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- Felix Klein,Elementary Mathematics from an Advanced Standpoint, Dover reprint, 1945, Vol. 1, p. 268)
"In concluding this discussion of the theory of assemblages [sets] we must again put the question which accompanies all of our lectures: How much of this can one use in the schools? From the standpoint of mathematical pedagogy, we must of course protest against putting such abstract and difficult things before the pupils too early. In order to give precise expression to my own view on this point, I should like to bring forward the biogenetic fundamental law, according to which the individual in his development goes through, in an abridged series, all the stages in the development of the species. Such thoughts have become today part and parcel of the general culture of everybody. Now, I think that instruction in mathematics, as well as in everything else, should follow this law, at least in general. Taking into account the native ability of youth, instruction should guide it slowly to higher ideas, and finally to abstract formulations, and in doing this it should follow the same road along which the human race has striven from its naive original state to higher forms of knowledge. It is necessary to formulate this principle frequently, for there are always people who, after the fashion of the medieval scholastics, begin their instruction with the most general ideas, defending this method as the only scientific one. And yet this justification is based on anything but truth. To instruct scientifically can only mean to induce the person to think scientifically, but by no means to confront him, from the beginning, with cold scientifically polished systematics".
- 파인만의 견해 http://calteches.library.caltech.edu/2362/1/feynman.pdf
- The difference between 'naive' and axiomatic approaches to set theory
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