Late to commenting on this post, but where would Grigori Perelman, the prover of the Poincare conjecture, fall then? I remember this quote from his biography:
Golovanov, who studied and occasionally competed alongside Perelman for more than ten years, tagged him as an unambiguous geometer: Perelman had a geometry problem solved in the time it took Golovanov to grasp the question. This was because Golovanov was an algebraist. Sudakov, who spent about six years studying and occasionally competing with Perelman, claimed Perelman reduced every problem to a formula. This, it appears, was because Sudakov was a geometer: his favorite proof of the classic theorem above was an entirely graphical one, requiring no formulas and no language to demonstrate. In other words, each of them was convinced Perelman’s mind was profoundly different from his own. Neither had any hard evidence. Perelman did his thinking almost entirely inside his head, neither writing nor sketching on scrap paper. He did a lot of other things—he hummed, moaned, threw a Ping-Pong ball against the desk, rocked back and forth, knocked out a rhythm on the desk with his pen, rubbed his thighs until his pant legs shone, and then rubbed his hands together—a sign that the solution would now be written down, fully formed. For the rest of his career, even after he chose to work with shapes, he never dazzled colleagues with his geometric imagination, but he almost never failed to impress them with the single-minded precision with which he plowed through problems. His brain seemed to be a universal math compactor, capable of compressing problems to their essence. Club mates eventually dubbed whatever it was he had inside his head the “Perelman stick”—a very large imaginary instrument with which he sat quietly before striking an always-fatal blow.
Late to commenting on this post, but where would Grigori Perelman, the prover of the Poincare conjecture, fall then? I remember this quote from his biography:
from Perfect Rigor.