Let us digress to the spirit of mathematics. This is the view I hold and the reason for these blogs. It is adapted from “Non Analytic Aspects of Mathematics and their Implications for Research and Education” by P J Davis and J A Anderson, SIAM Review, (1979), pp. 112-125. That article goes by the title “The Doctrine of the Whole Man”.
“Mathematics has elements that are spatial, kinesthetic, elements that are arithmetic or algebraic, elements that are verbal or programmatic. It has elements that are logical, didactic and elements that are intuitive, or even counter-intuitive. It has elements that are rational and elements that are irrational or mystical. These may be compared to different modes of consciousness.
To place undue emphasis on one element or group of elements upsets a balance. It results in an impoverishment of the science and represents an unfulfilled potential. The doctrine of the whole man says that we must bring everything we have to bear on our subject. We must not block off arbitrarily any mode of experience or thought. “There is a Nemesis,” says Alfred North Whitehead,”which waits upon those who deliberately avoid avenues of knowledge.
We must realize that the future of the subject depends only in part on the contribution of those who have rigid establishment interest or training in the subject. As regards this training and our own teaching, we must
1) restore geometry
2) restore kinesthetics and mechanics
3) restore combinatorics
4) restore intuitive and experimental mathematics
5) deemphasize somewhat the theorem-proof style of lecturing
6) give a proper place to computing and programmatics
7) make full use of computer graphics
8) eliminate the fear of metaphysics, recognizing that in such principles may lie the seeds of future growth.
What we want to do is create as rich and diverse a brew of thought and action as we can. This is the kind of culture that has fostered mathematics in the past and and should be our very present hope for the future.”