A theoretical relationship between mathematics and mechanics

Classical mathematics began during the Egyptian and Babylonian time and solved problems analytically with no proof of theories being performed. In the late eighteenth century, theoretical problems began emerging into traditional mathematics where the theoretical approach to classical problems began to be explored. Traditional mathematics included group, field and ring theory and can be applied to other subjects such as molecular symmetry in chemistry. Traditional mathematics expanded and provided discovery of the newest field of study, idempotent mathematics. Idempotent mathematics emerged in the nineteenth century stemming from the definition of an idempotent element and an algebraic structure known as a semiring. Idempotent and traditional mathematics have been said to have a correspondence to each other just like quantum mechanics and classical mechanics do through Neil Bohr's correspondence principle. Using Erwin Schrödinger's particle in a box experiment, the beginning steps were taken to find the theoretical relationship between the two subjects.