How does one give a good colloquium lecture?
At the address www.math.vt.edu/people/day/advice/YMN3_4.html there is an essay by Curtis Bennett and Frank Sottile on how to give a good math talk. The comments below are inspired in part by their article.
1. One does not necessarily need to know all the details of the proof of a theorem in order to lecture about it. On the other hand, one should talk only about theorems whose precise statement one is familiar with. If one is scheduled to talk about even an extremely important theorem whose precise statement one is not familiar with, the wise course of action is either to cancel the talk or to speak on another subject.
2. While not everything one says needs to appear on the board, a meaningful minimum should appear so that even a deaf person sitting in the audience would get some non-empty information out of the talk. Thus, the main hypotheses of a theorem discussed should appear on the board.
3. It is important to convey to the listener the importance of the subject as well as the speaker's enthusiasm for it. However, this should be done through uplifted tone, voice, and appearance, rather than through generic discussions of "main ideas". This does not mean there should be no such discussion, only that it should be minimized if prolonging such discussion risks being at the expense of providing substantive indication of the actual proof. One could ask, why do the greats of this world give such talks, such as Gromov, etc? The answer is, they can give such talks successfully, but most people can't.
4. Experience shows that it is helpful to use transparencies. They help the lecturer organize thoughts. There is a certain risk involved in using transparencies, namely going too fast for the audience. This risk can be overcome by means of a sandclock and some discipline on the part of the lecturer.
5. The slides / pages must be sparse, contain only the minimum
necessary notation, and as few words as possible so that they are
meaningful but still leave something for the speaker to say.
Use a large font. Each slide should contain no more than 10 lines.