I like this anecdote  involving Hassler Whitney.

> I worked with Hassler Whitney for two years at the Institute for Advanced Study, and the mark he left on me goes deep. I guess I'm attracted to unconventional, original sorts, and Hass was surely that. His undergraduate days were at Yale, so one might expect that here was just about the most incredible math major ever. But his major was music, not math. Well, then, he must have taken all sorts of math courses, and.... Actually, he took almost no math courses. Mathematically, he was largely self-taught.
>
> Anyway, one day, in his office, I happened to mention Bézout's theorem, which basically says that two curves of degree $n$ and $m$ intersect in $nm$ points. He says he never heard of it (Bézout's theorem is in fact highly under-appreciated), and seems galvanized by it. He jumps up and heads toward the blackboard, saying "Let's see if I can disprove that!" *Disprove it?!* "Wait a minute!" I say, "That theorem is nearly two centuries old! You can't disprove anything... really..." As he begins working on some counterexamples at the blackboard, I see that my well-meant words are simply static.
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> His first tries were easy to demolish, but he was a fast learner, and ideas soon surfaced about the complex line at infinity, and how to count multiple points of intersection. After a while, it got harder for me to justify the theorem, and when he asked, "What about two concentric circles?" I had no answer. He argued his way through, and eventually found all four points. Finally he was satisfied, and the piece of chalk was given a rest. He backed away from the blackboard and said. "Well, well—that *is* quite a theorem, isn't it?"
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> I think I mostly kept my cool during all this, but after I left his office, I realized I was pretty shaken. I remember thinking to myself, "Golly, Kendig, you just saw how one of the giants does it!" He'd taken the theorem to the mat, wrestled it, and the theorem won. I'd known about that result for at least two years, and I realized that in 15 or 20 minutes, he'd gained a deeper appreciation of it than I'd ever had. In retrospect, it represented a turning point for me: I began to think examples, examples. Whitney worked by finding an example that contained the essential crux of a problem, and then worked relentlessly on it until he cracked it. He left it to others to generalize. It is to Hass that I affectionately dedicate this book. 


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  [1]: https://i.sstatic.net/bsoU3.jpg