Mathematician Goro Shimura, speaking of Yukata Tamayana (1927-1958) said:
"He was gifted with the special capability of making many mistakes, mostly in the right direction. I envied him for this and tried in vain to imitate him, but found it quite difficult to make good mistakes."
as quoted by Simon Singh in Fermat's Enigma. The challenge, as Shimura notes, is to make "good mistakes", and to learn to differentiate them from unproductive blunders.
In the same vein, Amir Aczel's Fermat's Last Theorem quotes Andrew Wiles:
"Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room ..."
That's life: a succession of dark chambers. Learning experiences, if taken rightly.
Monday, September 06, 1999 at 21:09:39 (EDT) = 1999-09-06
I recall the following story about Thomas Edison, perhaps apocryphal:
While Edison was trying to find an appropriate material for a light bulb filament, he met with failure after failure. Someone commented to him that it must be frustrating to be making no progress and not to have discovered what he was seeking.
He replied, "On the contrary, I now know of 100 different materials that are unsuitable for filaments!"