I have no experience with NSA so I cannot comment on its merits, but I have heard rumors that some analysts and ergodic theorists like "thinking in it" for cert

I have no experience with NSA so I cannot comment on its merits, but I have heard rumors that some analysts and ergodic theorists like "thinking in it" for certain problems in infinite combinatorics. Now, filters and ultrafilters are now extensively used in ergodic theory and probability to "soften" tricky analytic arguments; they have proven especially fruitful for tackling problems in combinatorics and Ramsey theory. Vitali Bergelson is a big proponent of their use, and recently Moreira, Richter and Robertson proved a fundamental result [0] in that style. For me, the most intuitive way of thinking about filters is as measure 1 sets in a (finitely additive) probability space. Their basic properties then become very clear. Principal ultrafilters, for instance, correspond to delta masses at individual points. As a little challenge, try to find "a programmer's way" of thinking about filters and ultrafilters. [0] https://annals.math.princeton.edu/2019/189-2/p04 https://annals.math.princeton.edu/2019/189-2/p04