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Most mathematicians are sympathetic to utilitarian constructive mathematics, i.e. finding constructive proofs for the sake of actually computing the results in

Most mathematicians are sympathetic to utilitarian constructive mathematics, i.e. finding constructive proofs for the sake of actually computing the results in applications, as opposed to some philosophical reason. However, nonconstructive mathematics (or at least mathematics that cares little for avoiding nonconstructive arguments) will probably continue to dominate mathematical research, since many major research areas now depend heavily on its results as a basis for a conceptual framework.

defrost 14y ago
You can get a pretty good feel for the practical level of sympathy by popping down to your local math library and looking at the checkout histories of the works of Brouwer [1] and Bishop [2]. [1] http://plato.stanford.edu/entries/brouwer http://plato.stanford.edu/entries/brouwer [2] http://en.wikipedia.org/wiki/Errett_Bishop http://en.wikipedia.org/wiki/Errett_Bishop 'Sparse' would be an understatement & poor old Errett got such wonderfully backhanded reviews as: > "Even those who are not willing to accept Bishop's basic philosophy must be impressed with the great analytical power displayed in his work." and > Bishop's historical commentary is "more vigorous than accurate".
- cwzwarich 14y ago
  Well, both Brouwer and Bishop fall into the category of constructivism for philosophical reasons. As I mentioned, this doesn't garner much sympathy from ordinary mathematicians. Brouwer and Bishop wrote against the practice of classical mathematics with considerable vitriol, as opposed to proposing constructive mathematics as an additional lens for viewing classical results. In the era of widespread use of computers to perform calculations, the advantages of this latter point of view are obvious.
  - defrost 14y ago
    That's a fair assessment. Still it's a shame their work more or less petered out due to politics, personality and philosophical disdain, had they played better with others and taken a slightly different path they could well have been better regarded than they are now.

defrost 14y ago

You can get a pretty good feel for the practical level of sympathy by popping down to your local math library and looking at the checkout histories of the works of Brouwer [1] and Bishop [2]. [1] http://plato.stanford.edu/entries/brouwer http://plato.stanford.edu/entries/brouwer [2] http://en.wikipedia.org/wiki/Errett_Bishop http://en.wikipedia.org/wiki/Errett_Bishop 'Sparse' would be an understatement & poor old Errett got such wonderfully backhanded reviews as: > "Even those who are not willing to accept Bishop's basic philosophy must be impressed with the great analytical power displayed in his work." and > Bishop's historical commentary is "more vigorous than accurate".

cwzwarich 14y ago
Well, both Brouwer and Bishop fall into the category of constructivism for philosophical reasons. As I mentioned, this doesn't garner much sympathy from ordinary mathematicians. Brouwer and Bishop wrote against the practice of classical mathematics with considerable vitriol, as opposed to proposing constructive mathematics as an additional lens for viewing classical results. In the era of widespread use of computers to perform calculations, the advantages of this latter point of view are obvious.
- defrost 14y ago
  That's a fair assessment. Still it's a shame their work more or less petered out due to politics, personality and philosophical disdain, had they played better with others and taken a slightly different path they could well have been better regarded than they are now.