Alexander Grothendieck used the analogy of opening a nut to illuminate two different styles of doing mathematics. One way is to strike the nut repeatedly with a hammer and chisel.

I can illustrate the second approach with the same image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? 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!