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Contrasts in Number Theory
- Smaug123 11y agoOn a less advanced level than this, people find it very hard to publish expository work. Journals want papers with new results, not papers which explain known results in a way that lets people (students) understand them. I know from experience that there's a lot of demand for the latter, though! I've started trying to write such things myself [1], because it's almost impossible to find fully-motivated proofs for anything more advanced than first-year undergraduate material. Mathematicians tend to the slick and short, rather than the comprehensible; I have met professors who think their job is done if they take thirty seconds to prove a result, and the student needs ten hours to understand it. This is one of the primary reasons why lectures, rather than textbooks, are still relevant: the lecturer gets a chance to explain rather than just to prove. [2] Interestingly, in computer science where basic category theory has some traction, the Internet is full of exposition. Methinks there is something of a culture clash between the academics who created category theory, and the compscis who use it. [1]: http://www.patrickstevens.co.uk/misc/AdjointFunctorTheorems/AdjointFunctorTheorems.pdf http://www.patrickstevens.co.uk/misc/AdjointFunctorTheorems/... [2]: https://www.dpmms.cam.ac.uk/~twk/Lecture.pdf https://www.dpmms.cam.ac.uk/~twk/Lecture.pdf
- tokenadult 11y agoThanks very much for the link to the essay "In Praise of Lectures" (it's not a lecture) by T. W. Körner. Both the points he makes and the way he makes his points (with his characteristic sense of humor) are well worth reading.