Look around when you have got your first mushroom or made your first discovery: they grow in clusters. - George Pólya

I shall often discuss mathematical discoveries... I shall try to make up a likely story how the discovery could have happened. I shall try to emphasize the motives underlying the discovery, the plausible inferences that led to it... everything that deserves imitation.

If we deal with our problem not knowing, or pretending not to know the general theory encompassing the concrete case before us, if we tackle the problem "with bare hands", we have a better chance to understand the scientist's attitude in general, and especially the task of the applied mathematician.

In plausible reasoning the principal thing is to distinguish... a more reasonable guess from a less reasonable guess.