> because of how implicit most everything is in mathematics. Which is a completely wrong impression due to how it is taught in school and to undergrads in the

> because of how implicit most everything is in mathematics. Which is a completely wrong impression due to how it is taught in school and to undergrads in the US. Speaking as a mathematician, since one is reasoning about abstract objects everything necessarily is pedantically explicit (otherwise proofs could not possibly work). Hence, in US graduate courses or EU undergrad courses you start from scratch and rigorously define every symbol you ever write and justify every step you take (e.g. given a field, why is "1" distinct from "0"? What is a derivative? Prove that it is actually well-defined, exists for such functions etc.). What many people confuse for being implicit is the heavy polymorphism and terseness in mathematical notation. For instance, one often identifies a function, its graph or its image depending on type makes sense in context. Here, rigorous courses spent much time to prove that any possible ambiguity in notation is actually no ambiguity at all; one is allowed to use short-hand notation because all interpretations are equivalent.