This is a manifest about how Arnol'd views mathematics, and it's meaning becomes more clear if you read some of his books and see how he does actual math. It do

This is a manifest about how Arnol'd views mathematics, and it's meaning becomes more clear if you read some of his books and see how he does actual math. It doesn't mean his is the only view possible, but it is the view of an absolute giant of mathematics and physics, developed after a lifetime of practice in both research and education, so you would better spent some time thinking more deeply about why he says what he says, instead of brushing it off with what frankly are platitudes for anyone interested in the subject. For a start, you might want to think about the intertwined history of the two subjects, about how mathematical ideas might at all arise in human cognition, about what are the available criteria for choosing mathematical theories in the huge space of theories that are possible and true, and finally about what are the productive ways of searching for theories that have any value. Then you might want to ask yourself if school pupils are really best served by immediately being presented with the most abstract presentation of each subject, while the abstractions themselves were often a result of a whole sequence of generalizations from some first very intuitive basis. Those are complicated questions, and there are no clear answers, but Arnolds view was likely rather more sophisticated than you think. This lecture of his might help to interpret the article in a more productive way: https://www.msri.org/workshops/390/schedules/2714 https://www.msri.org/workshops/390/schedules/2714