Euclid and Beauty

I’ve found it fascinating that Euclid’s Elements has lasted for over two thousand years. We don’t know much about Euclid himself, he might’ve even been a team of mathematicians (a little bit like some theories surrounding Shakespeare), but his influence is everywhere. What makes The Elements so timeless, I think, is how it captures the heart of what math really is, starting with a few simple truths and building something incredibly complex and elegant from them.

The postulates and “common notions” are so simple that they almost sound poetic. Take “things which are equal to the same thing are equal to each other.” It sounds obvious, but it’s the foundation for a whole logical universe. That’s the beauty of Euclidean geometry for me, how order and meaning can grow from something small and self-evident. Even now, when we have computers and non-Euclidean geometry and all these new mathematical worlds, Euclid’s work still feels like the purest expression of reasoning.

In class, when we tried to draw leaves using only a straightedge and compass, I was surprised by how much I enjoyed it. I only really knew how to make a perpendicular bisector, so my "leaf" was made entirely of that, and somehow, it still looked good. It reminded me that there’s a kind of beauty that comes from limitation. The same way Daina Taimina uses crochet to bring hyperbolic geometry to life, using Euclid’s tools made me feel connected to math as something creative, not just logical.

If I had to define beauty in Euclid’s geometry, I’d say it’s the combination of simplicity and inevitability. Every line and circle feels like it belongs, like there’s no other way it could have been drawn. Even after all these centuries, The Elements reminds me that math is about finding beauty in the structure of our own thoughts.