[Rescued from my old blog.]
What teacher hasn’t heard a student complain, “When am I ever going to have to use this?” Didn’t most of us ask it ourselves, once upon a time? And unless we choose a math-intensive career like engineering, the truth is that after we leave school, most of us will never again use most of the math we learned. But if math beyond arithmetic isn’t all that useful, then what’s the point?
If you or your student is singing the Higher Math Blues, here are some quotations that may cheer you up — or at least give you the strength of vision to keep on slogging.
We study mathematics…
To Understand Creation
I don’t want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that — by some mysterious agency — capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature.
— Ian Stewart
The Magical Maze
To Train Our Minds
The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.
— George Washington
quoted by William Dunham, The Mathematical Universe
To Understand History
I will not go so far as to say that constructing a history of thought without profound study of mathematical ideas is like omitting Hamlet from the play named after him. But it is certainly analogous to cutting out the part of Ophelia. For Ophelia is quite essential to the play, she is very charming. . . and a little mad.
— Alfred North Whitehead
quoted in The Viking Book of Aphorisms
To Appreciate the Beauty
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful. The ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.
— Godfrey H. Hardy
A Mathematician’s Apology