The conjecture of Syracuse (better known as the Collatz conjecture) is one of the many mathematical conjectures still waiting for proof. In this essay it is addressed by highlighting some of its features. From one of these features takes its cue a process that leads to a theorem whose proof solves the conjecture in a complete and definitive way. With few steps we exit the maze, we reach sea level from high altitudes and we tame the crazy lift of a very high skyscraper. The solution of the conjecture of Syracuse reveals the magical harmony of odd numbers and opens new horizons to the number theory. Attached charts of links odd numbers 5 - 1999