And 20 years later, this essay is still as relevant as the day it was written. I agree with pretty much everything that's in the essay, except for a few small p

And 20 years later, this essay is still as relevant as the day it was written. I agree with pretty much everything that's in the essay, except for a few small points. > There is nothing wrong with keeping the functional notation for density functions – as physicists and engineers always did – as long as one bears in mind that density functions cannot be evaluated, but only integrated. This always bothered me, since, as noted in the very next section, distributions don't have an analogue to pointwise multiplication. Even worse, there is a perfectly servicable notation for such "dual functions/vectors" that physicists have been using throughout the second half of the 20th century. We could just use a consistent notation and not confuse new students, but no. "It's always been done this way" is a terrible argument and leads us to the confusing mess of notations that people still use for integrals and integral transforms... --- Apart from that I would teach people recurrence equations/stream calculus before going into the limiting case of differential equations. It's true that differential equations are sometimes easier to handle analytically, but this is neither relevant (as the article notes) nor a great point in their favor, since we just end up teaching students a bag of tricks instead of explaining why something works...