In terms of reductionism differential equations are more fundamental than sets.
Would you care to give an argument for this? This strikes me as wildly implausible, and my default interpretation is as a rhetorical statement to the effect of "boo set theory!!"
I've never seen set theory reduced to differential equations. On the other hand, the reduction of analysis (including differential equations) to set theory is standard and classical.
There are a lot of phenomena -- in mathematics, in the cosmos, and in everyday experience -- that you cannot understand without knowing something about differential equations. There are hardly any phenomena that you can't understand without knowing the difference between a cardinal and an ordinal number. That's all I mean by "fundamental."
But here is a joke answer that I think illustrates something. Differential equations govern most of our everyday experiences, including the experience of writing out the axioms for set theory and deducing the...
Did computer programming make you a clearer, more precise thinker? How about mathematics? If so, what kind? Set theory? Probability theory?
Microeconomics? Poker? English? Civil Engineering? Underwater Basket Weaving? (For adding... depth.)
Anything I missed?
Context: I have a palette of courses to dab onto my university schedule, and I don't know which ones to chose. This much is for certain: I want to come out of university as a problem solving beast. If there are fields of inquiry whose methods easily transfer to other fields, it is those fields that I want to learn in, at least initially.
Rip apart, Less Wrong!