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Wiktionary
a rolling stone gathers no moss

prov. 1 A person who never settles in one place will never be successful / prosper. 2 (rft-sense) A person must keep active in order to avoid stagnate.

Wikipedia
A rolling stone gathers no moss

A rolling stone gathers no moss is an old proverb, credited to Publilius Syrus, who in his Sententiae states, People who are always moving, with no roots in one place or another, avoid responsibilities and cares. As such, the proverb is often interpreted as referring to figurative nomads who avoid taking on responsibilities or cultivating or advancing their own knowledge, experience, or culture. Another interpretation equates "moss" to " stagnation"; as such the proverb can also refer to those who keep moving as never lacking for fresh ideas or creativity.