Euclid and Beauty?

 

• Why is Euclid and Euclidean geometry still studied to this day? Why do you think this book has been so important (and incredibly popular) over centuries?
• Is there beauty in the Euclidean postulates, common notions and principles for proofs? How can we define beauty if these are considered beautiful?

Euclidean geometry has stood the test of time. It is still studied today because it is still true and I think this relates to the second question. There is beauty in the postulates and axioms because it so concisely summarizes these mathematical "truths". Philosophically, there are ideas in mathematics that are absolute "truths" that must remain true anywhere (2+2=4) and I think that is a beautiful aspect of Math. Humans innately know that combining two and two equals four. And in some ways Euclid's Axioms are similar. For example, drawing a connection between two dots is a line. It provides a foundation for more mathematical curiosity and discoveries when there is a set of principles relied on. "Euclid has handed down methods for the clearsighted understanding of these matters" (last page of the article).

Perhaps this is a more spiritual perspective, but I think beauty is something that resonates in our souls. Nature is beautiful because it connects us to the earth and what is alive. Music is beautiful because it can evoke emotion in our souls and transport us to a different time or space. I think Mathematics is beautiful because it connects us with ideas that resonate - they just must be true!  When we read Socrates, I think this was the point he was making - that anyone (even someone who hadn't been exposed to math) could be taught a proof because it expands on these fundamental ideas that resonate with people.