Learning math fundamentals from a textbook, rather than via one’s own sense of where the densest confusions are, is sort of an oxymoron. If you want to be rigorous, you should do anything but defer to consensus.
And from a socioepistemological perspective: if you want math fundamentals to be rigorous, you’d encourage people to try to come up with their own fundamentals before they einstellung on what’s been written before. If the fundamentals are robust, they’re likely to rediscover it; if they aren’t, there’s a chance they’ll revolutionize the field.
Learning math fundamentals from a textbook, rather than via one’s own sense of where the densest confusions are, is sort of an oxymoron. If you want to be rigorous, you should do anything but defer to consensus.
And from a socioepistemological perspective: if you want math fundamentals to be rigorous, you’d encourage people to try to come up with their own fundamentals before they einstellung on what’s been written before. If the fundamentals are robust, they’re likely to rediscover it; if they aren’t, there’s a chance they’ll revolutionize the field.