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

That vast book which stands forever open before our eyes, the universe, cannot be read until we have learnt the language in which it is written. It is written in mathematical language, and the letters are triangles, circles, and other geometrical figures, without which means it is humanly impossible to comprehend a single word.

— Galileo Galilei

quoted by Clifford Pickover, A Passion for Mathematics

### 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

I told myself, “Lincoln, you can never make a lawyer if you do not understand what demonstrate means.” So I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what “demonstrate” means, and went back to my law studies.

— Abraham Lincoln

quoted by William Dunham, The Mathematical Universe

### To Understand History

In most sciences, one generation tears down what another has built, and what one has established another undoes. In mathematics alone, each generation adds a new story to the old structure.

— Herman Henkel

quoted by Noah benShea, Great Quotes to Inspire Great Teachers

Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals — the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.

— Martin Gardner

quoted by G. Simmons, Calculus Gems

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

The mathematician does not study pure mathematics because it is useful, he studies it because he delights in it, and he delights in it because it is beautiful.

— Henri Poincaré

quoted by Theoni Pappas, More Joy of Mathematics

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

### And Most of All, to Play

Mathematics is a world created by the mind of men, and mathematicians are people who devote their lives to what seems to me a wonderful kind of play!

At age eleven, I began Euclid, with my brother as tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world.

— Bertrand Russell

The Autobiography of Bertrand Russell

I love mathematics … principally because it is beautiful, because man has breathed his spirit of play into it, and because it has given him his greatest game — the encompassing of the infinite.

— Rózsa Péter

quoted by Rosemary Schmalz, Out of the Mouths of Mathematicians

Did you enjoy these? You can find plenty more on my Math & Education Quotations page.

**I would LOVE to hear YOUR favorite mathematics, education, or inspirational quote. Please share in the Comments section below!**

CREDITS: Never Ending Math Problem photo (above) by Danny via Flickr (CC BY 2.0).

Great.

This list I found titled “Life Skills Learned In Math Class”

https://mathmaine.com/2010/01/23/life-skills/

On this blog titled “Life Skills Learned In Math Class”, on the blog site MathMaine Michael describes life skills according to topics.

It might fall under the “To Train Your Mind” category, however, it is a list of 11 things.

Either way I found it quite interesting and practical.

Nice article. Thanks for sharing!

I think you’re right, many of his points would fall under “To Train Your Mind.” But also, he has some just plain “Because It’s Useful” points. I skipped that category above because I was looking for inspiration.

Too bad. Being useful is good.You can inspire there to study math by showing them how it will help them. What is your definition of inspiration?

I’m sorry. You are looking for quotes and I gave you an article. If it helps, there’s a a whole blog to explore.

If I find any quotes soon I’ll share them with you.

Being useful is very good! And I don’t doubt that some people find usefulness motivating — the above category “To Understand Creation” could be seen as encompassing the usefulness of math in science and engineering. And “To Train Our Minds” is useful, too.

What I find inspiring, though, are ideas that touch my heart or my mind, that make me wonder, that draw forth some feeling of awe or delight. Those are the things that motivate me, so they are the things I was trying to share.

Throw away that calculator!

– Danica McKellar