The problems to which Paul refers in his last paragraph seem to me to rest partly in a lack of analysis by the general mathematical community (and in this I tend to exclude category theorists who as part of their trade do analyse directions and foundations) of how mathematics progresses. I make some remarks on this in a recent article `Promoting Mathematics' in MSOR Connections Vol 7 No 2 downloadable from http://mathstore.gla.ac.uk/articles/new.asp, and an analysis of the Research Assessment Exercise Methodology is given on www.bangor.ac.uk/r.brown/publar.html The problem seems to be partly that the great and the good go along with the idea that they can decide which mathematics of today will play a key role in the future, and therefore there should be funding direction to those `important' trends. Paul Adrian Dirac said in one of his last addresses that `You should follow a mathematical idea wherever it leads, however far from the original starting point'. Indeed it seems reasonable to say that a professional methodology is to follow through one's ideas in this way. Many, or some, of the great and the good, however, will take opportunities to use words like `rubbish' and `nonsense' and to criticise work from a sociological viewpoint: Are important others following you? Is it relevant to the `mainstream'? They have not realised the `mainstream' flaps around like the sail on a yacht (to mix metaphors). A visitor to Bangor in 2001 said to me `You are not mainstream.' I retorted `Not yet!'. My impression is that the great and the good in the UK have not heard of the word `pioneering', and are unaware of the history of important mathematical ideas. Indeed they are quite prepared to leave out the words `category' and `groupoid' from an evaluation of 20th century mathematics. (I name no names.) Perhaps this all part of the fight for funding, and for Governments to prove that money is `well spent'. For an individual outside a `top centre', the best bet might be to look for `childish questions' (Grothendieck) which the `top centres' ignore. The history of science shows the hazards of this approach for individuals! There are sociological reasons for this! Part of my argument is also that mathematicians need to argue strongly for their subject, not just for its applications. My friend John Robinson was proud of his last sculpture donation of `Prometheus', to Frome Community College, and the giving of the name `Prometheus' to their new Mathematics Centre. www.fromecollege.somerset.sch.uk/ See also http://www.popmath.org.uk/sculpture/pages/2hearth.html That was John's view of the contribution of mathematics to humanity! Anyone want to argue against it? Or elaborate it? Ronnie
The problem lies with the academic establishment, starting from professors like you who are editors of journals, organisers of conferences or heads of department, through the managements of universities, up to the ministers of education in our respective countries. These are the people who hold the guns to our heads while companies like Elsevier rob us of our intellectual property.
If certain of my colleagues want to set up new open-access on-line journals in topology or whatever subject, then I strongly welcome that, and am willing to help if they ask me to do so.
However, this does not solve the problem of the pressure that is put on us by our lords and masters, especially when they specify lists of "approved" journals, or employ - inherently fraudulent - methods of bibliometry to "assess" our work.