The hero lives their life, but plots and twists arise. They meet positive or negative characters, in a world governed by its own rules, its own internal logic. Eventually, unexpected events occur and the quest moves forward. Finally, we understand something we didn’t know before.

The same goes for a proof. Faced with a familiar situation, we can develop a few small concrete examples, but then we must generalize and solve a much larger problem, initially as vast as a mountain. But thanks to scrolls from the Ancients containing magical formulas effective under certain conditions, after a little work, the solution emerges and we finally understand.

Remembering a proof is very similar to telling a story. You need to identify the key points, the timely intervention of this or that character, an old bearded Greek and his theorem, applying under certain conditions, so that the internal rules change the context until the happy ending. But if you forget a detail, the whole story risks collapsing.

Marking your path, leaving traces—breadcrumbs or little pebbles—whether fragile or persistent, is a common feature in many tales and in mathematics. It allows you to find your way back, if you can rely on them. Otherwise, you risk getting lost.

Taking notes is crucial in mathematics. You detail the calculations. This relieves working memory, freeing up space to process other information. If you make a mistake, you can backtrack and check where you went wrong. If you succeed, following the same path will lead to another success, faster the second time.

The strategies adopted by the hero are varied. Their task is rarely accomplished on the first try. They try again and again, with a different angle of attack, flexibility in their approaches. This transforms the hero: they gain experience, like the three little pigs who can be seen as three versions of the same character maturing with each attempt. Failure changes you and can make you better. Solving a significant problem requires perseverance, originality, flexibility, and effort.

This is true in both tales and mathematics. A good story is worth its weight in sweat. And as Corneille said: "To conquer without risk is to triumph without glory."

Being fast or slow, tall or short, is neither good nor bad when facing a problem. What matters is taking the time to think, postponing an obvious decision, and being critical. Because what seems simple is often more convoluted, in tales. You must prove your worth, just as a mathematical statement requires rigorous, formal proof. A mere accumulation of evidence is not enough. Lies can hide behind the obvious, a small problem can be difficult to solve, a major problem can be solved by a simple but powerful trick.

The world of a tale may not be obvious at first glance. You have to assume things, accept certain axioms, animals can talk, characters can be as tiny as a thumb, and this creates a context in which certain tricks will be consistent with the story's internal logic.

The same applies to most mathematical concepts: you have to accept that things work this way or that. Sometimes, "I don’t understand" simply means "I don’t accept your axioms." You need to realize that sometimes there is nothing to understand, just a few axioms to accept as they are, otherwise the story cannot unfold.