Change Your Perspective on the History of Mathematics with These Eight Learning Journeys

This is an excerpt from a post written by Bernat Espigulé-Pons that was originally published on the Wolfram Blog. The full post can be viewed here.

Amid COVID’s first wave, I had the privilege to join forces with Eric Weisstein and his team at Wolfram Research to create the History of Mathematics Project, a virtual interactive gallery highlighting physical artifacts that are important to the history of mathematics, for the National Museum of Mathematics (MoMath) in New York City. Most of my mandatory confinement at home was spent navigating through online collections from world-class museums, locating outstanding mathematical artifacts and creating interactive and computational explanations for them.

The Interactive Exhibits

The site contains more than 70 artifacts divided into virtual exhibits, grouped into nine general topic areas of mathematics: counting, arithmetic, algebra, the Pythagorean theorem, geometry, primes, π, polyhedra and mathematics education.

Each of the nine virtual exhibits gives a brief textual description of a mathematical area and its historical context, together with navigation to other exhibits, clickable thumbnails for individual artifacts within the exhibit and a clickable timeline.

Each artifact’s page contains a description of how the relic was used, detailed images, dimensions, location and additional suggested reading. Visitors can easily navigate to related artifacts and get a comprehensive historical overview in the timeline. Interactive content gives a hands-on exploration of each artifact, while computational explanations provide details about the mathematical content; both make extensive use of the Wolfram Language.

The Learning Journeys

After spending the first few months of the project populating artifact pages with interactive content and computational explanations, I moved on to creating eight Learning Journeys. These highly visual and hands-on computational essays connect the dots between different mathematical artifacts while providing engaging and fun learning journeys for middle-school students on up:

• Mathematical Beans and Knotted Strings: Counting Methods from the Moche Culture
• Balancing Ducks, Frogs and Grasshoppers: Weights and Measures in Ancient Mesopotamia
• Show Your Work!: Doing Math Homework on Clay Tablets, Papyri, Wax Tablets, Bamboo Strips and Birch Bark
• Squaring the Apsamikku Circle: The Search to Solve One of the Oldest Problems in Math
• Making Machines Fly: Overcoming the Square-Cube Law
• The Mathematics of a Masterpiece: Portrait of Luca Pacioli
• Ancient Right Triangles: The Pythagorean Theorem and the Gou-Gu Rule
• Ancient Games of Chance: The Beginnings of the Mathematical Theory of Probability

Learning Journeys are graphical, interactive computational essays that explore mathematical ideas across cultures and time. They are primarily visual and descriptive with minimal advanced mathematics, making them ideal for classroom exploration or as a teaching tool. At the same time, they contain images and links to more detailed mathematical artifact write-ups.

Ancient Games of Chance

Motivated by the ancient dice in the Polyhedra virtual exhibit, I embarked on a journey researching games of chance. I wanted to better understand their use throughout history and their connection to the development of the mathematical theory of probability.

I learned a lot of interesting things along the way. For example, a 1970s Italian expedition to the Burnt City (Shahr-e Sukhteh), located in the southeastern part of Iran, explored a graveyard in the ancient city and found a set of four elongated dice and 27 tokens, crafted about 4,500 years ago. This four-value die evolved into the modern six-sided cubical die.

And here are the probabilities for obtaining a given total using two six-sided dice:

The product of my discoveries is an exploration into ancient games of chance. Did you know early dice were made of the knucklebones of sheep? Read the rest to find out more.

The History of Mathematics Project, a virtual interactive gallery highlighting physical artifacts that are important to the history of mathematics and that is hosted at history-of-mathematics.org, was generously funded by Overdeck Family Foundation for the benefit of the National Museum of Mathematics (MoMath) in New York City. The virtual exhibits and their navigation were built entirely from source notebooks using the Wolfram Language, the Wolfram Knowledgebase and the Wolfram Cloud, which allow the content and website to be easily maintained and extended. Thank you to Heidi Kellner, Sarah Keim Williams, Lori Goodman, Andrea Gerlach and Eric Weisstein for all of your great contributions to the project!

Check out the original post to explore scale weights, with an interactive explainer about weight stones and how they would have balanced merchants’ goods. Don’t forget to visit the virtual exhibits, which launched in 2021 but are still active today.