## The History of Mathematics## Into Modern Mathematics |

## When was quantum mechanics developed? |

There was not one major year in which quantum mechanics developed, or even one major scientist who proposed the idea. This modern physics theory evolved over about thirty years, with many scientists contributing to it. Beginning about 1900, Max Planck proposed that energies of any harmonic oscillator (such as the atoms of a black body radiator) are restricted to certain values. Mathematics came into play here, too, with each value an integral multiple of a basic, minimum value. Planck developed the equation E = hv (or “nu”), in which E (the energy of the basic quantum) is directly proportional to the v (the frequency of the oscillator) multiplied by h, or Planck’s constant (6.63 × 10^{-34}joule-second).

From there, mainly with the use of rigorous mathematics, others expanded or added to Planck’s idea, including German scientist Albert Einstein (1879–1955), who explained the photoelectric effect; New Zealand-born British physicist Ernest Rutherford (1871–1937) and Danish physicist Neils Bohr (1885–1962), who explained both atomic structure and spectra; Austrian physicist Erwin Schrödinger (1887–1961), who developed wave mechanics; and German physicist Werner Karl Heisenberg (1901–1976), who discovered the uncertainty principle. Out of these studies came quantum mechanics (in the 1920s), quantum statistics, and quantum field theory. Today, quantum mechanics and Einstein’s theory of relativity form the foundation of modern physics. These theories continually change or are modified as we get closer to understanding more about the physics—and mathematics—of our universe.