MathOverflow answer argues the goal of mathematics is clarity and understanding for humanity, not theorem production or priority claims.
Key Takeaways
Mathematical understanding decays over time as experts retire, move on, or encode ideas in symbolic forms that strip out conceptual meaning.
Translation from conceptual to symbolic is easy; the reverse is hard, so deep understanding is constantly being lost and needs rebuilding.
Fermat’s Last Theorem and the Poincare conjecture matter not for their statements but for the mathematical development they forced.
Mathematics exists only inside a living community; isolated individual contribution is less important than spreading and preserving understanding.
Following passion over pure intellectual calculation is advised because second-order effects of mathematical work are impossible to predict rationally.
