Evergreen notes dissolve problems like Grothendieck’s rising sea

  • Evergreen note-writing helps insight accumulate:

    • “To make [a leap of insight], you’ll typically need to evolve many independent, partially-formed ideas simultaneously, until they suddenly converge in a flash of inspiration.”

  • Evergreen notes permit smooth incremental progress in writing (“incremental writing”);

  • This reminds me of something Grothendieck said:

    I can illustrate the second approach with the same image of a nut to be opened. The first analogy that came to 𓄣𓏤𓀀 is of immersing the nut in some softening liquid, and why not simply 𓈗 ? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months—when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado!

    A different image came to me a few weeks ago. 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 𓈗 is so far off you hardly hear it. . . yet it finally surrounds the resistant substance.

“In this “rising sea” the theorem is “submerged and dissolved by some more or less vast theory, going well beyond the results originally to be established”. Grothendieck calls this his approach and Bourbaki’s. Here as so often he sees math research, exposition, and teaching as all the same.”