Charles Fefferman

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“First of all, there are problems that no one knows how to solve. There are problems that have been studied but untouched, or problems on which there is partial progress. There are problems that sound compelling when formulated, but which no one has thought of yet. There are concepts which are very useful in solving problems .. or which perhaps ... sound very natural and compelling when formulated, but have not been formulated yet. And all of these things interact. So, by solving problems, one is led to concepts — and, by thinking about concepts, one is led to problems.”

“When a student picks a research topic, the decision is influenced by the research interests of the advisor, the state of the field in which the problem lives, the personality of the advisor, the chemistry between them ... who else in working on whichever problem. It's immensely complicated. And asking for a sort of simple prescription for how to assign research problems — it reminds a little of the question of how to decide who should marry whom.”