I ran across this quote and link (below) on a forum I frequent. I found it fascinating to read about a mid-19th century woman with a genius for mathematics and the kinds of road blocks she faced to practice her 'art'. And, because I will probably not become a mathematician myself but am still endlessly curious about what it means to do and think math, I am greatly appreciative of anyone inside mathematics who is able to express it's basic nature (and beauty) so clearly for the rest of us.
"Many who have never had occasion to learn what mathematics is confuse it with arithmetic, and consider it a dry and arid science. In reality, however, it is the science which demands the utmost imagination [which is more than just making things up] ..... It seems to me that the poet must see what others do not see, must look deeper than others look. And the mathematician must do the same thing. As for myself, all my life I have been unable to decide for which I had the greater inclination, mathematics or literature."
For me, this is just one more piece of evidence that there are more connections and similarities between disciplines than there are differences. This is especially true when the focus is on creating meaning rather than building a set of technical skills. And, in my mind, this connectedness is a good thing. Kids who get to learn under this assumption show great enthusiasm and effort because it's real. They know the real world is connected, not broken up into indiscriminate, arbitrary pieces. When subjects are taught as parts of 'the whole' and not as isolated chips of knowledge, everything makes more sense. Math taught out of context or without beauty or with a single minded focus on procedure, well...doesn't.
You can read a short and fascinating biography of Sonya Kovalesky, 1850-1891, here.
There are also Wikipedia entries for her in over 40 languages, some of them selected articles.
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