Answer by Mozibur Ullah for Each mathematician has only a few tricks
Saying mathematicians have only "a few tricks" makes mathematicians seem rather limited. But I recall some saying that great philosophers are engaged with only one big question. Perhaps this is true...
View ArticleAnswer by Sylvain JULIEN for Each mathematician has only a few tricks
Characterizing a class of integers sharing some property $P$ by defining an arithmetic function taking a single value $k_{P}$ at those integers and then give an equivalent of this arithmetic...
View ArticleAnswer by Hollis Williams for Each mathematician has only a few tricks
Tao has recently submitted a preprint on exactly this topic in the case of the mathematician Jean Bourgain. The tricks in question are quantification of qualitative estimates, dyadic pigeonholing,...
View ArticleAnswer by Ian Agol for Each mathematician has only a few tricks
I have two tricks: Dehn filling and drilling. I've used the former to study subgroup separability, as a technical trick to reduce the proof of tameness of Kleinian groups in the cusped case to the...
View ArticleAnswer by marober for Each mathematician has only a few tricks
Not me, but Donald Ervin Knuth:Use clever notation! Especially for sums, recurrences, binomials, etc. he developed very useful variations (Concrete Mathematics [Graham, Knuth, Patashnik], The Art of...
View ArticleAnswer by A beginner mathmatician for Each mathematician has only a few tricks
I want to mention a trick of Gilles Pisier. This is an extrapolation method. Suppose you have some kind of inequality for some $L^p$ space and that you want to get a reverse Holder type inequality for...
View ArticleAnswer by David White for Each mathematician has only a few tricks
Gabe's answer, about Uhlenbeck's trick, reminded me of the Rabinowitsch trick in algebraic geometry. However, I don't know if Rabinowitsch used this trick in other work, or if it was indicative of his...
View ArticleAnswer by Stella Biderman for Each mathematician has only a few tricks
Erdős' trick is discussed at length in Gowers' classic essay Two Cultures of Mathematics, where he describes it as follows:If one is trying to maximize the size of some structure under certain...
View ArticleAnswer by Andrew for Each mathematician has only a few tricks
“Most mathematicians know one method. For example, Norbert Wiener had mastered Fourier transforms. Some mathematicians have mastered two methods and might really impress someone who knows only one of...
View ArticleAnswer by Gabe K for Each mathematician has only a few tricks
It feels a bit presumptuous to talk about another mathematician's favorite tools. However, there is something known as Uhlenbeck's trick, which definitely deserves mentioning. One recurring theme in...
View ArticleAnswer by David White for Each mathematician has only a few tricks
When I was an undergraduate, I attended a talk by Peter Lax in Budapest. He had recently been awarded the Abel Prize, but attributed all his success to "integration by parts." It seems he has said this...
View ArticleAnswer by David White for Each mathematician has only a few tricks
I like the idea of trying to recognize a mathematician by their tricks. It reminded me of the Brachistochrone problem, posed by Johann Bernoulli and solved by five mathematicians, including an...
View ArticleAnswer by Per Alexandersson for Each mathematician has only a few tricks
In my field (symmetric functions and representation theory) there are a few tricks that some people are quite notorious for.S. Assaf - Introduce new families of polynomials/(quasi)symmetric functions,...
View ArticleAnswer by Yemon Choi for Each mathematician has only a few tricks
In an effort to get the ball rolling, and to illustrate why I think several answers on the other question don't really work as answers to this one, let me offer an attempt which I think is in the...
View ArticleAnswer by LSpice for Each mathematician has only a few tricks
The question is worded in a way that seems to imply we might speak of other mathematician's tricks, but I'm not sure I know the tricks of even my closest collaborators, except by osmosis; so I hope...
View ArticleEach mathematician has only a few tricks
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...
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