Science and maths skills are widely celebrated as keys to economic and technological progress, but abstract mathematics may seem bafflingly far from industrial optimisation or medical imaging. Pure mathematics often yields unanticipated applications, but without a time machine to look into the future, how do mathematicians like me choose what to study? Over Thai noodles, I asked some colleagues what makes a problem interesting, and they offered a slew of suggestions: surprises, contradictions, patterns, exceptions, special cases, connections. These answers might sound quite different, but they all support a view of the mathematical universe as a structure to explore.
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