Thursday, November 09, 2006
Universalists or Specialists?
I was reflecting on a comment made in the discussion on the Poincaré Conjecture in the In Our Time podcast. To paraphrase, the panel member said that Poincaré was the last in a long line of Universalist mathematicians before the trend towards specialisation. Poincaré's problem solving method relied on his having a multi-disciplinary aproach to mathematics as it allowed him to apply seemingly disconnected methods to problems, thereby finding the key to unlock the problem. I believe that the same was true in the application of topological theory to Fermat's Last Theorum.
The trend to specialisation has continued on it's inexorable course ever since, as scientific endeavour demands ever increasing focus. It seems that this sets science on an evolutionary course of incremental improvements when much of the evidence suggests that the great steps forward or 'paradigm shifts' in Kuhnian terms ocur when there is a discontinuity in the evolutionary process caused by some form of externality.
I guess the point of this 'random ride' is: "Should we be actively encouraging a more multi-disciplinary approach to scientific method, by encouraging researchers and graduates to explore other disciplines, thereby harvesting a fresh crop of ideas to be stored in the sub-conscious".
Intellectual cross-training if you will?