Euclid & Beauty

 Hello twins.

The following is a response to a biographical evaluation of Euclid's work from St. Andrew's University.

Euclid's Elements provided a synthesis of mathematical thought at that point in history. It compiled centuries of Babylonian, Egyptian and Greek mathematics into a single text. The book was crafted in a logical manner which provided the framework of mathematical thinking for centuries. He outlined the fundamentals which could serve as a friendly starting point for beginners interested in the field. He then builds upon those basics to explore more advanced topics relevant to more advanced practitioners It also introduced key ideas for points, lines, angles, and shapes which likely had applications to other disciplines. There was likely an aspect of convenience as one could refer to a single book instead of tracking down many independent works. There is an inherent satisfaction in an all-encompassing text for a subject and these summaries are highly valued in modern contexts.

As a math student, I have often heard instructors refer to an aspect of beauty or elegance in certain mathematical ideas. A skeptical outsider's perspective may be quick to dismiss this claim by questioning how a subject like math could ever contain an element of beauty. However, as I began to take more abstract math classes which dived deeper into the theory I discovered what they had described. There is beauty in the contrast between using a simple argument in an explanation for more advanced and complex ideas. There is also a deep satisfaction that can occur when math problems conclude cleanly and concisely. For our recent math history project, we had a puzzle that we presented to the class involving arc geometry. After solving the puzzle on my own, I messaged a group member saying that the puzzle was a beauty. I was referring to the extremely satisfying way in which the problem worked out when solving it. There was a variety of cancellations in the algebra which led to a very concise formula. Thus I suppose one must get their "hands dirty" by working with math to see the beauty that others describe.

Thanks for reading,

Josh