Since one of the questions is Are these sensible statements?, allow me to answer that one with a resounding NO, and be on record against the size-ism inherent in the statements of Scientific American. As the largest simple exceptional Lie group, E8 deserves credit for both intricacy and beauty. but the author seems to imply that the size record makes E8 not only more intricate but also more beautiful than the other simple exceptional Lie groups.

Granted I don't know much about Lie groups, but it really bothers me that an aesthetic judgment can be based on size alone. Last I checked, paintings are not judged on their size.