In textbooks, history seems to be a train on a track, naturally progressing from one station to the next. However, to the people who lived it, history was more like hacking through dense jungle with machetes--metaphorically and sometimes literally! There is no clear destination and no clear path for history that is currently in the making, and certainly no track laid out for easy travel. The mathematics of millenia can be neatly summarized as a smooth progression through ideas, from concrete, natural and rational numbers to abstract, irrational and complex numbers. Most may not even be aware that these ideas developed in fits and stops around the globe, or of those who paid the price for these numbers with their lives.
The name Pythagoras may evoke the image of a studious introvert sketching right triangles, but I think of Pythagoras as a charismatic cult leader who happened to be a mathematician. His devoted followers were known to be deep thinkers, benevolent lawmakers, and devout vegetarians. Their interest in mathematics was not purely academic, for their faith was centered on the belief that all things of heaven and earth could be described with natural numbers and their ratios. Whole numbers were holy numbers; evens and odds were as sacred as gods.
Whether history or legend, the story is told of a geometer who sailed with some Pythagoreans. As the conversation naturally turned towards mathematics, the geometer discussed how the ratio of the diagonal of a square with its side was a new kind of number. As this relationship of dimensions was unable to be described as the ratio of two natural numbers, it was deemed irrational. (Get it? Ir-ratio-nal.) This idea was sacrilege to the Pythagoreans, the acolytes of rational numbers, who threw him overboard.
When I hear this story, I hear two tragedies—the murder of the geometer is obvious, but more insidious is the close-mindedness of the Pythagoreans aboard the ship. Their refusal of an idea that at first glance did not seem to be compatible with their notions of mathematics is an affront to the legacy of the Pythagoreans, pioneers in knowledge and learning.
The world is full of problems. Mathematicians love problems, but the world needs more than just mathematicians to think about problems. In fact, it’s not even just the responsibility of owlish, bespectacled professors from the breadth of academia to push and pull at ideas. We need everyone—old and young, educated and illiterate, people of different abilities, different perspectives, and different places to untwist the knots, unlock the doors, and expand the boundaries at the frontiers of every field.
I mentioned that I imagine history as the struggle of mankind to make their way through dense jungle. I take great pride in that struggle. I view our species as one who has an unstoppable drive to make spaces. Without claws or teeth, we made a space for ourselves among beasts. Without fur, we made a space for ourselves in every clime. Without fins or gills, we found ways to make ourselves a space through the oceans. Without wings, we made our space in the sky. These literal, physical spaces are within reach because of our ability to make space in our minds, in our personal frameworks, in our outlooks for new ideas—to examine, analyze, and evaluate, sifting through infinite information. This is often accompanied with the discomfort of having to re-evaluate our old ways of thinking, of speaking, of doing. But discomfort is a small price for truth. We never would have come so far as a human race had we not boldly championed truth in the face of denial. Each day I celebrate the triumph of the human mind and the human spirit, and invite you to join me in anticipation of the ideas we have yet to discover.
Megan Orton, a math teacher at Waterford School, is a graduate of the Westminster College where she earned a B.S. in Math Teaching, with a History Teaching Minor. She also received a M.S. in Mathematics from Western Illinois University. After completing her graduate studies, Megan worked as a full time Math Instructor at Western Illinois University for four years, spending her summers as an adjunct Math Instructor at Spoon River College. Megan started tutoring Waterford students privately while working on her Bachelor's degree, and after returning to Utah became formally employed as a Waterford Tutor. After this, she joined the Waterford math faculty in the fall of 2014. She loves working with the Waterford community, and in her spare time enjoys spending time with her husband and cat at her home in West Jordan.