As a mathematician, people tend to think that I must possess great facility for numbers and all kind of calculations. They infer I must be precise, well-organized and that my life must reflect what they think mathematics is: precision, rigidity and rule-driven behavior.
But nothing could be further from the truth.
While mathematicians are well-versed in the use of numbers – and therefore adept in a variety of diverse applied areas such as engineering or accounting – the real mathematician is much more akin to an artist than to an engineer.
Indeed, what drives mathematicians is, for the most part, the idea of beauty and creativity. Because our schools do such a terrible job with these concepts, you are probably surprised to hear them connected to mathematics. Most people don't think math is beautiful, nor do they see any creative aspect in it. After all, isn't it just about applying some arcane formulas?
But a mathematician is truly like an artist who needs to figure out a novel way to solve a problem when all previous methods have failed. And he or she will discover that the method to solving the problem also sheds some light of beauty on it.
So, what is beauty in mathematics? Or, even more daunting, what is beauty in general?
In this column, I will begin by trying to respond to the general question of beauty. In my next column, I will follow up by discussing beauty in mathematics in particular.
The question of what is beauty is an ancient one, and since almost every philosopher has devoted some time thinking about it, I am not so presumptuous as to believe that I can answer what is essentially an impossible question. But I can at least hope to offer some ideas as we explore this concept.
First of all, we need to acknowledge that there is some degree of subjectivity to beauty – some people like rock music, others like country.
This degree of subjectivity is certainly culturally related, as in the kind of music you were taught to like, but even within genres there is a subjectivity that cannot be avoided. If I talk with my friends who, like me, adore Beethoven, we will not necessarily agree on our favorite symphony or sonata.
At the same time, there is an inherent objectivity as well. We all would agree on the beauty of a Southern California sunset. But then what makes something beautiful if part of it is inherent in the object and part is related to the observers? I believe the answer must be sought by not contrasting these two points of view.
Maybe the reason why we recognize both subjective and objective qualities in beauty is because beauty is a consequence of the relation between us, the observers, and the object we regard.
Since all humans share some universal aspects but at the same time undergo different cultural experiences, it is not surprising that we would have some general agreement – and some specific disagreements – on what we consider beautiful.
If I were to venture a guess as to what is the nature of this relationship that allows us to define and see beauty, I would say that what we long for is a sense of unity.
We wish, consciously or unconsciously, to feel a unity with the universe and with other humans in that universe.