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.
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.