I’ve been clearing out my offices at home and at school recently. I came across this gem. It’s Professor Julius Sumner Miller’s response to the question posed in this post’s title, as quoted in the AMT (Australian Mathematics Teacher) Volume 4 2006.
Mathematics, when properly viewed, properly taught, properly learned, arouses the spirit, cultivates imagination, stirs curiosity, invites further learning. It is indeed one of the noblest creations of the human mind. It is, moreover, the product of the greatest minds of all time. It interprets nature, it unveils the harmonies of the universe. It is the priestess of clarity.
From the structure of mathematics emerges a sense of truth. It has no room for opinion or conjecture. It gives to our understanding what music is to the ear, what beauty gives to the eye. It is to the head what poetry is to the heart.
Mathematics lays bare the order and the beauty of the great scheme of things – the tides of the seas, the colours of the rainbow, the motion of the planets, the music in the pine trees, the gurgle of the brook, a worm in the good Earth, a bird on the wing. It tells us why raindrops are round; it can give us the geometry of a leaf; it describes the mechanism of light on the eye whereby we see, and sound on the ear whereby we hear.
Mathematics adds vigour to the mind, frees it from prejudice. Borrowing from Francis Bacon: mathematics makes men wise, witty, deep, subtle, able to contend.