The place of mathematics and geometry among the disciplines has always been central and confusing. As a pure science, its truths were often thought to be eternal and simple, and the entrance to Plato's Academy carried the motto, "Let no one ignorant of geometry enter." Yet, Aristotle and especially Archimedes reserved a special place for mathematics as applied to nature. The main image shows Mathematics staring intently at a simple triangle, within which the exact center is found through the kind of construction familiar to all students. Two smaller images depict quite different aspects of mathematics that had powerful utility and applications. One shows the ancient geometrical proof of the Pythagorean theorem depicted in this main image. When the Academy dome was being designed, the theory of relativity in physics and the cosmological implications of the expanding universe enthralled the public. Both relied on an underlying grasp of alternative geometries that Euclid or Archimedes could not have imagined. The other depicts an Abacus, the ancient Eastern calculation device that implemented the rules of arithmetic. When the Academy dome was being designed quantification was invigorating the social sciences as well as the life sciences. Electromechanical calculating machines, the forerunners of the digital computer, were making new studies feasible in physical, biological, and social sciences as well as in medicine.