The first Beast Academy books went off to the printer today. It's been fun watching various message boards and blog posts to see that some people are as excited about them as we are.

The internet makes dumb people dumber and smart people smarter. -Kevin Drum

A parent of one of our students wrote me an email today about his daughter's frustration with difficult problems. I started to write a reply, and it expanded into a new article about the importance of hard problems and how to deal with them in our articles section here.

Here is a series of answers to the question of what it is like to have an understanding of higher mathematics. I don't think I have the understanding referred to by the questioner, but several of the people here at AoPS do, and I see glimmers of their insights in the responses. Perhaps more interesting to me is that many of the answers are broadly applicable to descriptions of understanding many other areas or skills.

I do a lot of complaining about various aspects of the American education system, so when I see something at a systemic level that's spot-on right, I should publicly praise it.

I was at the gym last week and spent a long time talking to a guy who's taught me a lot about a few exercises. He was very excited because he just landed his first professional job. He's a great example of both one huge failure of the American education system, and one huge success. He's from a very rural area of Southern California, and went to a high school that isn't accustomed to dealing with very strong math/science students. He's clearly a smart guy, so I wasn't surprised to hear that he was the top math guy in his area, and skipped at least one grade before heading off to college.

College was a disaster. Perhaps he was too young. Perhaps his school hadn't prepared him. (I think this was certainly the case, as did he.) Perhaps he was unfortunate enough to go through high school pre-AoPS Regardless, his first run at college was unsuccessful. He spent some time playing poker, which he was good at because he's smart. But he eventually, or rather quickly, grew weary of that and started back at school, first through community college, and then at San Diego State. And he didn't study something relatively useless, like ________ Studies (beware majors with "Studies" in the title). He just landed a job as an aerospace engineer. He's back in the hard-core geek fold, and happy to be there.

Here's what the education system got right: the American system has lots of on-ramps for people who get sidetracked early in life, or who simply aren't ready for college at age 18. From what I understand, it's a lot harder in many Western countries to reroute or restart your education later in life, and to build a new career through education well after the typical age people might complete their education.

I have a lot of issues with so-called higher education in the US (and hoepfully I'll have time to write about some of them soon), but this is one thing it gets right. For people who know what they're doing and know why they're in school, the US system of higher education offers enormous opportunity to get yourself back on track.

Quick reminder for those of you participating in the Reel Math Challenge from MATHCOUNTS: the public voting starts Tuesday. Public voting is part of the evaluation of the videos, so obviously students who get their videos in early will have an advantage! That said, if you don't have your video finished by Tuesday, you can still enter. The voting runs until February 1st of next year, so there's still plenty of time to finish your video and rally your voting forces.

We need a whole lot more of them. Here's a symptom of the current problem. Gym teachers making 10-20% more per year than science teachers? What would that look like if we let market forces play a role here? That ratio would at least flip.

One of them dominates poker tournaments. More details here. Congrats, Valentin!

MATHCOUNTS has launched a new contest in which students are challenged to make movies out of MATHCOUNTS problems. (Hey, that sounds familiar!) The program is called Reel Math, and you can check it out here. Winners get a free trip to Nationals in Orlando!

I should have shared this sooner; crossposted from the AoPS blog: