Who is a philosopher? I think a mathematician who ponders about this topic is at least a philosopher of mathematics. Here are three:
Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap. [V.I. Arnold: "On teaching mathematics" (1997)]
But there is hope for a grand-unification! In twenty years (perhaps sooner!), mathematics can once again become a unified religion. All we need is to worship the new God of Experimental Mathematics! [D. Zeilberger: "Opinion 113" (2011)]
Mathematics as monologue, dialogue, and discourse needs tools of describing and communicating ideas. MatheRealism denies the existence of entities which, in principle, can never be observed or communicated – in particular thoughts that no-one can think. [W. Mückenheim: "MatheRealism" (2018) p. 351]
The most important theorems of a mathematics oriented towards reality can be proved in good approximation by means of experiments, performed mainly on efficient computers. Computers are the telescopes and microscopes of mathematicians. They improve the perspective and allow to distinguish details that cannot be seen otherwise. [W. Mückenheim: "Mathematik für die ersten Semester", 4th ed., De Gruyter, Berlin (2015) preface]