The Betz/Hoke Emporium

In the past few days, I’ve seen a couple of good little math problems posted on Twitter. I follow a number of mathematicians, including James Tanton (@jamestanton), who pretty regularly posts math problems that are sometimes easy enough that I have a fair chance of solving them (though he almost never provides any solutions, so it’s sometimes hard to tell if I’ve gotten it right). A couple of days ago, he asked a simple question:

What is the average power of a given prime p among the prime factorizations of the counting numbers?

— James Tanton (@jamestanton) April 26, 2017

This is not a terribly difficult problem to solve as long as you can sum a particular doubly-infinite series, but summing that series is probably the most interesting part of the problem.

In June, my wife Emmy Betz gave a fantastic TED talk at TEDxMileHigh about suicide prevention. The video of her talk is now up on YouTube, and I heartily recommend that everyone watch it. It’s a powerful talk about a tremendously important subject, and she did a wonderful job.

Due to a server problem, we lost our old website entirely. And the backups. So we’re restarting this website from scratch. We hope to get it up and running in the not-too-distant future, with links to family photos and periodic updates about our goings-on. But it may take awhile. In the meantime, we invite you to enjoy the silence!