I&#x27;ve taught a summer program in number theory for high school students for the past several years. Each summer, my classrooms fill with high school students that are intrigued by the idea of math and extremely capable. That is nice and inspiring, and generally more rewarding than when I teach  calculus classes to university students during the school year.<p>But my program is prohibitively expensive, and I&#x27;m acutely aware of the fact that when my students return to their high schools, they will almost certainly return to lackluster curricula. There are exceptions, of course. My summer program is filled with a far-above-average percentage of students attending private high schools.<p>The fact remains that students who attend the summer program are introduced to interesting math with no guided way to continue their exploration. Sometimes, students with supportive schools end up scheduling a self-study with some supervision from a high school teacher or counselor; I&#x27;ve been asked to help set up and guide self-studies, and I know at least a few of them have been successful. In my experience, this has been the best outcome for my students continuing exploration of advanced math. I&#x27;m not sure what this says about math and American high school education.