Philosophy of mathematics asks what numbers are and whether they exist beyond human thought.
This chart outlines the major schools.
- Platonism says mathematical objects exist independently of us.
- Formalism treats math as shuffling symbols under rules.
- Logicism grounds everything in pure logic.
- Intuitionism says math arises from valid mental constructions.
- Structuralism studies structures and relations.
- Fictionalism claims the entities need not literally exist; they just have to work.
Suddenly algebra feels like philosophy.