Classroom Inspiration: The Mathematics of Ancient Athens

By: Katie Sullivan, Upper School Mathematics Teacher

I was absolutely thrilled and honored to receive the Parents of Graduates (POG) Fund Award in May 2024 after having applied for several years. As an Upper School mathematics teacher I am often heard telling my students that the “rules we are learning today weren’t made up by a bunch of old Greek men,” but rather they are based upon the laws of nature and physical truths in the world around us that many of the Ancient Greeks, and other civilizations, discovered over time and out of practical necessity. I knew that exploring the historical and cultural roots of mathematics in Greece would provide unique and valuable opportunities to deepen my own understanding and appreciation of mathematics, as well as allow me to bring back new insights and resources to share with my students. 

In August of 2025, my husband Tim and I began our exploration in Athens. For five days, we visited several sites of mathematical importance, beginning with the Herakleidon Museum. Here we were able to see exhibits featuring replicas of inventions and innovations in Greek technology, including models representing the worksites for temples, boats, and theaters such as the Parthenon. Inventions such as Cryptographic Disks and Relay Transposition Ciphers were key for communication during battles, and the Antikythera Mechanism, a calendar computer circa 80 B.C., which had 38 gears and 7 pointers, predicted eclipses of the sun and the moon, calculated the movement of the planets, and determined the dates for the Olympic and other Hellenistic games. Noted mathematician Heron invented an automated servant, and this model, alongside his odometer, were on display with a model of his automated temple gates. The gates amazed worshipers because when a fire was lit for a sacrifice, the doors opened automatically. When the fire was extinguished, the doors closed by themselves. 

Our second museum visit in Athens was to the Kotsanas Museum where we enjoyed a private, guided tour affording us a greater and more in-depth explanation of ancient Greek technology. We learned about Plato’s alarm clock, Aeneas’ Hydraulic telegraph, and numerous inventions by Archimedes, including his famous water screw, which is still in use today in many wastewater treatment facilities locally, including right next door in Concord, N.H.

Our next day’s adventure took us on a road trip and guided tour of the Temple of Delphi and its archeological site and museum. One of the most important religious sites in ancient Greece, and home to the Oracle of Delphi and a number of important artifacts and inscriptions related to mathematics, including the famous "Delphic Maxims," a collection of 147 philosophical sayings that included several references to geometry and mathematics. They are believed to have been delivered to Apollo by the Oracle and inspired the Seven Sages, one of whom was Thales of Miletus, a famous philosopher, mathematician, and astronomer. Thales is famous for his theorem about a right angle inscribed in a semicircle. 

This visit to Athens would not be complete without a tour of the Parthenon and its museum. The following day, my husband and I made the climb up to the top of the Acropolis in 93-degree heat, while forest fires were burning in the mountains around us. Built in the 5th century BCE, the Parthenon is considered a masterpiece of ancient Greek architecture and features many mathematical principles and ratios in its design, including the use of the Golden Ratio in the proportions of the columns and the placement of the statues on the pediments. However, it is not only the Parthenon that attracts so many people to the Acropolis each year. Several temples and theaters are marvels in and of themselves, and you cannot help but stand in awe at the ingenuity and work that it took for each structure to be built.  

Our next adventure took us on a flight to Samos, a small island near the coast of Turkey. Why Samos? Who is the most famous mathematician that comes to mind when you think of Greece? Pythagoras, of course! He was born on Samos around 570 B.C. and the main town is Pythagoras, where you will find his statue. As important as it may seem for a math teacher to visit the birthplace of Pythagoras, there was actually a much more important and exciting site to see on Samos. The Tunnel of Eupalinos is an ancient underground aqueduct that was built in the 6th century BCE by the engineer Eupalinos, who used advanced mathematical and engineering techniques to construct the tunnel, including the use of complex geometric calculations to ensure the tunnel maintained a consistent slope and flow of water. It was carved through the core of a mountain 1,306 meters long, to carry water to the people of Samos. Fearing invasion from what is now known as nearby Turkey, the leader Polycrates wanted to ensure water was provided to his people. With only hammers, chisels, picks, and torchlight, hundreds of slaves were promised freedom when they began the project. Cutting through solid limestone from both ends of the mountain, the slaves met in the middle with only approximately a 15-centimeter difference. Having the opportunity to drive up into the mountains and then descend into this actual tunnel was incredible. Knowing that hundreds of men, most of whom did not survive, spent close to ten years in these cramped, airless, dark conditions was truly awe-inspiring. 

To finally walk the paths of the scholars that I have spent my career studying and teaching about is a debt of gratitude I owe to the Shore community. This journey has not only enriched my own understanding but has also provided artifacts and fresh inspiration for my classroom. I am thrilled to bring these first-hand experiences back to my students, turning centuries-old theories into vivid, living history. I look forward to translating these ancient landscapes and ideas into tangible lessons for my students.

Established in 1997, the purpose of the Parents of Graduates Fund (POG) is to provide a significant and meaningful professional growth experience for one Shore faculty member per year. Parents of graduating students pay tribute to the honored Shore faculty by contributing to the POG Fund. Past recipients have reinvigorated their teaching with new ideas, innovations, and excellence. Previous award winners have investigated Incan ruins, traveled across the United States, explored literary sites across England, and wandered through the Black Caves of Spain.