The philosophy of mathematics explores the nature and foundations of mathematical truths. It examines questions such as whether mathematical entities, like numbers and shapes, exist independently of human thought or if they are merely inventions of the mind. This field also investigates the meaning of mathematical statements and the nature of mathematical proof. Key topics in this philosophy include Platonism, which posits that mathematical objects exist in an abstract realm, and nominalism, which argues that these objects do not exist outside of language and symbols. Philosophers like Kurt Gödel and Bertrand Russell have significantly contributed to these discussions, shaping our understanding of mathematics.