What questions does the philosophy of mathematics examine?

The philosophy of mathematics is a branch of philosophy primarily concerned with two fundamental questions:

• Interpretation of Mathematical Language: What is the best way to interpret standard mathematical sentences and theories? A central task is to construct a semantic theory for the language of mathematics to clarify what ordinary statements—such as "3 is prime" or "2 + 2 = 4"—really mean or refer to.1
• The Existence of Abstract Objects: Do abstract objects exist? This question is deeply linked to the semantic issue; if mathematical sentences are true and refer to objects, philosophers must determine what kind of things those objects are. This has led to long-standing debates between realists, who believe mathematical objects exist, and antirealists, who reject their existence.12

Beyond these core inquiries, the field has historically examined the foundations of mathematics to ensure the discipline is reliable, leading to influential views such as logicism, intuitionism, and formalism.3