Tom Lehrer is a brilliant satirist and song writer, but he was never a "concert pianist" in the sense that that phrase is typically used, and I understand he essentially stopped being active as a research mathematician ~50 years ago.
That said, there are a number of active research mathematicians who are outstanding musicians, though they tend to not have the time to play enough concerts to be known for it (being busy with math).
What about Caribou ie Dan Snaith? The dude has PhD in Mathematics and an unbelievably talented musician...yeah I don't really know where I was going disproving your example
That said, there are a number of active research mathematicians who are outstanding musicians, though they tend to not have the time to play enough concerts to be known for it (being busy with math).