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Many people who have never had occasion to learn what
mathematics is confuse it with arithmetic and consider it a dry and arid
science. In actual fact it is the science which demands the utmost imagination.
One of the foremost mathematicians of our century [Weierstrass] says very
justly that it is impossible to be a mathematician without also being a poet
in spirit... It seems to me that the poet must see what others do not see,
must see more deeply than other people. And the mathematician must do the
same.

-Sofya Kovalevskaya, 1890

(from Anne Hibner Koblitz's charming and excellent biography of Kovalevskaya
'A Convergence of Lives' (Birkhauser, 1983), p.231. The reference to Weierstrass
is to a letter from him to Kovaleskaya, 27 August, 1883. I am grateful to
June Barrow-Green of the Open University for this information. )

If this spirit of imagination is so central, then it should be communicated
to undergraduates! Is this done? See also the article
`Promoting Mathematics'
(pdf file of this).

return to popularisation and teaching page

13 March, 2008