Sorbonne Université – CNRS.

A wall display in the Connecter space shows the “mathematical metro” with major branches of mathematics serving as metro lines, passing through areas labeled change, numbers, shapes, randomness, foundations, and structures (Figure 11). It is further decorated with objects that evoke many of these subjects: a roulette wheel, a Romanesco broccoli, a saddle surface, a bicycle wheel, a seven-colored torus. Nearby one can explore each area through hands-on activities, such as covering a sphere with magnetic tiles, drawing a cycloid, or packing cubes in a box to maximize the weight it holds.

In the Modéliser space, visitors can experiment with compression techniques for images, play with a double pendulum, or try to imitate a random sequence of coin flips. One table has a large interactive screen where players may try to corral either sheep or people, whose behavior can be adjusted by a parameter to be more inclined to congregate or disperse (Figure 12).

Figure 12.

Joshua Bowman’s daughter watches a virtual crowd try to escape from a room.

The former office of physicists Jean Perrin and Yvette Cauchois has been transformed into the space for the theme Devenir (“Become”). This room displays biographical sketches of two dozen or so contemporary mathematicians. Behind the biographies, the walls are mirrors, so that everyone entering can see themselves as part of the mathematical community. This space also holds a miniature version of the circular “pi room” whose full-sized version can be found in the Palais de la Découverte (a science museum also located in Paris).

Around the corner, past a nonorientable sculpture, the room for the theme Partager (“Share”) highlights the physicality of mathematics. Shelves boast mathematical sculptures and other objects from the IHP’s collection; an example is shown in Figure 13. One wall displays knots made from beaded necklaces. An interactive map (which intriguingly uses Fuller’s Dymaxion projection) provides detailed information about numerous mathematical artifacts from around the world, grouped by broad historical period. One delightful screen allows you to choose from an array of mathematical symbols, then shows (and reads aloud) an equation or formula in which the symbol appears.

Figure 13.

Model from the Brill–Schilling workshop, illustrating the imaginary part of the Weierstrass $\wp$-function’s derivative.

Next comes a refurbished lecture hall for the theme of Inventer (“Invent”). The hall is decorated with stories of collaborations and awards, and its walls feature prominent portraits of four mathematicians: Noether, Ramanujan, Turing, and Mirzakhani. A video at the front of the hall continuously plays interviews with current mathematicians, who share their enthusiasm for the discovery, the collaboration, and the challenges that come with doing math.

Outside, a small garden provides the space for the theme of Respirer (“Breathe”). Unlike the other more charged spaces, this one possesses a single focus of attention: a new sculpture by Ulysse Lacoste called Le Rulpidon (Figure 14). It was commissioned for the museum and serves as the symbol of the Maison Poincaré. The shape of this sculpture is a Steinmetz solid from which two orthogonal solid cylinders have been removed, resulting in a surface of genus $3$.

Figure 14.

Le Rulpidon – Ulysse Lacoste – Institut Henri Poincaré – Sorbonne Université – CNRS.

The final space Visualiser (“Visualize”), houses a mixed-reality experience called Holo-Math. Visitors are immersed in a world where they can explore Brownian motion, for example, through observation of bees, pollen, and flowers. Future “episodes” of the experience are in development.

The second floor of the museum, below ground, is a space for temporary exhibits. The first exhibit in this space examined artificial intelligence (AI) and its increasing impact on the world. Several displays showed positive applications of AI to fields such as medicine, robotics, recommendation systems, finance, and research assistance. However, the exhibit did not shy away from some of the risks of AI, such as its high energy consumption and the potential for bias and discrimination to be built into its algorithms. Some parts were clearly intended for longer workshops with groups. For example, an analog AI could “learn” to play Nim over the course of several games using colored balls in pouches (which the human player must place correctly).

Before I left France, I asked a couple of other mathematicians what they thought of the Maison Poincaré. They were certainly happy for its existence and pleased with its contents, but they seemed most impressed by the enthusiasm with which it has been greeted by the public. The success of this recent addition to the world of mathematical museums proves that a general desire for mathematical knowledge is alive and well.

Where to Next?

We have not provided descriptions of the MathLove Museum in Korea, the Garden of Archimedes in Italy, or the Museum of Mathematics in Catalonia (MMACA), all of which are well worth a visit. Nor did we include more general museums that have high-quality mathematical offerings, the Exploratorium in San Francisco being an excellent example.

New math museum projects are progressing in Chicago and Seattle, so readers in the US will soon have more domestic math-tourism options, as well. The Math Cultural Center of Chicago was just incorporated and earned its not-for-profit status. Over on the West Coast, the mission of the Seattle Universal Math Museum (SUMM) is “to spark each and every person to love math.” In 2022–2023 SUMM’s programming reached over 4000 participants with more than 100 events. So far in 2023–2024, they are on track to double that impact. Their long-term goal is to launch the West Coast’s first math museum. You’ll be able to find them at the Joint Mathematics Meetings (JMM) next January in Seattle.