Well, like all stereotypes, there’s a certain amount of statistical reality that supports this impression and obscures all examples to the contrary, no matter how many of them there are. Sometimes these “exceptions” tend to make news. In this case we have a 12-year-old, who may be either Nigerian or English—hard to tell from the news accounts—but who in any case discovered and proved a “new” quick test for divisibility by 7. The test definitely works, the proof is ingenious, and it’s a cool, feel-good story.
But is it news? Real news or fake news (in any sense of the word “fake”)?
It’s clearly real news. Chika’s test is much better than the “standard” test for divisibility by 7, which is too complicated to be useful. Everyone knows—or at least used to know and has now forgotten—the standard tests for divisibility by 2, 3, 5, and 10. They’re even (occasionally) useful. And those of us who construct proofs by mathematical induction have proved a variety of other divisibility tests, even if we don’t actually remember them. They tend to be a great combination of number theory and algebra. Chika’s technique does not use an inductive proof, not that one would expect one, but the proof is valid. So why are there some Debbie Downers around who consider it fake news? You’ve probably guessed it: some obnoxious miscreants have diminished its importance by pointing out that Chika is not the first to have made this discovery!
Oh, horrors! Are we supposed to clutch our pearls and ignore the story? So what that he wasn’t the first—the technique wasn’t new to the world, but it was new to him (and his teacher), and that’s what really matters. It’s certainly new to me. Yes, it’s not important to mathematics, but it’s important to education.
Now what does all this have to do with the 11-year-old Massachusetts girl mentioned in the title of this post? Simply this: 19 years ago I wrote a short introduction to a piece that was published as part of a letter to the Mathematics Teacher. It’s more or less the same situation: Felicia made a number-theory discovery that was new to her and to me, she proved it (with a lot of help from her dad), wrote it up, and published it as a letter to the Mathematics Teacher along with my intro… and then along came a couple of obnoxious critics who found the same theorem published elsewhere many decades earlier; in their eyes that diminished the successful discovery. Bah to them! They’re clearly not educators.