Thursday, June 6, 2013

W.W. Sawyer - Math Hero

As I've come across more and more really delightful math books, I've often regretted the fact that there weren't books like this available when I was young. But I was wrong. It turns out one of the best writers of engaging math books was writing in the forties, fifties, and sixties. W.W. Sawyer wrote over a dozen books, and every one I've read so far is engaging, worth reading more than once, and full of ideas I can use to improve my teaching.

I started with Vision in Elementary Mathematics, then read Mathematician's Delight (mentioned in this post). At some point, I may have read Prelude to Mathematics. They're all great, but I read them when I was too busy to write up a detailed review. (I'm getting frustrated by the hodgepodge state of my bookshelves. I want to be able to find these three books, so I can say more about them.)

Now I've just finished What Is Calculus About? Also fabulous. I wondered what else the great W.W. Sawyer had written, and found this lovely archive.

I'm glad to see he agrees with my assessment of limits:  
The first chapter dealt with limits. No one sees any reason for thinking about limits before having some exposure to calculus, so I left chapter 1 for much later in the course. (from

I also liked Notes on the art of passing exams. 

So here was this great teacher, very aware of the issues we discuss on blogs - being less helpful, project-based learning, etc. - and yet I had never heard of him until recently. His books sold widely when they were first published, but now are treasures we uncover.

It's so sad to think of these wonderful books sitting on bookshelves, unknown. And it's exciting to know how much the internet helps us learn about good resources, however old they are.

I just got my copy of W.W. Sawyer's A Concrete Approach to Abstract Algebra in the mail. I would love to work through it together with a few friends. Anyone interested?


  1. A Long Way from Euclid, by Constance Reid, is somewhat similar in spirit to Mathematician's Delight.

    I hadn't realized there was an Abstract Algebra book by Sawyer.

  2. More to add to my summer reading list...

  3. Sue,
    My favorite Sawyer quote, posted in my classroom for many years: success would mean that every individual felt,
    "I enjoyed the mathematics that I had time to learn.
    If I ever need or want to learn some more,
    I shall not be afraid to do so."

    Nice post

  4. Are we doing favorite Sawyer quotes? I have so many of them! Like this, from Mathematician's Delight:

    "Earlier we considered the argument, ‘Twice two must be four, because we cannot imagine it otherwise.’ This argument brings out clearly the connexion between reason and imagination: reason is in fact neither more nor less than an experiment carried out in the imagination.

    "People often make mistakes when they reason about things they have never seen. Imagination does not always give us the correct answer. We can only argue correctly about things of which we have experience or which are reasonably like the things we know well. If our reasoning leads us to an untrue conclusion, we must revise the picture in our minds, and learn to imagine things as they are.

    "When we find ourselves unable to reason (as one often does when presented with, say, a problem in algebra) it is because our imagination is not touched. One can begin to reason only when a clear picture has been formed in the imagination. Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination."

    And you might enjoy a review by Sawyer of Hardy's Mathematician's Apology.

  5. I do like it. I did not enjoy Hardy's book, and I'm glad Sawyer pointed out both bad (yes! Hardy is full of himself to think that teachers are second-rate) and the good (on mathematical beauty).

    I just received two more of his books in the mail today, Prelude to Mathematics and A Path to Modern Mathematics. They're so nice and small compared to most modern books - easy to carry around.

    Someone said to me that his writing feels old and clunky. I agree that it sounds old-fashioned, but I'd add charming to that instead of clunky. He's charming like someone in suspenders and a bow tie.


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