What we learn


“Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. If we see ourselves as students of advanced mathematics might, then the basic set-theoretic facts of life must matter, and must be known to us with the minimum of philosophical discourse and logical formalism.  From this point of view the concepts and method are merely some of the standard mathematical tools; but unconventional thinkers will find nothing new here.

This is not to say that naive set theories are unusually difficult or profound. What is true is that the concepts are very general and very abstract , and that, therefore, they may take some getting used to. It is a mathematical truism, however ,that the more generally a theorem applies, the less deep it is.The student’s task in learning set theory is to steep him or herself in unfamiliar but essentially shallow generalities till they become so familiar that they can be used with almost no conscious effort. In other words, general set theory is pretty trivial stuff really, but, if you want to be a mathematician, you need some, you need to read it, absorb it, and forget it.”

Naive Set Theory, Paul. R. Halmos.

A jump point | What would be the equivalent in your area of study or expertise? What does the general, abstract, familiar discourse look like? How much do you need? And where to from there?


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