I am a math student at Stony Brook University. I believe mathematics is about communication, rigor, and insight. The most beautiful mathematics is produced when these three qualities shine through

1. easily communicated
2. logically rigorous
3. Deep Insight into an abstract, physical, chemical, psychological, sociological, or other problem

When only one of the the conditions is met we have a problem. When two are met we have good math. When three are met we have great math.