Euclid

Euclid's Elements is widely regarded as one of the most important works in mathematics. It has been in use for over 2000 years and remains important until this very day. Although it is not unknown that the content found in the book are not uniquely Euclid's, Elements was groundbreaking for its organization, clarity and exposition. How Euclid proved his theorem's and proofs have become a standard. Aside from his remarkable communication in mathematics, I think the topic itself is why Elements has stood the test of time. The concepts touch on both basic and advanced, and geometry is ever present in our lives and in education/academia. His proofs can be learned as foundational understanding for kids in the public school system. Elements can also be a core part of those pursuing higher education in mathematics - in fact, one might argue that it is imperative to learn about Euclid's work for anyone pursuing such a field of study. 

If there is beauty in Euclid's postulates is subjective - it depends on who you ask. I think I can find beauty in the simplicity of it and certainly, I can appreciate Euclid's thought process in using these simple (but proved rigorously) facts to prove much more complicated theorems. I think where I have difficulty finding the beauty in it is its specificity to mathematics. A line segment isn't such a common aspect. 

What do they say, "beauty is in the eye of the beholder"? That's my best answer to the last question, "how can we define beauty if these are considered beautiful?" It's always about perspective, and one's opinion on what's beautiful cannot be held with higher importance or validity than someone else's opinion. We may bring in the aspect of popularity or the opinion of the masses. For example: if one hundred people think something is beautiful and one person does not, then maybe we have an argument but what is important to note is that it would still be something to be argued - it is not a fact. 

Something I find beautiful is a small aspect of relativity. Stephen Hawking in his book "The Universe in a Nutshell" speaks on Einstein's theory of relativity. He brings up an example of two planes starting at opposite ends of the earth. Both airplanes are set with extremely accurate clocks and they set off at the same time - one flies east and one flies west. Both planes arrive at their initial point having recorded slightly different times! The rotation and speed of the earth contributes to the plane flying east. I find that the beauty in this lies in the fact that it goes against basic human understanding. If you describe this scenario to someone and ask them what the clocks will show, they will most likely say the same time. I don't know, my sister gave me this book many years ago (I think I was in middle school) and I never got past that page with the airplane because I couldn't comprehend it. At my big age, I still don't think I do. 

Maybe that's where the beauty lies; beauty in the sometimes amazing yet incomprehensible nature of science and mathematics.