"Most people's idea of what I do as a research mathematician is long division to lots of decimal places. But fundamentally, mathematics isn't about numbers - it's about finding structure and logic and connections." Yes, but do not despise long division !! Certainly, mathematics is about "finding structure and logic and connections", but it is also about numbers and particulary about "long division to lots of decimal places". I belive that those who did not found any pleasure in developing the ability to perform long division to a lot of decimal places when they were kids, will never find and/or develop mathematically meaningful "structure and logic and connections". I belive that good mathematicians are able to perform complicated calculations, and find pleasure on it, even if it is not what they currently do. "Numbers, algorithms and calculations" as well as "structure, connections and logic", are at the core of mathematics. Ah !, and do not forget "proofs". e.d.