How to taste mathematics

We are facing a real danger as mathematics continues to be driven further outside the realm of modern culture. The danger lies in the fact that mathematical structures reflect all possible patterns of mental activity, which are creative and unlimited. This proves itself especially in mathematical breakthroughs. Mathematics is integral to culture. In fact, mathematics merits as legitimate a place in modern culture as music.
The fundamental sequence of doing mathematics is as follows. In the first phase, the mind formulates some simple or rather involved problem. Soon the problem transforms into a sort of obsession that pushes the mind into a lengthy search for a solution. In the case where a solution is found, the mind is satisfied at least temporarily – until it creates a new problem.
Mathematics is not a pragmatic science in any sense. Hence, there is a rarity of great mathematicians in our epoch. Another reason for a dearth of modern, brilliant mathematicians is that mathematics is, unfortunately, being relegated primarily to the economic sector. Music is moving towards the same fate. No one discipline can attest to having a monopoly on how to appeal to our deepest aesthetic sensibilities – not music or any other of the arts. And, in fact, mathematics has more in common with music than students of either are led to believe.
Unfortunately, the prevailing classical methods of teaching mathematics, are partly responsible for the decline in this great art. We have to modify these methods so as to achieve a deeper understanding of mathematics. Our incomprehension of a thing often leads to our criticism of it as being too involved or complicated, followed by our tendency to thus render it unimportant, and then to our conveniently neglecting it altogether. To experience the beauty and wonder – the exaltation – of mathematics, just like that of music, requires only that we attempt to truly understand it.

Article originally published in “International Journal of mathematical Sciences and Applications”, V. 1 (January 2011), n. 1, as open access article. Reprinted with permission.

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