Logic (and formal systems) is a contribution of philosophy.
The point is that up to recent times (~1800), mathematics was a discipline of philosophy, just as music was a discipline of mathematics at the same level as arithmetics, geometry and astronomy. It was impossible for a mathematician not to study philosophy.
So you question is meaningless up to 1800. Just read Leibniz or Newton to see that the question of how god made the universe was a mandatory base to justify axioms, which we nowadays consider as hypothesis.
As far as modern science is concerned, philosophy is a science of human ideas and beliefs which escape to any mathematical models, and will probably ever be.
During the transition period (1800-1900), lots of work has been done on the common part of mathematics and philosophy, which resulted in a formalisation of logic and a pedestal to base mathematics.