Manabu (学ぶ): to learn. The Digital Daijisen dictionary notes that it has the same origin as manebu (まねぶ), to imitate. The Nihon Kokugo Daijiten adds that which of the two came first is not known.
Momo kuri sannen kaki hachinen (桃栗三年柿八年): peaches and chestnuts take three years, persimmons eight. Everything takes its due time before it bears fruit.