i mostly agree with this but I think the philosophical position might have an impact on how open one is to new methods in mathematics. If one holds the view th

i mostly agree with this but I think the philosophical position might have an impact on how open one is to new methods in mathematics. If one holds the view that mathematical objects can be understood as 'language games' rather than real ontological objects I think it creates a more pragmatic view on what is permissible, what constitutes a proof, whereas I think the more Platonic views might make someone more purist in how they approach maths.