At each step, we feel hoodwinked: we were only shown a part of the puzzle! As it turned out, there was a 'better' set of numbers waiting to be discovered, more comprehensive than the last.Īlong the way, we feel like our intuition is mostly preserved. We learn about the natural numbers, the integers, the fractions and eventually the real numbers. Unfortunately that exploration is mostly absent from math class and we are fed pre-packaged, pre-digested math pulp instead.Īnd so it also goes with the numbers. The act of mathematics is to play around, to put together ideas and see whether they go well together. That algebra, calculus, geometry are just words we invented to group the most interesting choices together, to identify the most useful tools that came out of them. Rarely is it made obvious that all of these things are entirely optional-that mathematics is the art of making choices so you can discover what the consequences are. "You'll need this stuff in real life!", they say, oblivious to the enormity of this lie, to the fact that most of the educated population walks around with "vague memories of math class and clear memories of hating it." A long ladder of subjects is set out before you, and you're told to climb, climb, climb, with the promise of a payoff at the end.
Each theorem and proof is provided, each formula bundled with convenient exercises to apply it to. You'd think otherwise, going through the modern day mathematics curriculum.
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