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. 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. To experience the beauty and wonder – the exaltation – of mathematics just like that of music requires that we attempt to teach mathematics and music as one and the same course.