Real and complex numbers extend the rational number system, providing solutions to equations like x2 = 2 and x2 = -2. They’re pretty handy things to have around. But real and complex numbers are not the only way to extend the rational numbers. P-adic numbers also do the job. P-adic math has some really peculiar properties, but because it encodes congruence information very naturally, it turns out to be easier to do certain things in P-adic math than in real/complex math.

Like proving that no three positive integers a, b, and c can satisfy the equation an + bn= cn for any integer value of n greater than two.

But P-adic math is worthy of your attention even if you’re not trying to come up with your own proof of Fermat’s Last Theorem. Because it will stretch your mind. Mark Chu-Carroll’s introduction to the bizarre world of P-adic math, where numbers run backward and closeness doesn’t mean what you think it means, is a mind-stretcher.

The other articles in this issue should give your mind some exercise, too. Like our lead article by Ron Jeffries on estimation. Two months ago in these pages Ron convinced you that estimation is evil. He’s back this month to tell you that estimation is necessary. And he’s right both times.

Paul Callaghan will stretch your mental muscles with his article on dependent types. Paul’s done a lot of work on dependent types and thinks the idea is so powerful and important that it could just be a whole new programming paradigm.

Johanna Rothman warns about the questions you should never ask when interviewing prospective team members. And Steven K. Roberts continues sharing his secrets for pursuing your crazy dream without going broke in the process. John Shade puts in a good word for fear. And our new “Coming Up” page describes one of the new departments we have in the works.

One other thing: We’ve been polling you on whether you’d be willing to pay something for PragPub. We’d love to keep giving the magazine away, but it’s just not sustainable. The answer seems to be, “Yes—something.” So we’re soon going to be asking you to pay a little something for PragPub. We’re still nailing down the details, and the system won’t be everything we want immediately. We’ll continue to tweak it based on your feedback. Because you’re the boss. Particularly if you’re paying us.