In the last 30 years we have gained much knowledge of the polylogarithms that result from many, but not all, Feynman
diagrams. In this talk, I consider a set of Feynman integrals that take us beyond polylogs. At first, modular
forms occur. In general, there are quadratic relations between integrals, encoded by rational matrices. I shall not assume familiarity with such structures, but will sketch how concrete Feynman integrals continue to inform mathematics.