Einstein once said, "If A equals success, then the formula is A = X + Y + Z. X is work. Y is play. Z is keep your mouth shut."
This more or less reflects the advice I was given when I met to consult on the work I've been doing on mathematical topics that are far over my head. It is good to be enthusiastic about some of the difficult problems, but so many people have been working on them, many who are very gifted and resourceful, and they still remain unsolved. While it is true that I have come up with a unique approach, the formality of checking to see if it leads anywhere is far beyond my present ability.
What is within my reach, though, is a wonderful opportunity I was given last week. The professor I work with supported me to come and research full-time next summer on the congruent number problem and related topics. I presented my results to him and he suggested that we look into getting a grant. It was a straightforward process and within the day we were putting the application in. This grant is not as competitive as NSERC, and as I qualified for NSERC, we expect there is a very good chance I will get it. I have my fingers crossed!
Meanwhile, all my energy is on my studies. This is a formal second year, with all of the honours math topics, and it is teaching me that my talent is mediocre. Real analysis is a lot of work, particularly because it forces one to part with lazy thinking habits. There is no hand-waving. Mathematics is a language of exactness and precision. Sometimes this leads to a headache, but I suppose its no different than the cramps I remember feelings when I trained to run in the marathon.
Needless to say, I'm working very hard, and making sure to balance my week out with a bit of exercise, some fun on the weekend, and of course, writing. Please be sure to check out my Twitter feed, as I tweet on a mathematician every day.