The Professor of Legend

The traditional mathematics professor of the popular legend is absentminded.

    He usually appears in public with a lost umbrella in each hand.

      He prefers to face the blackboard and to turn his back to the class.

        He writes a, he says b, he means c; but it should be d.

          Some of his sayings are handed down from generation to generation.

            • “In order to solve this differential equation you look at it till a solution occurs to you.”
            • “This principle is so perfectly general that no particular application of it is possible.”
            • “Geometry is the science of correct reasoning on incorrect figures.”
            • “My method to overcome a difficulty is to go round it.”
            • “What is the difference between method and device? A method is a device which you used twice.”

            George Pólya
            How To Solve It

            If you’re not familiar with Polya’s work, here’s a 4-page summary of his problem-solving method.

            Or check out David Butler’s wonderful Solving Problems Poster, which encapsulates Pólya’s system in a visual, easy-to-follow way that works with younger students, too.

            4 steps to solving problems

            CREDITS: “Professor” cartoon (top) by André Santana via Pixabay.
            THE FINE PRINT: I am an Amazon affiliate. If you follow the book link above and buy something, I’ll earn a small commission (at no cost to you).

            Have a Mathematical Thanksgiving Dinner

            With the pandemic still raging, most of us will have to adapt our normal holiday traditions to fit the new reality. We may not be able to have a big family gathering (except over Zoom), but we can still enjoy great food.

            So for those of you who are planning ahead, here is a mathematician’s menu for next week’s Thanksgiving dinner.

            Optimal Potatoes

            Green Bean Matherole

            Borromean Onion Rings

            Thanksgiving Turduckenen-duckenen

            And for Dessert

            May I suggest some of Don Cohen’s Infinite Cake?

            Click here for cake

            CREDITS: “Thankful” photo (top) by Pro Church Media via Unsplash.com. Food videos by mathemusician/doodler Vi Hart.

            Football as a Game of Fractions

            I couldn’t quite figure out how to fit it into the Playful Math Carnival, but this post made me laugh:

            “In football, a tie counts as a half-win (and a half-loss). But half-wins are sometimes worth more than half a win, sometimes they’re worth less than half a win, and sometimes they’re worth exactly half a win. Let me ‘splain…”

            —Patrick Vennebush
            When a Half Is More Than a Half (and When It Ain’t)

            CREDITS: Feature photo (top) by Dave Adamson via Unsplash.com.

            What Is Mathematics?

            Here’s a bit of fun to brighten up your Monday:

            Mathematics: Measuring x Laziness² by Zogg from Betelgeuse (Martin Kuppe).

            For Further Exploration

            James Grime explains the “Aldebaranian” curve calculator in this video:

            And here is the “Map of Mathematistan”. Click to zoom in.

            MathematistanHiresWithoutRoads

            Credit: I contacted @ZoggTheAlien for permission to use the sketch. He said, “Feel free to use it. It’s a Galactic Commons license; you can use it if you don’t claim it’s made by one of your species.”

            Please Add Your Comments Below

            What-Is-Math

            • Do you have a favorite place in the Land of Mathematics? Why do you like it?
            • Most children find themselves stuck in the inner city of Arithmetics. How can we help them get out and explore the landscape?

            howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.


            Reblog: Calculus Tidbits

            [Feature photo above by Olga Lednichenko via Flickr (CC BY 2.0).]

            This week I have a series of quotes about calculus from my first two years of blogging. The posts were so short that I won’t bother to link you back to them, but math humor keeps well over the years, and W. W. Sawyer is (as always) insightful.

            I hope you enjoy this “Throw-back Thursday” blast from the Let’s Play Math! blog archives:


            Finding the Limit

            Eldest daughter had her first calculus lesson last night: finding the limit as delta-t approached zero. The teacher found the speed of a car at a given point by using the distance function, calculating the average speed over shorter and shorter time intervals. Dd summarized the lesson for me:

            “If you want to divide by zero, you have to sneak up on it from behind.”


            Harmonic Series Quotation

            This kicked off my week with a laugh:

            Today I said to the calculus students, “I know, you’re looking at this series and you don’t see what I’m warning you about. You look and it and you think, ‘I trust this series. I would take candy from this series. I would get in a car with this series.’ But I’m going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it.”

            —Rudbeckia Hirta
            Learning Curves Blog: The Harmonic Series
            quoting Alexandre Borovik


            So You Think You Know Calculus?

            Rudbeckia Hirta has a great idea for a new TV blockbuster:


            Common Sense and Calculus

            Sawyer-MathDelight

            And here’s a quick quote from W. W. Sawyer’s Mathematician’s Delight:

            If you cannot see what the exact speed is, begin to ask questions. Silly ones are the best to begin with. Is the speed a million miles an hour? Or one inch a century? Somewhere between these limits. Good. We now know something about the speed. Begin to bring the limits in, and see how close together they can be brought.

            Study your own methods of thought. How do you know that the speed is less than a million miles an hour? What method, in fact, are you unconsciously using to estimate speed? Can this method be applied to get closer estimates?

            You know what speed is. You would not believe a man who claimed to walk at 5 miles an hour, but took 3 hours to walk 6 miles. You have only to apply the same common sense to stones rolling down hillsides, and the calculus is at your command.


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            Every Day Is Math Day

            Happy 11-12-13

            Happy 11/12/13, otherwise known as “tenty-one, tenty-two, tenty-three.”

            Do your young children have trouble counting in the teens? Try making up Funny Numbers to help them! It’s a great habit to develop, because Funny Numbers will come in handy as mental math tools throughout their school math career.

            If you’d like to make your own Happy Math Day post, check out the instructions here: Every Day Is Mathematics Day. And please share a link in the comments section below — I’d love to see what math holiday you invent!

            Update: The numbers 11, 12, and 13 form an arithmetic progression. If that sounds too scary for your kids, check out Patrick’s bedtime math discussion Making Progress, Arithmetically.


            howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.