Plimpton 322 is arguably the most interesting, most sophisticated mathematical document from the ancient world. It tells us that past civilizations understood mathematics a lot better than we thought. In particular, the Mesopotamian understood Pythagorean triples at a level of sophistication that we never expected. And at the time, we didn't realize how important it was. And it wasn't until 1945 that it was revealed to contain Pythagorean triples. Subsequently, it has become one of the most studied objects from the ancient world. The traditional history of geometry really starts in ancient Greece when you've got these astronomers who are using geometry to understand the movement of celestial bodies through the night sky. The most famous relation in geometry is the relation between the sides and the hypotenuse of a right triangle. Now, in modern times, we call this Pythagoras' theorem. In reality, elements of this understanding are apparent throughout history. You see, about a thousand years before the Greek astronomers were looking at the night sky, you've got Babylonian surveyors who have their own unique understanding of right triangles and rectangles, and they're using it. But they're not looking at the sky, they're looking at the ground. Now they didn't have what we call the theorem. Instead, they knew all these particular cases where the theorem held true. So all these different examples of rectangles, which have very pleasant, easy to manage measurements. These are called the Pythagorean triples. This tablet, Si 427, shows us that the application is actually surveying. These people are making boundaries and they're making really accurate boundaries using their understanding of geometry. Pure mathematics is the study of mathematics for its own sake. But it's often motivated in the problems of the day. Plimpton, 322, arguably fits into this category because we see a mathematician generating all these rectangles and then analyzing them to see which ones have regular sides, which is a relevant problem in contemporary surveying. This tablet shows us that Babylonian surveying became a lot more accurate during this time, which is understandable because people are starting to own land privately. And when you've got land owned by private individuals, you've got disputes over who owns which parts of land or who owns which date palms and boundaries. Plimpton 322 is arguably the most interesting mathematical artifact from the ancient world. It tells us that past civilizations understood mathematics a lot better than we thought. We know about this today because we have thousands upon thousands of clay tablets from the lost cities of ancient Babylon. These have been preserved beneath the sands of modern-day Iraq and finding their ways into libraries, private collections, and museums. I believe that there's so many tablets out there just waiting for someone to read them, and they are going to surprise us because the Babylonian understanding of the world was so different from how we see it today.