Despite the fact that he only trains Aang within a single episode from Avatar: The Last Airbender season 1, Bumi (André Sogliuzzo), the King of Omashu and Aang’s (Zach Tyler Eisen) former childhood friend, proves to be his most important teacher since his lessons help Aang become a fully realized Avatar by the conclusion of the series. While many of Aang’s official bending teachers help him master the four elements, the tests that Bumi devises for Aang within the episode “The King of Omashu” teach him not only how to become a better Avatar, but provide him with the tools he’ll need to defeat Fire Lord Ozai (Mark Hamill).
In the episode “The King of Omashu,” Bumi captures Aang’s friends Katara (Mae Whitman) and Sokka (Jack De Sena) and agrees to set them free if Aang first completes three challenges: retrieving Bumi’s “lunch box” key from a waterfall, capturing his pet goat gorilla Flopsie (Dee Bradley Baker), and dueling a person of Aang’s choosing. While each of the tests are seemingly random, Bumi uses them to gauge Aang’s current progression on his quest to master all four elements, since each individual challenge could've been resolved quickly using one of the types of bending. Since Bumi knew Aang 100 years before the Avatar was frozen in the iceberg, he most likely knew that Aang had only mastered Airbending when they crossed paths in Omashu. With this in mind, Bumi’s challenges were rather a test of Aang’s intelligence and creativity when faced with a particularly difficult task.
After completing each of Bumi’s tests, Aang reflects on how each of the challenges forced him to think outside the box and approach the task from an angle he normally wouldn’t have thought to try. Just as Bumi taught Aang to view the mail system within Omashu as “the world’s greatest super slide” when they were kids, Bumi wanted Aang to open his brain to the possibilities and uncover an unorthodox solution to the problem before him. While each of Bumi’s tests could’ve straightforwardly been solved using Waterbending, Earthbending, or Firebending, Aang was able to solve the tests without them, suggesting that while Aang needs to master the four elements as the Avatar, they aren’t the only tools he can use to restore balance to the world. “You must master the four elements and confront the Fire Lord,” says Bumi. “And when you do, I hope you will think like a mad genius.”
Since Bumi was a close, personal friend of Aang’s from the past, he understood that Aang’s greatest weakness is his non-confrontational fighting style, which is a result from his training as an Airbender. Since the Air Nomads were a very peaceful race, Bumi had probably already considered that Aang wouldn’t resort to killing Ozai when it came time for Aang to confront him. With this in mind, Bumi’s advice to “think like a mad genius” when he finally faces the Fire Lord was Bumi’s way of indirectly suggesting that Aang keep an open mind and consider alternative methods of subduing the Fire Lord in ways that didn’t involve murder. While Bumi’s advice was given to Aang within season 1, those lessons stayed with Aang until season 3 when Aang discovered that he could defeat the Fire Lord by taking his Firebending away using the Energybending technique he learned from an ancient Lion Turtle.
Apart from testing his intelligence and creativity in battle, Bumi was the only teacher who tested Aang’s ability as an Avatar in ways that didn’t involve the mastery of different types of bending. While learning to master the four elements is an important part of Aang’s role, the Avatar’s main purpose is to bring balance and peace to the world, which also means learning how to diffuse potential conflicts with a sense of patience and diplomacy. When Aang first met Bumi, his advanced age prevented Aang from recognizing him as his childhood friend, and so he perceived him rather as a manic tyrant. By pushing Aang to his limit with ridiculous and seemingly pointless tasks in Avatar: The Last Airbender season 1, Bumi provided Aang with additional training on how to calmly resolve conflicts and maintain peace in ways that bending alone couldn’t fix.