Let’s Play Math!

Photo by Brian - Progressive Spin.

Logic is the science of making valid deductions and proofs — and it is also a fruitful topic for blackboard quotes. Here are a few of my favorites:

You can only find truth with logic if you have already found truth without it.

— G. K. Chesterton
The Man Who Was Orthodox

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Photo by foundphotoslj.

Here are a few mathematical gems from my co-op class blackboard:

I must study politics and war that my sons may have liberty to study mathematics and philosophy.

— John Adams

When I was a child, the Earth was said to be two billion years old. Now scientists say it’s four and a half billion. So that makes me two and a half billion.

— Paul Erdös

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He doesn’t learn algebra
in the algebra course;
he learns it in calculus.

I have been catching up on my Bloglines reading [procrastinating blogger at work --- I should be going over the MathCounts lesson for Friday's homeschool co-op class], and found the following quotation at Mathematics under the Microscope.

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Priorities, motivation, and a little bit of math from my blackboard…

We make a living by what we get, but we make a life by what we give.

— Winston Churchill

In mathematics, the art of asking questions is more valuable than solving problems.

— Georg Cantor

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Quotes from my blackboard during October:

Experience is the hardest kind of teacher. It gives you the test first, and the lesson afterward.

— Vernon Law

What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?

— David Eugene Smith

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Classes are back in session at our homeschool co-op, so I am again collecting short quotes for the blackboard. Here are the ones I used in September:

Any fool can know. The point is to understand.

— Albert Einstein

Life without geometry is pointless.

— Anonymous

You don’t understand anything until you learn it more than one way.

— Marvin Minsky

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• Quotations XV: More joy of mathematics
• Quotations XII: Mathematicians at play
• Math jokes
• Nothing is everything
• All odd numbers are prime — a corollary

Mathematics is a vast adventure; its history reflects some of the noblest thoughts of countless generations.

— Dirk J. Struik
A Concise History of Mathematics

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!

— Constance Reid

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I found this worksheet on the KISS Grammar website, and I loved the quotations so much I just had to share them:

In a cat’s eye, all things belong to cats.

— English proverb

One cat just leads to another.

— Ernest Hemingway

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Someone asked me if I was ever sorry I had chosen mathematics. I said, “I didn’t choose! Mathematics is an addiction with me!”

—Marguerite Lehr

If we are to teach mathematics at all, real success is not possible unless we know that the subject is beautiful as well as useful. Mere utility of the moment without any feeling of beauty becomes a hopeless bit of drudgery, a condition which leads to stagnation.

…What would mathematics have amounted to without the imagination of its devotees—its giants and their followers? There never was a discovery made without the urge of imagination—of imagination which broke the roadway through the forest in order that cold logic might follow.

—David Eugene Smith

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Procrastination is the art of keeping up with yesterday.

— Don Marquis

Joyful Days kindly nominated me for the Thinking Blogger Award back in the days of the dinosaurs. Well, she isn’t that old, really — it was only last April. I am grateful to her for thinking of me, and ever since then I have been thinking deeply about whom to nominate in my turn. Or, to be more precise, I printed out the nomination post as a reminder, and then it got lost in a pile of “to sort/read/file” papers on a shelf under my desk…

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Registrations have been rolling in for our homeschool co-op, and the most popular classes are full already. Math doesn’t seem to be a “most popular” class. I can’t imagine why! Still, many of my students from last year are coming back for another go, and I am getting spill-over from the science class waiting list.

Anyway, I have started planning in earnest for our fall session. As usual, I look to those wiser than myself for inspiration…

Many teachers are concerned about the amount of material they must cover in a course. One cynic suggested a formula: since, he said, students on the average remember only about 40% of what you tell them, the thing to do is to cram into each course 250% of what you hope will stick.

— Paul Halmos

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This week’s quotes for teachers:

It is the duty of all teachers, and of teachers of mathematics in particular, to expose their students to problems much more than to facts.

— Paul Halmos

There are many things you can do with problems besides solving them. First you must define them, pose them. But then, of course, you can also refine them, depose them, or expose them, even dissolve them! A given problem may send you looking for analogies, and some of these may lead you astray, suggesting new and different problems, related or not to the original. Ends and means can get reversed. You had a goal, but the means you found didn’t lead to it, so you found new goal they do lead to. It’s called play.

Creative mathematicians play a lot; around any problem really interesting they develop a whole cluster of analogies, of playthings.

— David Hawkins
The Spirit of Play [pdf, 1.4MB]
quoted by Rosemary Schmalz, Out of the Mouths of Mathematicians

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• That’s mathematics
• Can you graph a cubic function?
• For those really long family trips…
• Nothing is everything
• All odd numbers are prime — a corollary