A Timeline of Symmetry in Physics, Chemistry, and Mathematics.

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This page contains many links to the MacTutor History of Mathematics archive at the University of St Andrews.
Links to other interesting archives can be found at the bottom of the page. The page is still under construction. Corrections and contributions are invited.

- 400 Description of the 5 Platonic solids.
- 300 The geometry of polyhedra described by Euclid.
1528 'De symmetria partium' by Dürer, a study of symmetry in art.
1596 In 'Mysterium Cosmographicum' Kepler suggests that the orbits of the then known planets are defined by the Platonic solids.
1609 Kepler publishes 'Astronomia Nova' where he announces his hree famous laws for planetary motion. The 2nd law we can now understand as the conservation of angular momentum, a consequence of the O(3) symmetry of the gravitational force from the sun.
1611 In 'De nive sexangula' Kepler studies the hexagonal symmetry of snow crystals.
1669 Investigation of crystal angles by Steno, alias Niklas Stensen, the Danish geologer and anatomist.
1687 'Principia' by Newton, where the first law states the conservation of momentum due to the homogeneity of space (translation invariance).
1830 Hessel derives the 32 crystal classes.
1832 Galois introduces the group concept and applies it to permutations of the roots of equations. This work was not published until 1846.
1844 Cauchy studies the theory of permutations. The permutations of a fixed number of N elements is now called the symmetric group SN.
1849 Bravais derives the 14 space lattices in 3 dimensions.
1860 Pasteur discovers the connection between optical activity and enantiomorphic molecular structures. Chiral molecules which are mirror images rotate light in opposite senses.
1872 Felix Klein proposes the Erlanger program where geometry is classified by invariance groups.
1878 Cayley formulates the abstract group concept.
1890-91 Derivation of the 230 space groups in 3 dimensions by Schönflies and Fedorov
1893 Lie and Engel: 'Theorie der Transformationsgruppen'.
1886-1904 FitzGerald suggests what is later called the FitzGerald-Lorentz contraction, Larmor, Lorentz and Poincaré introduce the transformations which make up what is now called the Lorentz group. It is shown that they leave Maxwell's equations invariant. The Lorentz group with the space-time translations added is often called the Poincaré group.
1905 In his most famous paper Einstein gives a set of physical assumptions from which the Lorentz transformations follow. He thus creates Special Relativity as a physical theory and an alternative to the Newtonian theory. The latter uses a different set of transformations connecting the inertial reference frames, namely the Galilei group.
1895-1910 Frobenius and Schur create the theory of group representations.
1912 Experimental evidence for the lattice structure of crystals through x-ray diffraction by Max von Laue and others.
1918 Emmy Noether shows the general connection between symmetries and conserved quantities.
1918 Weyl introduces a classical unified field theory for gravitation and electromagnetism. It includes invariance under scale transformations, called gauge invariance, which implies the conservation of electric charge.
1924 Bose introduces what is now called Bose-Einstein statistics for photons.
In 1925 there is a generalization, by Einstein, to those particles or quanta we now call bosons. Their many-quanta states are invariant under all permutations.
1925 Pauli proposes the 'exclusion principle', later called the 'Pauli principle' for the states of electrons.
1926 Born, Heisenberg and Jordan introduce the quantum theory of angular momentum and spin 1/2.
1926 Fermi-Dirac statistics introduced (by Fermi and Dirac!) for those particles (e.g. electrons) we now call fermions. Their many-particle states change sign under odd permutations. This statement includes the Pauli principle.
1927-28 London and Weyl introduce gauge transformations into quantum theory, with total electric charge as the conserved quantity.
1928 Dirac proposes a relativistic wave equation for spin 1/2 particles, i.e. one covariant under the Poincaré group.
1928 Weyl: 'Gruppentheorie und Quantenmechanik'.
1929 Bloch describes the electron wave functions in periodic potentials.
1929 Bethe derives the splitting of atomic levels resulting from the crystal field symmetry.
1930 Wigner studies the effects of the symmetry of molecular configurations on the vibrational spectrum.
1931 Wigner introduces time reversal symmetry (T) into quantum theory and publishes 'Gruppentheorie und ihre Anwendung auf der Quantenmechanik der Atomspektren'.
1931 Pauling studies the theory of chemical bonding using the symmetries of orbitals.
1932 Heisenberg introduces a symmetry between protons and neutrons in nuclear theory, it is later called isospin symmetry.
1932 Carl Anderson finds the positron in a cosmic ray experiment, the first of the antiparticles (predicted by Dirac in 1931).
1932 van der Waerden: 'Die gruppentheoretische Methode in der Quantenmechanik'.
1935 V. Fock derives the spectrum of the H-atom from the SO(4) symmetry.
1936 Heisenberg introduces charge conjugation (C) as a symmetry operation connecting particle and antiparticle states.
1937 Jahn and Teller derive a connection between the symmetry of molecular configurations and the stability of degenerate molecular electron orbitals (Jahn-Teller effect): for a non-linear molecule there is always a distortion into a shape of lower symmetry to remove any orbital degeneracy of its electronic state.
1939 Wigner studies the unitary representations of the Poincaré group. The results allow us to classify all relativistic wave equations and the transformation properties of quantum fields.
1940 Pauli proves the spin-statistics theorem: particles with half-integer spin have Fermi-Dirac statistics, those with integer spin are Bosons.
1954 Yang and Mills introduce local isospin transformations as an internal symmetry, i.e. they are transformations of the field operators which depend on the point in space-time.
1954 Wick, Wightman and Wigner introduce the notion of superselection rule.
1954-5 The PCT theorem is proved by Lüders and Pauli, involving space inversion (P), charge conjugation (C) and time reversal (T): in a local quantum field theory the product PCT of these transformations is always a symmetry.
1956-7 A parity breaking weak interaction is proposed by Yang and Lee and verified experimentally by Wu. Yang and Lee share the 1957 Nobel prize for physics.
1959-61 Heisenberg, Goldstone and Nambu suggest that the ground state (vacuum) of relativistic quantum field theory may lack the full global symmetry of the Hamiltonian, and that massless excitations (Goldstone bosons) must accompany this 'spontaneous symmetry breaking'. In 1964 Higgs and others find that for spontaneously broken gauge symmetries there are no Goldstone bosons but instead massive vector mesons (Higgs phenomenon).
1961 Gell-Mann and Neeman propose SU(3) as a symmetry for the strong interactions (the Eightfold Way). This includes the isospin symmetry in a larger symmetry group which also acts on the strangeness quantum number. In 1964 Gell-Mann and Zweig propose a new, deeper, level of quanta, the quarks, to account for the SU(3) symmetry.
1964 The CP breaking part of the weak interaction is found experimentally by Cronin and Fitch.
1965 Woodward and Hoffman describe how the conservation of orbital symmetry influences the course of molecular reactions, the 'Woodward-Hoffman rules'.
1973-74 The essential features of the presently accepted Standard Model of particle physics are established.
1977 Penrose demonstrates an aperiodic tiling of the plane using only two different tiles and an approximate 5-fold symmetry. In 1984 Shechtman et al find the first quasicrystal in the laboratory with evidence of dodecahedral structure, one not expected to exist by conventional wisdom.
1985 Curl, Smalley and coworkers produce the first observed C60 molecules by laser-vaporizing graphite in a jet of helium.

UP - Modified 16 Jan 2004