Whenever you see a string of quadrature nodes, you can consider it as a branch cut defined by the poles of a rational approximation to the Cauchy transform of a weight function. The aim of this talk is to explain this strange statement and show how it opens the way to calculation of targeted quadrature formulas for all kinds of applications. Gauss quadrature is an example, but it is just the starting point, and many more examples will be shown. I hope this talk will change your understanding of quadrature formulas. This is joint work with Andrew Horning.