Be patient with problems

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The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration… the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it.. yet it finally surrounds the resistant substance.—Updated on 2024-07-04 14:58:25
what he did was explore the problem in an open-ended way, building intuition, introducing notation—growing an entire theory around the problem. This could go on for years. Until one day, the solution had become self-evident, a natural consequence of the theory. The problem essentially disappeared. It had been swallowed by the sea.—Updated on 2024-07-04 14:58:37
After going through the [time-consuming process of deeply understanding a proof,] I had a rather curious experience. I went for a multi-hour walk along the San Francisco Embarcadero. I found that my mind simply and naturally began discovering other facts related to the result. In particular, I found a handful (perhaps half a dozen) of different proofs of the basic theorem, as well as noticing many related ideas. This wasn’t done especially consciously–rather, my mind simply wanted to find these proofs.—Updated on 2024-07-04 14:58:49 #to-process

The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration… the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it.. yet it finally surrounds the resistant substance. — Updated on 2024-07-04 14:58:25
what he did was explore the problem in an open-ended way, building intuition, introducing notation—growing an entire theory around the problem. This could go on for years. Until one day, the solution had become self-evident, a natural consequence of the theory. The problem essentially disappeared. It had been swallowed by the sea. — Updated on 2024-07-04 14:58:37
After going through the [time-consuming process of deeply understanding a proof,] I had a rather curious experience. I went for a multi-hour walk along the San Francisco Embarcadero. I found that my mind simply and naturally began discovering other facts related to the result. In particular, I found a handful (perhaps half a dozen) of different proofs of the basic theorem, as well as noticing many related ideas. This wasn’t done especially consciously – rather, my mind simply wanted to find these proofs. — Updated on 2024-07-04 14:58:49