It is easy to criticise others but I think there is a general problem with mathematics teaching (in my limited experience in the UK) of mathematicians not explaining what the subject is about, or even thinking that this is necessary, or useful. I would like to direct attention to our `Knot exhibition' http://www.popmath.org.uk/exhib/knotexhib.html and the discussion of what we were trying to achieve in http://www.bangor.ac.uk/~mas010/icmi89.html : in broad terms, this was to show through the medium of knots some of the methodology of mathematics. The advantages of knots for this aim are many. In some ways the spirit of this exhibit is expressed by the slogan `advanced mathematics from an elementary viewpoint'. So how much of the baggage can you throw away and still get to, say, a real calculation? I once did a sample Todd-Coxeter enumeration of a presentation of a finite group of order 8 to a class of unprepared 14 year olds, (fortunately I was prepared to do this!) and had them helping me fill in the table (just as well , too) and draw the Cayley graph. I feel there is a real hunger in the public and in other sciences to find out what is going on in mathematics which has some kind of excitement, preferably in terms of new ideas, rather than solving say the Goldbach Conjecture. Higher dimensional algebra is quite useful in this respect. One can discuss what is or should be a higher dimensional formula, and why the idea might, or might not, be relevant to brain function! (I've done this too for an audience of neuroscientists.) Also discussed in http://www.bangor.ac.uk/~mas010/promotingmaths.html is the heretical idea of `promoting mathematics' to students of mathematics! The point I am getting at is that there may be something we can do about `But generally, science documentaries are disappointing, and maths ones even more so.' as suggested by Robert, and the start may be conveying certain attitudes to the many students studying mathematics seriously. Is this done enough? Perhaps those interested in category theory are in a better position to deal with these problems than those with no such interest!!??? Ronnie Brown Robert Seely wrote:
Actually, I think Dana understates the problem with this program. It suffers from what I call the "PBS documentary syndrome" (equally afflicting the BBC, however, so the name is not universal enough!): it repeatedly tells you what's cool about its topic, without ever actually telling you what the topic really is. Afraid to scare viewers away with the actual details of the topic, it just talks about it in terms so general (and often over-inflated or sensationalized, which was Dana's point) they are really quite meaningless.
Though not perfect by any means, I think a recent 4-part series "The Story of Maths" narrated by Marcus du Sautoy does better - he even tries to sketch some proofs. (The episode closest to "Dangerous Knowledge" would be the fourth.) Even better is an old series (but still to be found on Youtube!) called Mathematical Mystery Tour.
But generally, science documentaries are disappointing, and maths ones even more so. It's a pity, because you actually can get an audience of non-specialists to understand (at least a little) what mathematical results etc are about. I teach an honours Liberal Arts maths & logic class, and a surprisingly large percentage can actually appreciate the beauty of (eg) natural deduction proofs in predicate logic, basic theory of natural numbers (infinitude of primes, irrationality of primes, the fundamental theorem of arithmetic, ... ), simple axiomatics (we do Boolean algebras as an example), and even Godel's theorems, and the "Lambek calculus" for linguistics (even a bit of category theory there!). This isn't a mickey mouse course (sample class tests available on request!), and it's a challenge to many of the students. The point is: they are willing to make the effort if they know you're not being condescending, and that you are giving them "the real thing", not some pablum that only looks good in the box.
I wish more TV documentary producers took that attitude - they might get a slightly smaller audience, but their audience will appreciate their efforts more.
-= rags =-
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