Mathematics is the most beautiful and powerful creation of the human spirit
– Stefan Banach, 1892-1945, Polish mathematician.
I was recently doing KenKen, a Japanese math puzzle, on a plane when a fellow passenger asked me why I bothered. I replied that I did it for the beauty.
Okay, I’ll admit it’s a silly game: you have to make the numbers within the grid follow certain mathematical constraints, and when they do, all the pieces fit together nicely, giving you a rush of harmony and order.
Still, it makes me wonder what it is about mathematical thinking that is so elegant and aesthetically appealing. Is it the internal logic? Is it the unique combination of simplicity and explanatory power, or perhaps just its pure intellectual beauty?
I’ve loved math since I was a kid because it felt like a big game and because it seemed like the easiest mental activity. After all, how many facts do you need to remember to do math?
Later, during my economic studies, I became increasingly fascinated by advanced calculus, which you could say is essentially an extensive exercise in applying math to understand the universe. My German roommate, a brainy math major, used to tease me, claiming that I never truly understood the math I was using. I would argue back that he never understood the practical applications of the math he studied.
As it turns out, we were both right. However, he would be pleased to know that I’ve now come around to his perspective: math possesses beauty on a purely abstract level, regardless of its immediate usefulness in explaining the workings of the world.
We all recognise that art, music, and nature are beautiful. They captivate the senses and evoke emotions. Their impact is swift and instinctive. How can a mathematical idea inspire the same feelings?
There’s something deeply reassuring about the notion of universal truths, especially in a time when misinformation is rampant and people talk about alternative facts. Math is like rock-solid facts that remain unchanged, regardless of what anyone says.
For example, we have equations like the Pythagorean Theorem, which states that in a right-angled triangle, the square of the longest side equals the sum of the squares of the other two sides. It’s always true, no matter what. Then there’s pi, the never-ending number used for circles. It goes on forever without repeating, and it works for every perfect circle, regardless of its size.
But it’s not just that these equations are true; they are also inherently beautiful. Our brains seem to respond to their beauty in the same way they do to other aesthetically pleasing experiences.
Sometime in November, I participated in an experiment conducted by a team of neuroscientists at University College London (UCL). I joined fifteen other mathematicians from Columbia University for this study, which aimed to explore the neural processes involved in mathematical thinking using fMRI scanners.
Two weeks before the brain scans, we were shown sixty equations. During the scanning session and afterwards, we were asked to contemplate these equations and rate our level of understanding and subjective emotional response, ranging from ugly to beautiful.
The researchers discovered a strong correlation between finding an equation beautiful and activation of the medial orbitofrontal cortex, a region of the prefrontal cortex located behind the eyes. This is the same area that lights up when people find music or art beautiful, indicating a common neural signature of aesthetic experience.
Hey geeks, take heart: while we can’t see or hear mathematical ideas, they too can evoke a sense of beauty.
You might be curious about which equation won the beauty contest. It was Euler’s identity. This equation, named after the 18th-century Swiss mathematician Leonhard Euler, is deceptively simple yet profound, connecting five fundamental mathematical constants: a combination of real and imaginary numbers that add up to zero.
And the ugliest equation? It was Ramanujan’s infinite series for the reciprocal of pi. This equation, attributed to the early 20th-century Indian mathematician Srinivasa Ramanujan, lacks the finesse and elegance of Euler’s identity. Even to the untrained eye, it appears clunky and cumbersome.
While we were more likely to find equations beautiful if we understood them well, the correlation was not perfect. This led the researchers to conclude that the observed brain activation was a result of the experience of beauty without necessarily associating it with meaning. This makes sense, as there were equations that we completely understood but still found plain ugly.
In essence, beauty is somewhat mysterious here. It doesn’t solely depend on how much we understand or relate to something. Even in the world of mathematics, where things may seem straightforward, beauty remains subjective and sometimes surprises us by appearing where we least expect it.
My passion for mathematics originated in the physical world. Despite being illiterate, my father’s insatiable curiosity and persistent nature as a street hawker often drew me into his ventures.
Every Friday, we would scavenge cans, bottles, and various devices at Penrissen Army Camp— radios, electric generators, all sorts of exciting contraptions — in our pursuit of earning a quick buck.
One evening, I found him tinkering with a mysterious metal box in the backyard. It turned out to be a ruby laser. When he flicked the switch, a brilliant thin red light shot out of the laser and reached into the night sky.
“How far does it go?” I asked.
“To infinity,” he replied, smiling, “or beyond.”
I was completely in awe. And I still am.
The views expressed here are those of the columnist and do not necessarily represent the views of New Sarawak Tribune.
