Perhaps in agreement with Eduardo one should publicise an apochryphal dedication to a PhD Thesis (learned from Michael Barratt): "I am deeply grateful to Professor X, whose wrong conjectures and fallacious proofs, led me to the theorems he had overlooked. " Good supervision! I also once felt after a day long discussion with MGB, `If Michael can try one damn fool thing after another, then so can I.' Of course they were not so `damn fool' but the thing I learned was the value of persistence. Grothendieck was insistent that `Pursuing stacks' should be published (if at all!) as written, so that young people could see that even very well known people can and do make mistakes. I found the transition from undergraduate mathematics to postgraduate mathematics a cultural shock, and took a long time to get going in research. Thus the methodology of research is to my mind well worth discussion, even if there is no final conclusion, except, possibly, things to be avoided. I put down some things in the Prefaces to `Topology and Groupoids'. See also Brown and Porter, ` The methodology of mathematics', on http://pages.bangor.ac.uk/~mas010/publar.html G. Spencer-Brown wrote (something like, see wikipedia): `We teach people to be proud of knowledge and ashamed of ignorance. This is doubly corrupt, since the natural state is one of ignorance.' Ronnie On 01/04/2011 18:55, Eduardo J. Dubuc wrote:
Concerning certain sarcastic answers given in this list to some trivial questions (trivial for the expert, but not trivial for the ignorant), I just read the following (I ignore the author):
"Productive stupidity means being ignorant by choice. Focusing on important questions puts us in the awkward position of being ignorant. One of the beautiful things about science is that it allows us to bumble along, getting it wrong time after time, and feel perfectly fine as long as we learn something each time. No doubt, this can be difficult for students who are accustomed to getting the answers right. No doubt, reasonable levels of confidence and emotional resilience help, but I think scientific education might do more to ease what is a very big transition: from learning what other people once discovered to making your own discoveries. The more comfortable we become with being stupid, the deeper we will wade into the unknown and the more likely we are to make big discoveries."
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