Ana is doing work with primes. So is Eva, actually.

[conuly]

Ana did her work first, and immediately looked at the chart she'd written up, the Sieve of Eratosthenes, and started looking for a pattern. When I realized what she was doing instead of finishing her work (finding prime factors of numbers) I quickly popped her bubble by pointing out that primes HAVE no pattern (or at least, none that's become obvious in literally centuries of study) and if there IS one, she won't discover it by looking at the list of primes under 100.

The next day, Eva did her work on primes. She was only looking at primes under 35. She had, with help, seen that of course she could eliminate multiples of 2 by crossing out every OTHER number, and multiples of 3 by crossing out every other-OTHER number (as she phrased it), though she seemed completely unable to generalize this to "cross out every fifth number" and whatnot. At any rate, once she was done, she also began looking for the pattern in the primes. "I see the pattern at the beginning, but it doesn't stay like that, so it can't be a real pattern!"

I burst her little bubble as well. They could easily spend all day on this. I wanted to go pick up the CSA.

At any rate, they're both really intrigued by the subject, especially when I told them that you can make a couple thou by finding new primes! (Which you won't do by hand, because they're all in the 25 digit range by now, but that's beside the point.) They guessed intuitively when asked that if the set of all numbers is infinite, the set of primes probably is infinite as well (we should walk through that proof), but what the heck else can we talk about or read about on the subject?

Comments

[kyrielle]

Warning: this is Quora so fact-check anything first. http://www.quora.com/What-are-some-interesting-facts-about-prime-numbers

[conuly]

Thankies :)

[eofs.livejournal.com]

You could talk about prime twins (http://en.wikipedia.org/wiki/Twin_prime) (and triplets etc).

I love that that Wiki page has a sidebar stating simply:

List of unsolved problems in mathematics
Are there infinitely many twin primes?

As if that's the only one.

It makes me so happy to see the girls get excited by maths. So many people (girls/women in particular) get so turned off maths, especially when they see themselves as someone who is "rubbish at maths". It's lovely to hear about them really engaging with and showing interest in the subject. That's how I felt at their age and I could never understand why so few of my peers felt the same way.

[conuly]

It makes me so happy to see the girls get excited by maths.

Gosh, me too. I'm trying to find a line between progressing with our curriculum and stopping to talk about an interesting tangent slightly longer.

[eofs.livejournal.com]

Have you come across the Murderous Maths (https://en.wikipedia.org/wiki/Murderous_Maths) series? They're in the vein of Horrible Histories, but about maths. They started out as a single book within a series called The Knowledge which set out to cover all the random subjects which didn't fall under Horrible Histories or Horrible Science. Evidently the first book was a huge success (I loved it as a child) so they made another, and then turned it into a series in its own right. I wish there had been so many of them when I was younger, I only ever had one.

They're written by a chap with the marvellous name Kjartan Poskitt. If the books aren't available in your library system (though I imagine they would be) then it looks like there's an excellent website.

[conuly]

*scribblescribblescribble*