Hooray for summer! Now that finals are finally over, you can expect a lot more from me over the next few months. I’ve got a lot of exciting things planned, including

- a description and explanation of an algorithm for finding square roots by hand (which most people don’t know anymore);
- finally FINALLY for real finishing my series of posts on Recounting the Rationals (yes, Jason, this one is for you!);
- going through a neat little paper by Ivan Niven giving a proof that pi is irrational;
- a little number theory, focusing on the Fundamental Theorem of Arithmetic;
- fun links to interesting mathematics around the web;
- and whatever else tickles my mathematical fancy!

To get things started, here’s a link for you: Norman Wildberger’s MathFoundations, a series of videos explaining the foundations of mathematics. I don’t agree with all his opinions—particularly regarding infinite sets—but this is a subject on which I’m willing to agree to disagree; as a legitimate, published research mathematician who’s been doing mathematics longer than I’ve been alive, he’s certainly entitled to his opinions! And I certainly *do* agree with many of his opinions, especially regarding mathematics education. In any event, the videos are very well-done, and there’s lots of interesting stuff there!

Oooh! Square roots by hand! It’s true that few people know anymore, but even more rare is the elusive hand algorithm for cube roots.

I’m also interested in seeing a proof I can understand of the irrationality of pi.

Hand algorithm for cube roots! I’ve never heard of such a thing. Do you have a link?

Looking forward to all of this! Thanks Brent.