It may seem obvious or second nature, but I often have to remind myself when working on something to make sure that I\u2019ve taken a look at what was done before. I am going to provide a story to illustrate what I mean and how this has helped me in my career.<\/p>\n
I still remember \u201cthe dark days\u201d of my years in graduate school. It was 1989-1990, my 4th<\/sup>-5th<\/sup> year in the mathematics Ph.D. program at UC Berkeley. I had passed my written and oral exams, had Henry Helson (a world-famous analyst) as my advisor \u00a0and was now \u201cdoing research\u201d in functional analysis. I use the quotes for emphasis (perhaps sarcasm is a better word), because what I was doing was trying to work on a problem that I\u2019d found myself and was literally getting nowhere. I was learning new mathematics, but was really not making any headway on the unsolved problem that I hoped would bring me the coveted three letters after my name. Yup, each day I would bang my head against the wall for hour after hour, and at the end of the day I would be nowhere closer to solving the problem. I would talk to my advisor on a regular basis, but he also didn\u2019t know how to approach the problem that I was trying to tackle using ideas\/techniques that I felt might lead to a solution.<\/p>\n <\/p>\n Eventually, Prof. Helson noticed that I had learned some things that could be useful in a different context. He said, \u201cWhy don\u2019t you take a look at the thesis of my last doctoral student, G. Choe.\u201d At first, I was somewhat annoyed with his advice. Why should I look at what his last student had done? I wanted to do something original and not look at something that had already been done. But I took his advice, and started looking at Choe\u2019s thesis.<\/p>\n I quickly realized that during the time that I had been cracking my head on the other problem, I had learned techniques that could get a significant improvement on one of the theorems in Choe\u2019s thesis. That was my first breakthrough! I finally had something new that I could call my own. Yes, even though it was a generalization of something already done, I had done it! I had a piece of original mathematics research. This first, very modest result, gave me confidence to look at other problems that I was able to solve. Some of these were different proofs or improvements on recently-proved results, but they were new, i.e., my own.<\/p>\n The lesson of looking at what has been done before, whether on a problem or some other context, is one that I have grown to very much appreciate. For example, now as a faculty member, whenever I teach a class that I haven\u2019t taught before, I ask the colleague who taught it before me to share her\/his material with me. I may end up only glancing at it, but it ends up informing my work. Whenever I become interested in a partially solved problem, I\u2019ll try to understand the technique that was used to make headway on it, even though I understand that new techniques likely will be needed to further the work. I guess my point is that originality will most of the time mean variations on what\u2019s been done before, and not a whole \u201cnew color.\u201d<\/p>\n When I think about it, this is the norm and not the exception. For example, (in another setting) many of us Angelinos still remember Magic Johnson\u2019s \u201cbaby hook\u201d in the 1987 NBA Finals against the Celtics. Was it new? Not totally. It was really a variant of what he\u2019d seen Kareem Abdul Jabbar do on a daily basis for years! What about when we read about the new gotta-eat-there restaurant. We most likely will read a review that says that the \u201cYYY\u201d is a \u201cmust-order.\u201d That \u201cYYY\u201d is a dish whose name we will recognize so it really is an improvement on something that already exists. Both of these are examples of improvements, or new variations, on what has been done before.<\/p>\n I\u2019ll end with a story that I believe is relevant to paying attention to what has been done before. I, like many graduate students, wanted to write a thesis that was groundbreaking and would set the mathematical world \u201con fire.\u201d I didn\u2019t. I wrote a thesis that \u201cgot me out.\u201d I wrote a thesis that furthered solutions to problems that had been studied before. I didn\u2019t prove the Riemann hypothesis nor even solved the problem that I racked my brains on for about two years. (BTW, that problem is still unsolved.)<\/p>\n I\u2019m not quite sure if I ever came to grips with this until a few years ago when I had the privilege of meeting Elwyn Berlekamp, a world famous mathematician\/computer scientist. In a conversation about being practical about one\u2019s work, especially during graduate school, he said to me (something like this), \u201cA lot of graduate students want to write a thesis that will \u2018set the world on fire.\u2019 They fail to realize that the world is a difficult place to burn.\u201d<\/p>\n