I recommend Ian Stewart's Letters to a Young Mathematician. He addresses your question (Platonism vs formalism) pretty succinctly, in my opinion as a noob.

Accordingly "the working philosophy of most mathematicians is a mostly unexamined Platonist-Formalist hybrid ... Math is a product of human minds but not bendable to human will. Exploring it is like exploring a new tract of country ... but the mathematical countryside does not come into existence until you explore it."