First, a wonderful article from The Boston Globe emphasizing how difficult it will be to check Shinichi Mochizuki's lengthy claimed proof of the ABC conjecture, because of the complexity and newness of the math involved:
http://tinyurl.com/a8srze4
The piece ends thusly:
"And this, [Minhyong] Kim thinks, might pose the greatest challenge of all. 'When you’ve been wrapped up in your own research program for a long time sometimes you lose a sense of what it is that other people don’t understand,' he says. 'Other people feel quite mystified as to what he’s [Mochizuki] doing and part of him, I suspect, doesn’t quite understand why.'"
On a simpler note, do you wish to engage your own math students… well, so does Tim Gowers...
British Field Medalist Gowers (who deserves to be read/discussed whenever possible) has a piece in The Spectator regarding math education:
http://www.spectator.co.uk/features/8744071/should-alice-marry-bob/
from it: "...rather than explaining mathematical ideas (about statistics, say) and then discussing how they can be applied to the real world, a teacher should instead start with a question that is interesting for non-mathematical reasons and keep a completely open mind about what mathematics has to contribute to the discussion."
Gowers' take is that teachers need to be utilizing real 'real-life' examples in the classroom, not the 'if 2 painters can paint 2 houses in 5 days how many houses can 4 painters paint in 15 days' sort of story problem that often gets passed off as an application.
This is more-or-less a followup to a fantastic earlier piece he did on same subject:
http://gowers.wordpress.com/2012/06/08/how-should-mathematics-be-taught-to-non-mathematicians/
[On a side note, just yesterday, Gowers put up another interesting post about probabilities and surgery he is undertaking for an atrial fibrillation condition… hopefully, we'll soon hear that all went well!]:
http://gowers.wordpress.com/2012/11/05/mathematics-meets-real-life/
Finally, hat tip to John Golden for leading me to this TED video (~16 mins.) by Alan November that piggy-backs nicely onto Tim Gowers' views, in describing student engagement in learning:
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