Some of my favorite quotes from the past month regarding math and research:
On counting, from my real analysis professor Dr. H: How do you count things? [holds up fingers] One, two, three, four... [laughter from class] we map things from the world around us to our fingers. How do mathematicians count things? We don't have enough fingers, so we use the natural numbers. Natural numbers are the mathematician's fingers.
From the methods of applied mathematics course I sat in on for one day (regarding perturbation theory): By the time you finish your graduate work, you will have thousands of solved problems under your belt. When you get into the real world, you suddenly realize that most of the problems you want to study are unsolvable. This class is about what to do next.
My research mentor, on being discouraged: It is good that you are going around talking to experts in the field about the research you want to do. I did the same thing when I was in your position. However, they are only going to give you their opinions, and sometimes they will be discouraging. Sometimes you have to disregard what they have to say and continue onward with what you are convinced you need to do.
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