  For any positive integer $q$, it is a question of Baker whether the numbers
$L(1, \chi)$, where $\chi$ runs over the non-trivial characters mod $q$, are
linearly independent over $\mathbb{Q}$. The question is answered in affirmative
for primes but is unknown for an arbitrary modulus. In this expository note, we
give an overview of the origin and history of this question as well as the
state-of-the-art. We also give an account of the mathematical ideas that enter
into this theme as well as elucidate the obstructions that preclude us from
answering the question for arbitrary modulus. We also describe a number of
generalizations and extensions of this question.
