Good Mathematician vs. Great Mathematician

[1] A good mathematician wants to know how. ("Problem solved! So satisfying.") A great mathematician wants to know why. ("Problem… solved? So unsatisfying!")

[2] A good mathematician selects the most powerful tool for the job. ("Welding torch it is!") A great mathematician selects the least powerful tool for the job. ("Nothing a little duct tape can't fix.")

[3] A good mathematician answers questions. ("Does it converge? My proof says no!") A great mathematician questions answers. ("Okay, so it doesn't converge… but… what if we redefine 'convergence'?")

[4] A good mathematician can make arguments intuitive or rigorous. (A graph: "it gets closer…"; or "∀ε>0, ∃δ>0: 0<|x−c|<δ ⇒ |f(x)−L|<ε!") A great mathematician can make arguments intuitive and rigorous. (A graph with ε and δ: "So, you pick a tiny allowable margin…")

[5] A good mathematician can get out of a tricky corner. ("Phew! Paradox averted!") A great mathematician can get into a tricky corner. ("Ooh… if I change the problem like this, the paradox gets even worse!")

[6] A good mathematician solves problems by making them more concrete. ("Before we build the skyscraper, let's make a model.") A great mathematician solves problems by making them more abstract. ("Before we build the skyscraper, let's study the skyline!")

[7] A good mathematician inventories what they know. ("I've got six types of screwdrivers!") A great mathematician inventories what they don't know. ("I'm still missing so many types of screwdrivers!") [an empty toolbox]

[8] A good mathematician loves math. ("How was the math today?" "Good! Even a little better than yesterday, which was already way better than the day before.") A great mathematician lives math. ("How was the math today?" "f(t) very large! And f'(t) > 0, though f''(t) < 0.")