English equivalent for the Indian saying

Solution 1:

A rolling stone gathers no moss.

Solution 2:

Here is the opening paragraph from Wikipedia's page on "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, 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.