Why Study Mathematics?

by d3 Dan via flickr

[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

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

To Enjoy the Mental Challenge

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


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9 comments on “Why Study Mathematics?

  1. As indicated above, my name is Oladipupo Joseph Olayemi, am a Nigerian, I love this site, in fact, I found all quotations quoted above for they give me more courage in my quest for Mathematics, I realy appreciate. Thanks a lot, may the Lord continue to increase your knowledge more and more {Amen}. But I want to ask this question and, I will really appreciate if I can get immediate response from you, I a preparing to take my Matriculation Examination, which will come up on the 31st of March this year, I want to study Economics, and Mathematics is one of the criteria for studying Economics in Nigeria, which means it is compulsary for me to take Mathematics and I know myself that I am not too good in Mathematics and this has being baffling my mind since, so I want to ask if there is any assistance you can offer, I mean something that can help and improve me on Mathematics, like books, softwares, CDs e.t.c I will joyfuly appreciate it. Please I will be looking forward to read from you as soon as possible. Thanks.

  2. My main advice in studying mathematics is that you should never be satisfied just to know how a calculation works. Always strive to understand why it works that way. When you understand the why of math, then you have a strong foundation on which to build more learning.

    As for book, software, etc., I do not know what to recommend. There are many websites that help explain math, and many books also. You can use any of these that you find, as long as you keep in mind the attitude I describe above. Whatever you study, always look for the reason why it works.

  3. Pingback: Carnival of Mathematics: Inaugural Edition « Abstract Nonsense

  4. What a wonderful post!
    I would say, though, that we do use higher mathematics in our lives much more than people realize — if we know it and have it available to us. It’s the basic calculations that we don’t use so much nowadays, since we usually rely on our calculators to do that for us.
    It is also important to keep options open. The students who complain about having to do that math today may be the same ones who end up wanting to major in physics or engineering in a few years. Without more advanced course work under their belts, they would have a hard time catching up.

  5. I considered myself to have been privileged to discover this site.Although I pit my tent in the study of STATISTICS, mathematics had be my first love.Yet I want to be in the field of data processing and management. I am sure with mathematics as my jack-knife and statistics my shield I could do well in the field. What do you think?

  6. I don’t know enough about data management to offer advice, but it seems reasonable that a strong background in math and statistics would be required.

    On the other hand, I don’t think the metaphors of a jack-knife and a shield fit well together — the mental image is comic.

  7. Pingback: Advanced Mathematics…? « Please, Feed the Curious

  8. Most people do not know for sure that they will or will not need some or any of the math they learn beyond Arithmetic. The reason for learning more math beyond Arithmetic is so people will be informed and have some sense of what Mathematics is needed or useful in a future situation and can reliably discuss that situation, and may at least identify the particular person who can deal with and solve the problem of that situation. Further, if someone learns some topics of math beyond basic Arithmetic, and retains this knowledge, he may solve that future problem situation on his own. Math is good.

  9. Pingback: Homeschooling High School Math | Let's Play Math!

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