Mathematics and the Imagination

I read a delightful book with this title by Edward Kasner and James Newman. The book was a sheer pleasure. There was no “dumbing down” of mathematics, no “let’s begin from the beginning.” I am sure a layman would still be able to enjoy it, but even for a serious student of Math like me, the authors had a few surprises in their book.

A lovely example is the following puzzle (I am not quoting verbatim): to multiply 2 numbers, form 2 columns. Put each of them at the head of one of the columns. Successively divide one column by 2 and multiply the other one by 2. When an odd number is divided by 2, discard the remainder. Take from second column those numbers which appear against an odd number in the first. Add them up to get the product of the two numbers.

Example: 23 * 11

Divide  Multiply

11            23

5              46

2               92

1               184

23*11 = 23+46+184=253

The question is: how do you explain this method?

Of course it is not rocket science, but it would be fun to ask this question in the class I am teaching, especially when we are not talking about binary representation. Catching the students off-guard once in a while keeps them on their toes 🙂

But back to the book…the last chapter was my favorite. It was in their conclusion that the authors’ love for mathematics shines through brightly. Sample this:

“Mathematics is an activity governed by the same rules imposed upon the symphonies of Beethoven, the paintings of Da Vinci, and the poetry of Homer. Just as scales, as the laws of perspective, as the rules of metre seem to lack fire, the formal rules of mathematics may appear to be without lustre. Yet ultimately, mathematics reaches pinnacles as high as those attained by the imagination in its most daring reconnoiters. And this conceals, perhaps the ultimate paradox of science. For in their prosaic plodding both logic and mathematics often outstrip their advance guard and show that the world of pure reason is stranger than the world of pure fancy.”

 

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