Mathematical Discoveries

It’s not everyday that a new mathematical discovery is made. It’s been three years since Perelman proved the Poincaré conjecture, and it was a decade-and-a-half before that when Wiles announced-retracted-resubmitted his proof of Fermat’s Last Theorem. So I was ecstatic when I heard the recent news:

Nation’s Math Teachers Introduce 27 New Trig Functions

My favorite new function: pomen.

My favorite old functions from the farm: swine and coswine.

And in case you didn’t make it to the end of that article, I wholeheartedly agree with the last line: “factoring will be cut from the math curriculum entirely because it’s ‘annoying and too fucking hard sometimes.'”

One of my favorite not-in-the-regular-curriculum classroom activities is to tell students that mathematicians have discovered a new integer between 3 and 4. Named after its discoverer, the new integer is called bleem, so counting now proceeds as 1, 2, 3, bleem, 4, 5, …

I then give students the following exercises:

1. bleem + 2 = ___
2. 11 – bleem = ___
3. 3 + 7 = ___
4. 5 + 8 = ___
5. 6 – 1 = ___
6. 2 × bleem = ___
7. 1 × 6 = ___
8. 4 × 8 = ___
9. 9 ÷ 2 = ___
10. 24 ÷ 4 = ___

It’s much cooler if you tell students that they haven’t yet assigned a symbol to this new integer, and then let the class decide what symbol should be used. You can then use the symbol instead of writing “bleem” in all of the exercises. (The best suggestion made by a student was to use 4 as the symbol for bleem, then use 5 to replace 4, use 6 to replace 5, and so on.)

Good luck with the problems above. And no, an answer key will not be provided.