Ancient Babylon had its heyday from around 2300 to 300 BCE. The city’s biblical fame harks back to the Tower of Babel and the notorious whore of Babylon in the Book of Revelations, who, according to Roman Catholic dogma, will ultimately bring about the end of the world. The apocalypse.
Babylon was located on the Euphrates River in Mesopotamia, which is about 50 miles due south of Baghdad, in present-day Iraq. But Babylon contributed more to world history, culture and learning than what you read in the Bible
Its fabled hanging gardens were one of the seven wonders of the ancient world. And it was the first civilization to use characters to represent numerals, and to develop the concept of place value (1’s place, 10’s place, etc.). Today, all of the world’s countries use a base-10, or decimal, numbering system, which allows any mathematical quantity to be represented with some combination of 10 symbols, or numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The Babylonians, however, used a base-60 numbering system. This required the use of 60 different characters to represent numbers, and place values representing the 1’s place, the 60’s place, the 3600’s place and so forth. What’s more, there was no zero. I guess that means that if you lost everything you had, you still had something left, since you could not have nothing. (It wasn’t until AD 350 that the Mayans “invented” zero.)
The base-60 system was so complex and difficult to master, that the economy on which it was based ultimately collapsed — nobody could do the math. It’s thought to have contributed to Babylon’s ultimate demise. Despite that, we have holdovers from Babylonian mathematics: we divide hours into 60 minutes and minutes into 60 seconds. Circles have 360 degrees. And a week has seven days — not base-60 but a Babylonian invention nevertheless!
Babylonian math also has a carry-over in algebra. Anyone who has taken Algebra 1 remembers their first encounter with the quadratic formula: that scary-looking expression used to solve quadratic equations that are not factorable. Well, the Babylonians derived a way to solve quadratic equations 4,000 years ago, and it is far more ingenious, and direct, than the method taught in algebra classes today.
Lost for millennia, it was recently rediscovered by Po-Shen Loh, an associate professor of mathematics at Carnegie Mellon University, who is the national coach of the US International Math Olympiad team. He discovered the forgotten Babylonian method by accident, while researching a “more thoughtful” way to teach the quadratic formula to middle-school students. Loh maintains a “daily challenge” math website for high school students and he maintains that, “Mathematics is still alive and in a way that every person can appreciate.”
The MIT Technology Review wrote about Loh’s discovery in December, 2019. Anyone who wants to learn more about it can click this link to watch a video in which Loh explains it. The video also has links to Loh’s daily challenge website.
As Edward Albee wrote, in The Zoo Story, “Sometimes it’s necessary to go a long distance out of the way in order to come back a short distance correctly.” Surely that is the case with the Babylonian method of solving a quadratic equation — even though the Babylonians may have missed the mark with base-60 numbers.