These are specifically things which mathematics has taught me which have applications outside the field of mathematics... there's a whole lot of much more boring stuff.

- That there are such things as unanswerable questions - indeed,
*provably*unanswerable questions - That Occam's Razor is fallible
- To assume nothing
- That the word "obvious" means "a proof springs immediately to mind"
- The importance of proof
- How to reason logically
*To*reason logically- How to recognise faulty reasoning and find counterexamples
- That intuition counts for zilch
- Point nine recurring equals one