The Joy of Understanding Math

So, we learn some concepts. We step back and ask ourselves; does this all make sense? An artist’s brushstrokes can be meaningless even though we can identify the orientation and hue. They are just brushstrokes. However, when we step back a little bit the strokes of paint come together some and we realize there are objects that have more meaning than the individual strokes by themselves. Our level of understanding has risen to the recognition of objects, but we shouldn’t stop there. If we step back just a bit more, we can see the entire picture. We start to understand the content of the artwork, another level. Can we seek another level of understanding if we ponder for a moment? What was the purpose of the painting? Did it influence us? Did it affect my thoughts? Moreover, what was the artist trying to evoke in our senses? It appears our higher levels of understanding can be difficult to attain.

To fully employ what we have learned we need to understand the purpose of what we have learned. Art can be a very subjective topic regarding its purpose or meaning. One could argue that a melting pocket watch represents effects of a nuclear age, while another could say the artist was envisioning a round of soft cheese. Poetry also can require subjective understanding. That is a cool aspect of art; while reaching for understanding, we take ownership of our comprehension because it is our perspective.

Subjects like math and science can render a subjective understanding also, but to a much lesser degree. Concepts and processes that are learned usually have specific purposes they are designed for. I say usually because new purposes are discovered all the time, leading to new understandings and new mathematical journeys that can be extremely exciting… for those who understand mathematics. When we start to understand the purposes of concepts and algorithms, and when our minds are open and willing to shed the “math is hard” stigma we may have been exposed to in school, we have the opportunity for a grand a-ha moment, a joyful moment. In math, the higher the level of understanding, the greater the joy, and whatever a person learns with joy they will remember the rest of their lives. That will hopefully engender a desire to learn more and again raise our level of understanding. When we understand concepts and we understand subjects at a high level we can open our minds to more creative applications. We also start to comprehend the language of math in nature, from particle physics, to the nature of black holes, and even the miracles of life. If we add to that comprehension an open mind and a spark of creative imagination, the joy of mathematics is realized.