The question "Every mathematician has only a few tricks" originally had approximately the title of my question here, but originally admitted an interpretation asking for a small collection of tricks used by all mathematicians. That question now has many answers fitting this "there exist a small set of tricks used by all mathematicians" interpretation. I find that swapping the quantifiers gives a better question. I.e. I am more interested in hearing about the small collections of tricks of individual mathematicians. Pointing back to the other question above, and Rota's article, what *are* the few tricks of Erdős, or of Hilbert?

Question:What are thefew tricksof some individual mathematicians?

Of course, as the comment in the earlier question quips, a mathematician never reveals tricks...but one can hope. In your answers, please include the name of the mathematician, and their few tricks...perhaps some cool places where the tricks are used, i.e. some "greatest hits" applications of the tricks.

Note, I don't think that knowing these tricks can make you into Erdős or Hilbert, but a long time ago a friend told me that a talented mathematician he knew would approach research problems by asking himself how other mathematicians would attack the problem. This is sort of like writing in another author's style, which can be a useful exercise. Wouldn't it be neat to be able to ask yourself "How would Hilbert have attacked this problem?"

MO is a good place to collect these, because it often takes extended reading (as intimated by Rota) to realize the few tricks used by a certain mathematician. As a community, we may be able to do this.

notachieve what Jon is asking for here. I mean, we've already had generic answers to the other question like "interchange the order of summation" or "the Cauchy--Schwarz inequality", and TBH I foresee the quality of answers over there going down rapidly, as every random user goes "oh hai what about this trick I saw" $\endgroup$12more comments