James Taylor saw a light bulb flicker on when he heard the student’s comment.

After half an hour of struggling through a single math problem, a Piñon

Elementary fourth grader murmured a math epiphany to the classmate beside her: An odd number plus 1 will yield an even number, she said.

“Your fellow mathematician has a comment,” Taylor announced, directing the student to enlighten her peers, who were charged with fitting a list of numbers into three witches’ cauldrons consistent with some rules.

The white-whiskered Taylor guided his students to more epiphanies. Switch from three cauldrons to five, he said, and you get a mystery that has gone unsolved for a hundred years.

“No one knows the answer,” he said, as if telling a campfire fable. “Not even with the fastest computers in the worl

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