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Mr. Smith was a teacher and had his son as one of his pupils. After Erwin asked his father a question during class, Mr. Smith eventually told his son of a dangerous theory. Official history books being full of contradictions and mysteries, Mr. Smith believed that humanity's memory has been wiped out at some point, which might explain why there is no story or memories of the Walls' construction. This theory cost Mr. Smith his life, but encouraged Erwin to seek out the truth about the world's origins and prove his father's guess was correct.
Later on, Erwin joined the army and then the Survey Corps.
At some point, Erwin came up with the Long-Distance Enemy Scouting Formation as a new tactic for the Survey Corps. At first rejected by his superior, it eventually became the formation used for every expedition once Erwin becomes the Commander.
After Eren had been captured by the Armored Titan and the Colossus Titan, Erwin led a group composed of Survey Corps and Military Police Brigade members. In order to weaken the Armored Titan's defenses, Erwin managed to lead a horde of Titans towards him. He lost his right arm and around 60% of the soldiers perished in the operation. Nevertheless they were successful.