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This is probably an obvious statement, but if you write such a reference, then there will be one more reference, and someone else will have to write a new, more
by wbhart 8y ago
This is probably an obvious statement, but if you write such a reference, then there will be one more reference, and someone else will have to write a new, more comprehensive reference based on all the existing ones, plus the new one you wrote. And so, on it goes.
To answer the question more seriously, there are a number of reasons for this: 1) terminology and notation changes over time, 2) there is not enough space in a standard textbook to include all material on any given subject in mathematics, even at an undergraduate level 3) there have been such standard textbook projects, e.g. the Bourbaki textbooks, but in order to cover everything in complete generality, they had to work at such a high level that the material is all but useless to a beginning student (many French professors may disagree with me on this point). 4) It is not uncommon for textbooks to start with different assumptions, to target the material for certain research applications, to give a different perspective on the material, to promote a favourite notation, to give new proofs or even new theorems, in lecture notes written by professors.
What this doesn't answer however, is why there is such a dearth of technological solutions to the problem of disseminating the 40 odd thousand pages of undergraduate mathematics taught around the world today. There are lots of videos at a very superficial level, very few in depth, and piles and piles of books and pdfs. There are virtually zero really well-produced, animated, scripted videos that cover mathematics in great depth.
The only reason I can come up with for not having such material is lack of time. Academics, especially professors, who would have to write and edit such material, would have to invest so much time, they would not have time to have families, or do research.
- mhneu 8y agoTeaching styles differ and student populations differ. And re: in-depth, this is a long tail problem. The profit is in the mainstream, not in the tail. Producing really good in-depth work isn’t that rewarding because the market is small.
- wbhart 8y agoI'm still talking about undergraduate mathematics here. There's billions of dollars spent worldwide on providing exactly that. The issue is that a standard undergraduate course, especially in mathematics, is quite deep, relative to, for example, a YouTube "science" video. On the other hand, technology offers new and interesting ways to disseminate this knowledge, but I see very little at the same depth as a standard undergraduate course, which is not just a video of someone doing the equivalent of a chalk-and-talk.
- WhitneyLand 8y agoSince we’re discussing mathematics may I attempt to generalize your thought? You can forget lack of time altogether and simply think of it as a lack of resources or money. The problem is to date, lack of an adequate self-sustaining model to provide these resources. In this case by “model”, I mean either a business model where the work was incentivized by profit, or a well organized community that is able to motivate its members to collaborate and volunteer as has been shown to be possible in other areas.