The latest Scientific American has an interesting article about the beauty of mathematics. According to a study from earlier this year, the brain uses the same region for sensory and mathematical beauty. If this is true I believe we should consider rethinking how we teach mathematics.
In the study, researchers asked 15 post-doctoral math students and 12 non-math students to rate 60 equations. The researchers then scanned subjects brains as they looked at the equations two weeks later.
The mathematicians and non-mathematicians responded differently to the equations. For example, when asked if an equation elicits an emotional response, 9 out of 15 mathematicians gave an unqualified yes. One student reported a “shiver of appreciation”. Fourteen math students said beautiful equations made them feel happy. Conversely, 9 out of 12 non-mathematicians said they didn’t feel any emotional response when viewing an equation.
Interestingly, brain scanning of mathematicians shows activity in the medial orbitofrontal cortex, the same region activated by listening to music or viewing art.
We tend to think of math as a non-creative, technical field, but perhaps the motivation for humanists and mathematicians isn’t all that different. The researchers hypothesize, math is beautiful when it gives insight into the fundamental nature of the universe.
For example Euler’s Identity was considered the most beautiful equation. The formula is beautiful because in one simple line it connects a lot of disparate areas in mathematics. It reaches different level mathematicians on different levels because it can be applied widely. The physicist, Richard Feynman called it the “most remarkable formula of mathematics.”
We talk a lot about America’s mathematical failings. We try to overcome our problems by drilling material into students brains. In my opinion, if we want more American math students, we don’t need to break math down into smaller and smaller easily digestible pieces. We need to do the opposite. We need to reignite our lust for understanding the universe and math’s part in that picture. We need to start from wonder and work for understanding. No matter how you teach, learning math is hard. Hopefully, if we teach students the beauty of math, they will find the motivation to persist when easier opportunities are available.