Algebraic numbers are complex numbers that are roots of polynomials with rational coefficients. All other complex numbers are called transcendental. It is typically a hard question to decide whether a given complex number is transcendental. A more general, classical question in 'transcendental number theory' (cf. e.g. works of Lindemann and Weierstraß, Gelfond and Schneider, Baker, Wüstholz) is the following: determine the dimension of the vectorspace generated by a (finite) set of complex numbers over the algebraic numbers. For example, the vectorspace generated by 1 and $\pi$ is two-dimensional since $\pi$ is transcendental by Lindemann's Theorem. For certain complex numbers called periods, we will try to explain how this transcendence question can (sometimes) be translated into determining dimensions of certain finite dimensional algebras – in other words, into counting (equivalence classes of) paths in 'modulated' quivers (with 'multiplicities'). The dimension formulas obtained in this way improve and clarify earlier results of Huber $\&$ Wüstholz and recover a dimension estimate of Deligne $\&$ Goncharov. This is based on joint work with Annette Huber (Freiburg).