Many of us come away from our compulsory math education with the impression that math and creativity have nothing to do with each other, that math is the epitome of convergent thinking: there is just one right answer, and just one way to find it. At best, this is only half true.

Mathematical statements are precise, and have binary true/false values (if they are well-defined), but those of us who enjoy math see it as a creative exploration of logical relationships. The answers in math may be convergent, but the ways of arriving at them are infinitely divergent.

For example, consider the question “what is 5 + 5?” Ostensibly, it has just one answer, 10. But how many ways are there to arrive at this answer? Some people might do it by counting. Others might do it by multiplying 5 times 2. Others might do it by looking at their hands. Many probably know it by rote memorization. In terms of the inner cognitive process of computation, there is literally no limit to the variations of thought involved even with such a simple calculation.

Now consider something a bit more sophisticated (yet still relatively simple), like a proof of the Pythagorean theorem. It has been known at least since the Babylonians, definitively proved at least since Euclid, yet over the centuries hundreds of proofs of the Pythagorean theorem have been recorded, including an original one by president James Garfield. The question “how many ways are there to prove the Pythagorean theorem” is a classic example of divergent thinking in action.

If the idea of math as a creative endeavor seems surprising to you, don’t worry, it’s not your fault. It’s simply a result of outdated teaching methods. When I teach math, I do it in a way that engages both sides of your brain, so that it is actually engaging, interesting, satisfying, and yes, creative.

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