FORMULAS and SIMPLICITY

Formulas in mathematics and physics are often distinguished by their simplicity. And simplicity in a mathematical or physical formula correlates with beauty. Some examples of this simplicity include Euler's formula for polyhedra, Euler's basic formula in complex analysis, the basic inverse factorial series representation of Euler's number, the de Moivre's theorem from complex analysis, the law of cosines, the law of sines, the formula for length in a Cartesian coordinate system, the Bragg law, Newtown's inverse square law, Coulomb's inverse square law, the first and second and third laws of thermodynamics, the formulas for lattice spacings in different crystal systems, the infinite limiting definition of the golden ratio, de Broglie's matter wave hypothesis, the matter wave-light wave hypothesis, the photon hypothesis and so on........It can thus be concluded from these examples that mathematical and physical profundity and beauty comes from simplicity of expression and parsimony in the choice of elements within a physical or mathematical expression. These expressions identified above are just some prominent examples of mathematical truth or physical truth that has an enduring and not ephemeral value. The introduction of too many elements (or factors) within an expression correlates directly with the dimunition of the meaningfulness of the expression. The meaningfulness of mathematical and physical equations tends to wilt away at the edges the farther such expression move from simplicity to complication.........One should always seek after economy and parsimony of expression in the formulation of profound statements.