Michael Paul Goldenberg <firstname.lastname@example.org> writes:
>This seems like apples and oranges. Some of us are talking about the >importance of giving students at an early age (but not so early that they >would be incapable of understanding or benefiting from it) the notion >that one MIGHT need mathematics only up to what was developed long ago >(or relatively long ago), but that as a career pursuit, it's not >identical to the pursuit of ancient history, classical studies, >paleontology, or Chaucerean manuscripts. [more stuff here] >One might become interested in applying the mathematical inventions of >others. One might become interested in creating new mathematics. But >obviously, the last thing on this list is less likely to pique >someone's interest IF THEY HAVE NO IDEA THAT SUCH THINGS HAPPEN EVERY >DAY.
OK. But can you be more specific about what modern (say in the last thirty years) mathematics you would teach?
I will also point out that there is no shortage of mathematicians -- indeed far more math PHDs graduate each year than can be gainfully employed in pure mathematics research. Of course, many go into other related fields (such as computer-based mathematics education :)), and many find their lives enriched by having studied mathematics (On the other hand, many are embittered by having spent so many years of their life on a pursuit that they must discard in order to earn a living). Then, too, just because there may be more people studying it than can be supported by the field is no reason not to encourage others to study research-level mathematics -- but it ought to be more than career boosterism.
I should also say that many research mathematicians did not have much idea of what modern mathematicians do until they reached college. Without exception, however, they did see the beauty and power of mathematics at a young age. Again, this doesn't mean that it wouldn't be an improvement to give students a sense of what modern mathematicians do -- but it is not immediately obvious that it would be, either.
>The other issue is the notion of authority and received knowledge. By >stressing ONLY the "accessible" past of mathematics, we communicate to >students that they're pretty much engaged in Bible Studies: read the >works of the masters (and I use that gendered noun advisedly), try to >grasp the ideas with your feeble mind, and some day, if you're very >lucky, you may be worthy of a few more revelations. No one here is >suggesting that students need to knock heads with Wiles' proof of Fermat, >but it seems reasonable to believe that students might get something out >of exposure to the fact that there are problems that challenge the best >mathematical minds on Earth for over 3 centuries, that some of these get >solved by folks not all that much older than they are, that it's exciting >to know about some of these problems, that there is an inexhaustable >supply of them, some of which they can grasp without too much difficulty.
>Do you think kids get hooked on basketball by studying James Naismith or >by watching Michael Jordan? They may realize that what Jordan does now is >something they can't YET, but the Michael Jordan of 2010 is probably >watching the Michael Jordan of today, and getting inspiration for the ideas >that will make basketball history in fifteen years.
Well, I have no fault with this, though I might point out that even on the rare occasions when the statement of a modern theorem might be intelligible to a young student, the mathematical content of the work is not. One has a better chance of grasping the ideas -- and not feeling feeble-minded -- when the material worked on is more accessible. Mathematics is most fun, and its beauty most appreciated, when you can actually play in the mud yourself. Basketball is something everyone can play and dream of doing better. The math that students can play in is mostly quite old -- and there's nothing wrong with that! Do you want the equivalent of the playground basketball courts on which the young mathematicians sport? Go get the New MathPro Press book of ARML contest problems -- or go get a translation of turn-of-the-century Hungarian Olympiad problems.
>Is it our belief as a community that there's NOTHING to be gained by >giving students a more accurate picture of what real mathematicians do? I >hope not.
I sure don't speak for the community -- but I hope I'm not drummed out, either. Also, I would hardly say there's nothing to be gained -- but I think it's very easy to exaggerate the importance of this.
Presumably everyone on this list has loved mathematics from a fairly young age. How many owe that love to a sense that there were modern mathematicians out there, tackling tough modern problems?