Outline of my mathematical results and some plans are presented in Research Statement.
The papers, or rather their list with bibliographic data and links to pdf- or ps-files, if available.
Twice I formulated publicaly my views on the nature of Mathematics, its objects of study, position in society and interaction of mathematicians with other sciences. In both cases this was done to mathematicians and hence the facts commonly known to mathematicians were mentioned without explanations. Eventually I am going to write about this something more intelligible to non-mathematicians.
The first occasion was in December 2005 in a meeting of Saint Petersburg Mathematical Society. Here is a transcript of my talk (in Russian).
A complete video recording of the meeting can be found on the web site of SPbMS. I would like to attract attention to a speech by Anatoly Vershik which followed my talk. In particular he discussed the differense between the part of applied mathematical work visible to a non-mathematician and anticipation of the same work by a mathematician.
A second more detailed attempt to present my views was made on conference "Perspectives in Analysis, Geometry, and Topology" in Stockholm, 2008.