In 1948, Claude Shannon wrote his landmark paper on "A mathematical theory of communication", which paved way to the field of information theory.

Network coding conjecture (NCC) by Li and Li asserts that network coding for undirected graphs does not bring any advantage over multicommodity flows.

Symmetry reduction is a well studied subject in geometric mechanics, where symmetries are usually described as an invariance under an action of a Lie group.

The problem of learning arithmetic circuits is the following: given a polynomial as a black box that is promised to have a small arithmetic circuit computing it, can we find this arithmetic circuit?

Randomness is a remarkably powerful tool in the design of algorithms. By giving algorithms the ability to use random bits and letting them err with some small  probability, we can solve many computational problems with remarkable efficiency.