In 1973, Wayne Roberts became Minnesota Coordinator for the American High School Mathematics Examination (AHSME). He noticed that Minnesota students did not do as well as those from other parts of the country. During a 1978 sabbatical leave in Massachusetts, he visited a small high school whose students consistently did very well on the AHSME. The reason, he concluded, was that the Massachusetts students participated in a mathematics league. On his return to Minnesota, he caused one to be created there and this book surveys its first twenty-five years.
In the Minnesota league, teams of fifteen students have meets, five or so a season, involving around eight schools. There is a variety of events, with problems on various topics and at various levels of difficulty. In recent years the number of teams participating has ranged between 160 and 180. At the end of the year there is a statewide Math Bowl for league winners.
It works. Minnesota's AHSME scores went up, and its students go on to more and better mathematical accomplishments than they had before the league existed. The league also has the large advantage of regularly bringing together groups of mathematics students and teachers.
There should be more mathematics leagues. They take money, though not a lot, and someone like Wayne Roberts to make them go, which may be more difficult to arrange than financing.
The book is a compendium of this and that: pictures, lists of winners, sample problems (quick — what's the largest prime factor of (25!)3 - (24!)3?), how the league has operated, and so on. The section "Our Guiding Philosophy" deserves to be widely read. Anyone interested in mathematics competitions will find this book useful.