At a forum in Palm Springs, California, in 2022 January, Professor Whalen just gave two wonderful talks for a lay audience on great works of literature by Homer (Oμηρoς), Vergil, and Shakespeare. These works have great historical importance and literary value. When we were chatting afterward he asked me what I do and I said I was a mathematician. He said when mathematicians and physicists talked about their work what he found most interesting, surprising, and pleasing was the prominence of aesthetic beauty, a beauty they were reticent to explain. Maybe they were shy, maybe they felt an English professor wouldn't understand, maybe they wanted to keep their appreciation to themselves, or maybe they really didn't understand the beauty of their work. In any case, I claim my work is aesthetically beautiful and, if I'm going to claim my work is aesthetically beautiful, then it is incumbent upon me to be able to explain that beauty, even to a non-mathematician. (Here is the Wikipedia page on beauty in mathematics.)
Like most disciplines, mathematics is cloaked in inclusion and exclusion, smart people who know the notation and rules are included and everybody else is excluded. Making fun of that attitude in one of our professors we joked among ourselves, "I have the funniest joke to tell, but first let me explain the notation." Picking up a math text or paper and just reading it is much harder than being part of a common group that understands it.
It's not just mathematicians. Picking up the Odyssey and reading it isn't easy either. First of all, the original is written in ancient Greek, not a language most of us know. Even in translation it's not an easy work to follow and there are a lot of cultural assumptions that require education and intellect to understand. Reading Homer makes the movie "O Brother, Where Art Thou" a lot funnier and easier to understand. Come to think of it, seeing the movie "Zero Hour" sure makes the movie "Airplane!" a lot funnier.
Please be patient that this exploration of the beauty of mathematics doesn't follow a linear, sequential curriculum. As I focus my vision on one beautiful part of a mathematical mind I'm like a dog seeing a squirrel when something else comes in the side window. I hope my not-always-direct presentation gives some insight into the beauty I see when I do mathematics.
PHYSICAL BEAUTY DUALITY ISOMORPHISM AND EXTENSION PROVING A LOT FROM A LITTLE SIMPLICITY NEGATIVITY AND EXTENSIONS ABSTRACTION MUSIC TRUTH NUMERICAL COMPUTATION CULTURE CONCLUSION |