image/svg+xml - inherently probabilistic- energy, momentum, and other physical quantitiescan only take on certain discrete values- in contrast to classical mechanics, where energy isexchanged continuously- the state of a physical system at a given time is described by a vector in a special type of vector space (a Hilbert space) All this notation meansis that we are assigning an invertible square matrix to each element of the group.   Undergraduate Colloquium - November 2017 A joke a man on an airplane once told me: 1900 Electron is discovered Max Planck Energy can only be exchanged in discreteunits. quanta? 1905 Albert Einstein Light is 'quantized' (photons) 1913 Niels Bohr Quantum theoryfor hydrogen atom 1925 Heisenberg, Born, Jordan First consistent theory of quantum mechanics: "Matrix Mechanics" Erwin Schrodinger "Wave Mechanics" No way! Check out my consistent theory: Carl Eckert Guys. They're the same. 1941 Richard Feynman Amplitude formulation of quantum mechanics - two parallel histories- two parallel philosophies- introduce the main characters- the scene where they meet A lingering question: Why didn't our existingmath predict this? A physical theory which describes the behaviorof nature at the atomic and subatomic scale. (Motto: things get weird when you zoom in far enough.) We won't go into the full formulation of quantum mechanicsfor this talk, but we do need this piece.