For instance, the vast majority of the mathematical community has never challenged its tacit assumption that doing mathematics will remain very much the same type of mental activity it has always been: new topics will come, flourish, and go as they have done in the past, but, the human brain being what it is, our ways of teaching, learning, and understanding mathematics, of problem solving, and of mathematical discovery will remain pretty much the same. Herbert Robbins clearly states why he rules out a quantum leap in mathematical ability:
"Nobody is going to run 100 meters in five seconds, no matter how much is invested in training and machines. The same can be said about using the brain. The human mind is no different now from what it was five thousand years ago. And when it comes to mathematics, you must realize that this is the human mind at an extreme limit of its capacity."
My comment in the margin was "so reduce the use of the brain and calculate!". Using Robbins's own analogy, one could remark that, for going from A to B fast, there could now exist alternatives to running that are orders of magnitude more effective. Robbins flatly refuses to honour any alternative to time-honoured brain usage with the name of "doing mathematics", thus exorcizing the danger of radical novelty by the simple device of adjusting his definitions to his needs: simply by definition, mathematics will continue to be what it used to be. So much for the mathematicians.
Slashdot Mirror
That reeeally makes you wanna shoot somebody...
Makes me wonder if we are near the edge of what humans can know.
But as Dijkstra notes, that might not necessarily halt progress "On the cruelty of really teaching computing science":
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For instance, the vast majority of the mathematical community has never challenged its tacit assumption that doing mathematics will remain very much the same type of mental activity it has always been: new topics will come, flourish, and go as they have done in the past, but, the human brain being what it is, our ways of teaching, learning, and understanding mathematics, of problem solving, and of mathematical discovery will remain pretty much the same. Herbert Robbins clearly states why he rules out a quantum leap in mathematical ability:
"Nobody is going to run 100 meters in five seconds, no matter how much is invested in training and machines. The same can be said about using the brain. The human mind is no different now from what it was five thousand years ago. And when it comes to mathematics, you must realize that this is the human mind at an extreme limit of its capacity."
My comment in the margin was "so reduce the use of the brain and calculate!". Using Robbins's own analogy, one could remark that, for going from A to B fast, there could now exist alternatives to running that are orders of magnitude more effective. Robbins flatly refuses to honour any alternative to time-honoured brain usage with the name of "doing mathematics", thus exorcizing the danger of radical novelty by the simple device of adjusting his definitions to his needs: simply by definition, mathematics will continue to be what it used to be. So much for the mathematicians.
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