We focus on the history and the mathematics of the apportionment problem for the US House of Representatives. An apportionment is a function from {1, 2, ..., s} (where s is the number of states) to the positive integers, A(i), so that the sum of the A(i) is H, the house size. Today s=51 (including the District of Columbia) and H=435, although s and H have had many values since 1790. Based on census data, one can compute the fair share of representatives for state i, call it f_i, which might turn out to be 4.69435. But A(i) must be an integer. Should it be 4 or 5 or something else? Different apportionments yield different answers. Many apportionments have been used over time. The mathematicians contributing to this problem include Washington, Adams (both), Jefferson, Franklin, von Neumann, Birkhoff, and others. The apportionment method in current use is unconstitutional! This is quite shocking! How did the mathematicians mess this up? What should we do? The punch line is astonishing! Wait and see. Undergraduates and everyone else are invited to think about this...

Cathedral of Learning 324