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It seems like there could hardly be fewer amateur mathematicians making great contributions to science.

The number of potentially great mathematicians who stop learning because they're satisfied with the informal coverage has to be absolutely dwarfed by the number of potentially great mathematicians who are scared away from mathematics entirely at an early age by excessive formality.




This.

I've Seen it time and again: Great mathematicians who are awful mathematics students get turned away. They end up making great full stack engineers.




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