
Contrasts in Number Theory - jonnybgood
http://blogs.scientificamerican.com/roots-of-unity/contrasts-in-number-theory
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Smaug123
On 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/...](http://www.patrickstevens.co.uk/misc/AdjointFunctorTheorems/AdjointFunctorTheorems.pdf)
[2]:
[https://www.dpmms.cam.ac.uk/~twk/Lecture.pdf](https://www.dpmms.cam.ac.uk/~twk/Lecture.pdf)

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tokenadult
Thanks 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.

