Start your talk by motivating it

Whenever giving a mathematical talk, whether this is at an important conference or at your home seminar say, your audience will probably consist of very busy people. So before you start you have to convince them that it is worthwhile devoting some of their time to hearing about your research rather than thinking about their own. In other words, you have to provide some motivation for your talk, and you should better do so at the very beginning, before losing some of them (you are allowed to believe that a "good" listener will be automatically interested in problems outside his own research, but still you don't want to lose "bad" listeners right away; for if you have this kind of attitude you will end up with hardly any audience after a couple of such decisions).

How to best motivate your talk will depend on the kind of material you want to present. Firstly, ask yourself why should the content of your talk interest the public. Is it because it is related to some well known problem or theorem that everybody is interested in? Then start your talk by talking about that problem or theorem, and then introduce your work and show connections. Are you about to present research that brings a breakthrough in an area where other people had worked with less success than you? Then start your talk by introducing the problem and stressing how hard it is by listing the results of those people; then try to impress them with your result. Or did you just invent some interesting new concept? Try to motivate it e.g. by showing examples that indicate that this concept fills an important gap. In any case, it is better to start your talk with a nice and elementary problem that will automatically attract everybody's interest than with a 4-line theorem or definition.

Having these naive examples in mind, the best thing to do is use your imagination when looking for a motivating introduction.

See also: Don't start with definitions

A. Georgakopoulos: How to give a talk that is not too bad.

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