Inventiveness

Early in my junior year, a college professor presented me with the following geometry problem: suppose a quadrangle Q has the property that a circular disc fits tightly inside it; that is, the sides of Q are all touching the disc. We call this type of quadrangles circumscribed. Is it possible to split Q, with two lines which cross inside Q, into four smaller quadrangles, each of which is circumscribed as well?

Previously, I thought that every math problem has a solution. Sometimes this solution was ingenious and required clever insight, some other times it was lengthy and tedious; nevertheless, I knew that I can retrieve the solution if unable to solve the problem myself.

The situation was entirely different this time: there was no known solution to this problem! Maybe this is why I accepted his challenge to come up with the proof, solely because he told me that I was treading new waters, and a proof has not yet been found.

I spent a few days looking at the problem before I was even able to formulate an approach. But with perseverance, I was able to crack the problem and find a solution. There was a sensation that went along with solving the problem that was entirely new to me, the feeling that I went where nobody has gone before; the thrill of discovery gave me a rush!

I began to appreciate mathematics beyond its useful merit and started to see math more from an aesthetic point of view. I enjoyed the thrill of experimenting with open problems. It is in this light that I concur with the analogy that the college professor told me, when he compared solving a math problem to creating a beautiful piece of art.