There shall be appointed only men or women to membership on the board of trustees of state institutions of higher learning as shall be qualified electors residing in the district from which each is appointed and at least twenty-five years of age and of the highest order of intelligence, character, learning and fitness for the performance of such duties to the end that such board shall perform the high and honorable duties thereof to the greatest advantage of the people of the state and of such institutions, uninfluenced by any political considerations.