It's one of the oldest and deepest philosophical questions. Is mathematics a human invention, or is it a discovery of a pre-existing truth?

The 'Invention' Camp (Formalism): Argues that math is a game we invented, like chess. We create the axioms (the rules) and see what logical structures emerge.

The 'Discovery' Camp (Platonism): Argues that mathematical truths (like 2+2=4 or the Pythagorean theorem) exist in some abstract, perfect realm.

They believe these truths would be the same for any intelligent species anywhere in theuniverse.

The question is: Would the ratio of a circle's circumference to its diameter (Pi) exist if no minds were around to think about it?

The discovery camp would say 'yes.' The invention camp would say 'no.'

Many mathematicians feel like they are discovering things. A beautiful theorem feels found, not made.

However, the way we choose to write and structure math (our notation, our axioms) is clearly a human invention.

Perhaps the truth lies somewhere in between.

The patterns are discovered, but the language we use to describe those patterns is invented.