AT SOME point in their career every mathematician comes up against the question, is mathematics invented or discovered? The query makes some cranky. The answer doesn’t directly affect their work, after all, and the discussion often leads nowhere useful. Spending time debating the ultimate nature of mathematics takes away from actually doing it.
Some scholars take issue with the terms themselves. In his 2008 essayMathematical Platonism and Its Opposites, Harvard University mathematician Barry Mazur called discovery and invention “those two too-brittle words”. One might be tempted to defuse the question altogether with a merger: perhaps maths involves inventing new relationships between things we have discovered.