Conclusion
Human activity and experience are an integral part of mathematics. They not only play a crucial role in the creative process of research but are also basic to the way human beings learn. I have suggested three lines of attack which would give students a better understanding of what mathematics is really about. First, we have to show them how (at least some of) the material they are studying originated and evolved into its present form through the combined efforts of generations of mathematicians. Second, we must encourage them to take an active part in their own learning, not just by practising routine exercises but by developing their own creative talents—thereby sharpening their insight into the way mathematics is created. Third, we have to find some way of relating higher mathematics to students’ previous experience. “The more abstract the truth is that you would teach, the more you have to seduce the senses to it” (F. Nietzsche,Beyond Good and Evil).
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References
F. J. Budden (1978)The Fascination of Groups. Cambridge: Cambridge University Press
R. P. Burn (1982)A Pathway into Number Theory. Cambridge: Cambridge University Press
J. D. Dixon (1973)Problems in Group Theory. New York: Dover
H. M. Edwards (1977)Fermat’s Last Theorem: A Genetic Approach to Algebraic Number Theory. New York: Springer
T. J. Fletcher (1972)Linear Algebra Through Its Applications. London: Van Nostrand Reinhold
L. Gaal (1973)Classical Galois Theory. New York: Chelsea
A. Gardiner (1982)Infinite Processes: Background to Analysis. New York: Springer
A. Gardiner (1977) The Art of Doing Mathematics (manuscript)
M. W. Han (1977) The Lecture Method in Mathematics: A Student’s View.Am. Math. Month.80:195–201
M. Kline (1972)Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press
I. Lakatos (1976)Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge: Cambridge University Press
H. Lebesgue (1966)Measure and Integral. San Francisco: Holden-Day
L. Lovasz (1979)Combinatorial Problems and Exercises. Amsterdam: North-Holland
E. E. Moise (1982)Introductory Problem Courses in Analysis and Topology. New York: Springer
D. J. Newman (1982)A Problem Seminar. New York: Springer
G. Polya and G. Szego (1972)Problems and Theorems in Analysis, Vol. 1. Berlin: Springer
C. Reid(1970)Hilbert. New York: Springer
J. Roberts (1977)Elementary Number Theory: A Problem Oriented Approach. Cambridge, Mass.: MIT Press
R. Thorn (1973) Modern mathematics: Does it exist? inDevelopments in Mathematical Education, A. G. Howson, ed. Cambridge: Cambridge University Press
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Gardiner, A.D. Human activity: The soft underbelly of mathematics?. The Mathematical Intelligencer 6, 22–27 (1984). https://doi.org/10.1007/BF03024124
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DOI: https://doi.org/10.1007/BF03024124