Per Enflo (see Wikipedia for a longer summary)
concert pianist, mathematician (solutions for the basis problem, the approximation problem, the invariant subspace problem in Banach space theory )
At a certain point in his life, he had to choose between the two.
He reasoned that the likelihood of ever reaching the top as a concert pianist was small, compared to the same thing in mathematics. He chose mathematics. But throughout his life, despite being a professor of mathematics, he continued to do piano performances. When I knew him (maybe 1980's) he still spent two hours a day practicing on the piano.
The basis problem was placed in the Scottish Book by Banach. The prize offered was a live goose. Enflo did, indeed, receive the prize.