When Pi refers to the "elusive, irrational number" in which he found refuge, he means that through the name of a mathematical symbol, he was able to create a new name for himself, thereby gaining the respect of his new classmates.

Anyone who has attended a school where kids are prone to mock others will understand that life isn't easy when your name is Piscine, which is easily mispronounced to sound like "pissing."

When Pi changes schools, leaving St. Joseph's behind him, he decides to leave the days of being called "Pissing Patel" behind him as well. At Petit Séminaire, he introduces himself as Pi Patel. To make his point, he doesn't just call out his name, but goes up to the blackboard and writes that while his name is Piscine Patel, he is known to everyone as simply Pi. He emphasizes the point by adding the mathematical symbol Pi.

In a nutshell, the "elusive, irrational number" named Pi enables Piscine Patel to rename and reinvent himself as somebody less likely to be a target for bullies. While scientists try to understand the universe through the concept of Pi, Pi Patel the person is using it to make himself a memorable new name. He thus finds refuge from a childhood in which he has commonly been called "Pissing."

He repeats the exercise with each of his teachers, which helps his classmates to become accustomed to the name Pi. To reinforce the introduction of his new name, Pi takes every opportunity to put up his hand and respond to teachers' questions in class.