As a physicist, when I hear the number 137, my mind immediately goes to a value historically called the fine-structure constant, a dimensionless measure of the "strength" of the electromagnetic interaction, which is very closely approximated by 1/137. Richard Feynman is quoted to say: "It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it."

I have no idea if that's where the show is going with this, but if it is, I called it!