‘The study of solutions of some equations and how different solutions are related to each other’
Or, the study of certain groups, known as Galois groups, that can be associated with polynomial equations.
Whether or not the solutions to an equation can be written down using rational functions and square roots, cube roots, etc., depends on certain group-theoretic properties of Galois groups.
‘Parity is not conserved in weak interactions between elementary particles’
Elementary particles interact by four types of forces: gravity (the attraction between all matter), electromagnetism (the force between charged particles), the strong force (such as in the atomic nucleus) and the weak force (another type of nuclear force).
The existence of antimatter leads to the idea of symmetry – every particle has a mirror-like twin.
The law of conservation of parity says that the laws of physics are identical in right- or left-handed systems. However, certain interactions of elementary particles always produce a particle always spinning in the same direction. When an atom emits a neutrino it always spins in the same direction – left-handedly. Many elementary particles display a preference for left over right.
In 1956 Lee and Yang suggested that the evidence for left-right symmetry is weak in interactions involving the weak force.