My favorite pastime in high school used to be banging my head trying to solve an olympiad level math problem.
1. It builds my problem-solving muscles
2. It makes me be explicit about assumptions
3. It builds and strengthens my abstract thinking muscle
4. Makes me feel like a philosopher. A bit like René Descartes
5. Makes me think in multiple dimensions; time, space, energy, motivation, goal, faith, etc.
6. It helps me construct logical arguments and expose illogical ones
7. I can impress my friend when I split the bill faster
8. It helps me appreciate History
9. It helps me calculates discounted good faster and impress my lady
10. It helps me communicate with anyone in the world who speaks mathematics
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