Inspired Mathematicians

I can illustrate the approach with the  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! 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 marble, 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 finally it surrounds the resistant substance. 

You want to get to the top of the cliff. But that's not what you focus on immediately. You focus on the next ledge just beyond your reach, because you need to do one clever thing to get up there. And then, once you get there, you do it again. A lot of this is rather boring and not very glamorous. But you can't jump cliffs in a single bound.

Instead of beating up the bad teachers, we focus on celebrating the good ones.

Mathematicians, like the poor Lady of Shalott in Tennyson’s Arthurian ballad, cannot look at the world directly, only at its reflection.

Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.