Date: Sat, 16 Jan 1999 11:30:24 +0900 From: Andrzej Kozlowski Subject: Re: response to R. Brown To most mathematicians this will seem like a good answer, but I suspect it will not satisfy many people who are not mathematicians. These people will ask questions like: what are these "things", "where" are they etc.? It seems to me that most mathematicians are in some sense "Platonists" (even if they never think about such matters) and most other people or at least most scientists are not. For example, many scientists like to say that mathematics is a "language". They see mathematics as a useful or maybe even essential way to describe "things", but the things themselves, the real objects of study, lie outside mathematics. This, of course, is not how most mathematicians think about their subject and it makes communication more difficult. What makes it even worse is that in their efforts to make their subject accessible and popular many mathematicians seem to adopt this sort of view when popularizing mathematics. In other words they tend to play down the abstract nature of mathematics and choose some concrete and cute "real world" objects with which to illustrate what they are doing. Often the result is that they make their subject and themselves seem ridiculous. As an example I will mention the solution of the Kepler problem on non-lattice packings. It was reported widely in the media as a curiosity which shows what weird people these mathematicians are. For centuries they have been trying to prove something that every green grocer has always known to be true, and now at last they have succeeded, big deal. This was the sort of reaction you could find not just in the popular media but also in serious publications like The Economist. Imagine what wonders this sort of publicity does for the other issue which concerns Ronnie Brown: the financing of mathematics. It seems to me that in search of greater public sympathy for mathematics there is a danger of de-emphasising its most fundamental aspect: its abstract nature. It is because the Kepler problem is not really about water melons or oranges that it is important and interesting. Making mathematics seem more concrete and accessible is no doubt desirable if you want more people to understand what you are talking about, but it carries the danger of making it also seem trivial. This is true of many of the cutest "applications" of topology that one finds in popularizing texts: the Moebius band, the "hairy ball" theorem, etc. I am not quite sure to what extent this applies to knots. I have looked at the Bangor knot site and I think it is both beautiful and serious, but I think this kind of quality is extremely hard to achieve and I suspect that most attempts to emulate it are likely to tend to the cute but trivial side. Andrzej Kozlowski On Fri, Jan 15, 1999, DON DAVIS wrote: >Date: Fri, 15 Jan 1999 14:15:56 -0500 (EST) >From: "Daniel H. Gottlieb" >Subject: answer to Ronnie Brown's posting. > >******************************** > >Ronnie Brown wrote: > >< >If you study subject X at University, is it reasonable that at the end of >your studies you should have be able to answer: >A) What are the objects of study of X? >B) What are the methods by which these objects are studied? >C) What are the main achievements of X? > >One distinguished colleague at another University said he would have >difficulty with question 1! This is interesting, since how can we >persuade Governments to support maths if we cannot answer these questions >in a convincing way to colleagues and to students? Tell me! > >Do people think Questions A-C are reasonable? > >...... > >I also find myself asking basic questions on the aims of topology, and >the fundamental structures to be used in pursuing these aims. >... >>> > >I think Questions A-C are reasonable. My answer to question A) for >X = Mathematics is that Mathematics is the study of well-defined things. >I thought of this answer over ten years ago, and I analyzed it and compared >it to what we are doing and to what happened in history. Nothing I have >found has convinced me otherwise. > >Advancing a point of view such as "Mathematics is the study of well-defined >things" brings in its train a series of questions, such as: >Are chess problems Mathematics? ; or Is the concept of well-defined things >well-defined? . An indication of the strength of my answer to A) is that my >answer to these and similar questions are such that as time goes on I find >myself unable to believe that I entertained serious doubts about their >answers. > >My answer to A) for X = Topology is that Topology is the study of >continuity. > >Dan Gottlieb >gottlieb@math.purdue.edu > > Andrzej Kozlowski Toyama International University JAPAN http://sigma.tuins.ac.jp/ http://eri2.tuins.ac.jp/