Study and Research in Mathematics

Extract

I propose to put before you today a few somewhat disconnected thoughts and reflections that have occurred to me as a result of my experiences as a student, as a researcher, and as a teacher. I cannot say that I think they are of much value ; some of them are obvious, and others are merely expressions of opinion. But it is good for us to stand back occasionally from our subject and look at it as a form of human activity, and an address like this provides a convenient opportunity for doing so.

Study and research have much in common. In both of these activities, an individual is striving to acquire knowledge which is new to him. He is engaged in discovery. When studying, he has guides in the form of teachers and books to help him, and even when he is not actually making use of them he has the comforting knowledge that they are at hand if he needs them. In research, he has to rely almost entirely upon his own efforts. Students vary a great deal in the extent to which they depend on their teachers and books, but it is a familiar fact that the more a student can discover for himself, the greater the mastery he achieves over the knowledge he has won. In other words, the most effective study is that which most closely resembles research.