michael_nielsen

Hmm. I'll have to think about that. I certainly don't know enough to be able to see immediately how or why that's interesting, so I'd have to dig into it. One result I did use to impress some 16 year olds was that in a group of even order there is an element a with a^2 = 1.

That's in a completely different league, but it served to show them something that without group theory wasn't obvious, but with group theory was completely obvious. That hinted at the power of the topic, but took about 2 minutes from nothing.

The things you're talking about would not be accessible to the youngsters I deal with, so I'm looking for something they wouldn't be able to show, but which becomes obvious with just basic group theory.

It's not quite that level, but Fermat's little theorem of course follows from Lagrange's theorem. I'll bet you could do an amazing elementary video that was Euclid's algorithm, Fermat's little theorem, Lagrange's theorem, and Pratt's theorem (!), all in about 15 minutes!

This is very close to what I currently do, but it suffers the problem that it all seems to be about numbers. You and I know that it isn't, but when you're trying to convince people that "real maths" isn't about numbers, it's a but awkward to do Fermat's Little Theorem.

You show Pratt's theorem?

Not Pratt's theorem, that's usually a step too far, but I do talk about primality testing, factoring without trial division, Diffie-Hellman, and RSA. All are really about groups, not numbers, but it all *looks* like it's about numbers.

Something like RSA or Solovay-Strassen could be really nice. Admittedly, I had RSA explained to me at 17, & didn't get it, but I suspect the explanation was so-so.