(the positivists kind of say 'how can we structure our thinking to anticipate surprises. could we functor our way to monstrous moonshine without looking at character tables?': the whole point of a surprise is that it's not something you can account into existence, ...
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... and surely mathematics would be less fun if we always knew how things played out in advance, spoils the mystery)
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Replying to @graveolens
I very much agree, but mathematics is not taught in way to show that it is a growing and changing field. The subject tends to carry a sense of completion rather than a sense of creation. Mostly because there are few who have a sense of the nature of mathematics.
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Replying to @TheAbstracteer @graveolens
In the UK this is because there are very few good teachers of the subject, many are very under qualified following textbooks etc. Also, people need, mentoring to help them believe they can contribute, as you clearly do!
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