Symmetry

In mathematics, an invariance: a transformation that leaves some structure unchanged. The formal, group-theoretic study of symmetry began with the question of which polynomial equations can be solved by a formula using only radicals. In 1824 Niels Henrik Abel published, at his own expense, a proof that the general equation of the fifth degree cannot be solved in radicals, opening by noting that geometers had long sought such a solution without proving one impossible; his argument was joined a few years later by Evariste Galois's theory of what are now called Galois groups, together founding the study of which symmetries of an equation's roots permit a solution and which do not. A second landmark came in 1918, when Emmy Noether presented her theorem, published as Invariante Variationsprobleme, showing that every continuous symmetry of a physical system corresponds to a conserved quantity: time-translation symmetry to conservation of energy, space-translation symmetry to conservation of momentum, and rotational symmetry to conservation of angular momentum.