I think that I truly, positively understand both the Fourier transforms I deal with (FS, FT, DFT, DTFT, as well as their subtle but very important differences),

I think that I truly, positively understand both the Fourier transforms I deal with (FS, FT, DFT, DTFT, as well as their subtle but very important differences), and the Laplace transform and the z-transform. I can recite them just by "concept", that means by knowing what they do, how they work, and why they work, I can piece together the equations in no time. Memorization is not necessary anymore. But I got there by, at first, "blindly" memorizing FS, FT, DFT, DTFT, and Laplace and z transforms. This allowed me to not only apply them to problems while, at the time, not being fully comfortable with them yet, but also, and this is really the biggest part of the point I'm trying to make, to "look at them" while I was either solving problems or just furthering my understanding of the field when, say, lying in bed before falling asleep. To an extent that would not have been possible if I had to "refer back" to their definitions on paper. It was a tremendous tool (that is what memorization is, a tool) to just be able to recite, say, the DFT, or the DTFT, even while my intuition was still gradually building up. And to internally look at the differences between DFT and DTFT. The same is true for the countless other little factoids in my arsenal of flashcards. I literally built a lot of math understanding, both abstract and of actual engineering problems I was working on, when sitting in my car, on my 45 minutes commute to work or back home. > Our brains are connection machines, not encyclopedias. And memorization is a tool for making new connections.