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But industrial mathematics is numerical methods, a rather different beast from the tricky closed form puzzles of Olympiads. I question your claims of causation

• newprint 7y ago
  Not entirely true. A lot of optimizations theory and practice are are straight-up inequalities. My claim is very simple: by being able to solve moderately-hard MO problems, you are developing excellent mathematical problem solving skills that let you solve problems in other branches of mathematics or draw interesting connections, because MO problems require ability to solve problem that are at the intersections of different branches of mathematics. I frequently see topics similar to this one popping-up on HM and a lot of people interested in learning or re-learning math as an adults. Excellent ! So let them learn discreet mathematics by solving problems in algebra, combinatorics and number theory. Once they are comfortable, they can move on to more abstract subjects. My view is very similar to Concrete Mathematics, by Knuth, Patashnik, Graham. Their "concreteness" is very down to earth: combinatorics, number theory and few other things in the mix.