Quality, not quantity...|
One of the things that really depresses me as I stand on the edge of entering academia, is the sheer flood of stuff available out there. The world of mathematics is no longer a handful of 20 prominent figures writing letters to each other across Europe on all things applied and pure. It's a sprawling burocracy covering the whole of the world, and like all burocracys it makes paperwork. Lots and lots of paperwork. Most of it pointless. I suppose I ought to be glad there's such a flowering of knowledge, opportunities for everyone, etc etc... but... there's just this overwhelming depressing feeling that people are reinventing the wheel over and over and over again. Thousands of papers in hundreds of different languages that noone has time to read because they're so busy rushing to get something published as a sign of their own worth. No one can carefully learn their way up to the cutting edge anymore, as there's more than a lifetimes worth of stuff to work through, and so the subject is advanced by isolated cliques of people working on different projects taking wild leaps to try and get a fingertip on the unknown. When there was probably a group working on a different problem in a different language somewhere, that had exactly the solution to your problem if you'd only known they were important. And so the literature gets greater and greater and greater, until you can't even read all the *reviews* on a topic in a lifetime, and...
It will be ok, won't it? People will catalogue it all, and write nice intelligent text books, and all academic study won't just drown in its own mess?
|Date:||May 8th, 2004 03:00 pm (UTC)|| |
|Date:||May 8th, 2004 04:02 pm (UTC)|| |
I obviously know much less than you about the subject, but I've thought the same sort of thing about mathematical academia. I think the problem is that, as opposed to other subjects (like anthropology!), you can only really cover a topic once - at least, something is only proved once, and after that proving it again, even with a different method, isn't very useful. Choosing what topic to work on looks like a massive gamble.
|Date:||May 8th, 2004 10:56 pm (UTC)|| |
I don't think that's necessarily true. A proof with a clearer, more extendable method is considerably more useful than one which lucks it's way into existance (for example, the four colour theorem proof holds few interesting insights as it stands, and I'm hoping for a better.) A different proof may come from a different area of mathematics, with mileage to be gained from tying the areas together. A proof may well be the same, just using more modern notation, enabling people to learn that the proof exists and how it works more easily.
Yes, people will make sense of it enough so that it doesn't drown in its own mass. There are people striking out in new directions, but a lot of mathematics is in doing things like seeing new things in old ways or seeing many things in one way. The really useful bits of mathematics get linked into the rest and shared around over time. Although, it must be a frustrating field, because it's hard to search for other bits that are applicable or that may be helpful, because so much is relevant to so much, much to its originators' surprise.
I am reminded of the German rocket pioneers who defected to the United States after the Second World War. Apparently, the Americans asked them how they got so far, and the Germans explained that they'd built on a largely-forgotten American's work, Robert Goddard. It's an apocryphal story AFAIK, as I'm not sure why the Germans would have known about him, but it's a neat one nonetheless.
|Date:||May 9th, 2004 12:53 am (UTC)|| |
I've heard the following description of a famous russian mathematician - that people in DAMTP would sometimes go to him with a brilliant new idea that they'd had, and he'd listen to them, say "ah yes, a very good idea", and reach down to the box file marked "papers 1955-1960" ...
|Date:||May 10th, 2004 10:47 am (UTC)|| |
David Wheeler at the CL is reputed to do the same.
Publish in English and you'll be fine. The world is odd like that.