homehome Home chatchat Notifications


This Babylonian Student's 4,000-Year-Old Math Blunder Is Still Relatable Today

More than memorializing a math mistake, stone tablets show just how advanced the Babylonians were in their time.

Mihai Andrei
December 20, 2024 @ 6:58 pm

share Share

Did you ever screw up your homework so badly that it gets preserved in stone and analyzed by researchers thousands of years later? Well, someone in Babylon did.

The artifact in question is a small, round clay tablet measuring approximately 3.2 inches (8.2 centimeters) in diameter. Unearthed from the archaeological site of Kish in modern-day Iraq, this tablet is now housed in the Ashmolean Museum at the University of Oxford. It stands among roughly two dozen similar tablets, all believed to be the remnants of ancient Babylonian mathematics education.

The clay tablet is written in cuneiform, a writing system used in several languages of the Ancient Near East. The task was essentially to calculate the area of a triangle. The student was given the height of the triangle (1.875) and the base (3.75). Can you solve the problem?

Image of the tablet and a schematic of the actual math problem.
The tablet (left) and a schematic of the math problem (right).

To get the of the triangle, you multiply the base and the height and divide them by 2. So, you have:

(1.875*3.75)/2 = 3.515625.

The number is long, but the formula is pretty straightforward. The Babylonian student, however, got 3.1468 — the wrong solution. The error appears to have arisen through misplacing the sexagesimal place of one part of an intermediate calculation, researchers from the Ashmolean note.

Babylonian mathematics was notably advanced for its time. They employed a base-60 number system, a vestige of which persists today in our measurement of time — 60 seconds in a minute, 60 minutes in an hour. Remarkably, Babylonian scholars understood the Pythagorean theorem more than a millennium before Pythagoras, recognizing that the sum of the squares of a right triangle’s two shorter sides equals the square of the hypotenuse.

Why these tablets are so interesting

The durability of clay tablets has ensured that these ancient records survive to this day, offering important insights into early human civilization.

The student’s miscalculation is trivial in itself, but it holds substantial historical significance. It shows how the ancient Babylonians transitioned from oral to written knowledge transmission, a shift that began around 3500 B.C. in Kish. This move towards documentation allowed for the preservation and dissemination of knowledge, laying the foundation for future educational systems.

Moreover, the error humanizes the ancient student. We’ve all made mistakes in school, and this reminds us that the learning process, with its trials and mistakes, is a timeless aspect of human development. It’s a direct link between modern and ancient society, one of the things that hasn’t changed. We all struggled at times with mastering mathematics.

Challenging problems

The problems the Babylonians were trying to solve in this educational system were not particularly simple. Take, for instance, the “reeds per rod” problem.

The reeds per rod math problem

The problem involves calculating the length and area of a field based on a decreasing slope pattern. In this problem, the width of the field is specified as 1 rod (approximately 5 meters), and a slope or “furrow” decreases by 0.06 rods for every unit length, which translates to a progressive decrease in width. To solve it, the student first determines how many reeds (a smaller unit of length, approximately 2.7 meters) fit into the rod. They then calculate how much each furrow decreases in length and ultimately derive the total length of the field. Finally, the area is computed by multiplying half the width by the calculated length.

The 4,000-year-old clay tablet from Kish not only reveals an ancient student’s mathematical mistake; it opens a window into the educational systems, mathematical advancements, and cultural developments of the time. It serves as an important reminder of the universality of learning and the shared human journey towards knowledge. These tablets bridge the millennia between the ancient and modern worlds.

share Share

AI-designed autonomous underwater glider looks like a paper airplane and swims like a seal

An MIT-designed system lets AI evolve new shapes for ocean-exploring robots.

Bees are facing a massive survival challenge. Could AI help them?

Our tiny friends are in trouble and it's because of us.

NASA finally figures out what's up with those "Mars spiders"

They're not actual spiders, of course, but rather strange geological features.

Cycling Is Four Times More Efficient Than Walking. A Biomechanics Expert Explains Why

The answer lies in the elegant biomechanics of how our bodies interact with this wonderfully simple machine.

We’re Starting to Sound Like ChatGPT — And We Don’t Even Realize It

Are chatbots changing our vocabulary? There's increasing evidence this is the case.

Scientists Just Showed How Alien Life Could Emerge in Titan's Methane Lakes

What if the ingredients of life could assemble on a methane world?

Can Dogs Really Smell Parkinson’s? These Two Good Boys Say Yes

Our best friend is even more awesome than we thought.

Scientists 3D Printed Microscopic Elephants and Barcodes Inside Cells for the First Time

What happens when you 3D-print an elephant and a microlaser inside a living cell?

AI-Powered Surgical Robot Performed a Full Operation With Zero Help From Humans

An AI robot performed gallbladder surgery without human help, and it worked every time.

These 18 Million-Year-Old Teeth Contain the Oldest Proteins Ever and They Came From Giant Prehistoric Beasts

The oldest protein fragments ever recovered challenge what we thought we knew about fossil decay.