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I love this analogy. One of my former professors once explained pure mathematics as a pitch black room, and writing proofs is like wandering around in that room

I love this analogy. One of my former professors once explained pure mathematics as a pitch black room, and writing proofs is like wandering around in that room looking for a light source -- often stubbing a few toes along the way. Once a proof is complete, a light has illuminated the room for others to enter safely. The mathematician often finds the room boring and moves on to another pitch black room. The hard work is wandering around in the dark. Intelligence is the ability and willingness to wander around.

calvins 11y ago
Andrew Wiles said much the same on solving FLT: "Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion. You enter the first room of the mansion and it's completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it's all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they're momentary, sometimes over a period of a day or two, they are the culmination of—and couldn't exist without—the many months of stumbling around in the dark that proceed them." http://www.pbs.org/wgbh/nova/physics/andrew-wiles-fermat.html http://www.pbs.org/wgbh/nova/physics/andrew-wiles-fermat.htm...