A huge part of maths today is about using mathematical formulas and algorithms and applying them to help us understand the world around us. I spend much of my time detailing the way we can use algorithms, breaking complex questions down into ever smaller inputs of information that can be strung together to help explain some facet of life experience. It’s a fascinating and exciting time to work in and witness the ever-changing tide of developing technology and new insights and discoveries.
But mathematics in ancient Greece was wildly exciting in an entirely different way. They were still at the infancy of an understanding of mathematical truths. While we build on what comes before us, they were busy working out the groundwork, the bigger picture, the very basics of what we now call mathematics. It was a bold time, motivated by pure curiosity and investigation. There was no drive to apply the things they discovered, simply a desire to know all that could be known.
With this came a focus on the huge gulf that runs between approximation and exactitude. No one exemplifies this pull towards precision more than Euclid.
Active in Alexandria around 300 BCE, Euclid was uncomfortable with anything that relied on assumption. He understood the massive potential for mathematical exploration, but he was acutely aware that for anything constructive to come out of it, there first needed to be the elimination of uncertainty. And so he took it upon himself to write what has become one of the most famous and important books ever to be written – The Elements.
Over 13 books he stripped mathematics right back to the very basic assumptions and set to work proving that they were true. His axioms included such things as “all right angles are the same” and “between any two points you can draw a straight line” – things that seem so incredibly simple that you wouldn’t think to question them now. Euclid not only questioned them but broke them down and tested them and provided evidence that they were true. He was the first to record mathematical proofs for what had previously just been assumptions. Euclid gathered the raw material from his contemporaries and crafted them into building blocks, laying them down neatly and orderly and, most importantly, without any space for doubt. His exhaustive work set in place the foundations for all that came after.
The Elements is just as relevant now as it ever was. Every page of it is as true today as it was when Euclid wrote it down. Mathematics has moved on in ways Euclid would barely be able to imagine, but all of it stands on the foundation that he built. He didn’t just offer us mathematical truths, he forged the way we engage and work with mathematics to this day. He showed us how to break things down before building up, and how to confidently accept and rely upon what has been previously proven in order to discover new truths and offer our own proofs to the world. We are once again in an era driven by curiosity and ambition to test the limits of what can be known and what can not. But even today we can feel confident to trust ourselves to reach out to these unknowns because over 2000 years ago Euclid provided an anchor.
Learn more about this story of Ancient Greek science in the Science Museum’s exhibition Ancient Greeks: Science and Wisdom (17 November 2021 – 5 June 2022). This collection also holds intriguing examples of how science is being used to uncover new insights about the Ancient Greek world.