Percolation theory is a branch of mathematics at the interface between probability theory and graph theory. The term 'percolation' originates from materials science. A representative question is as follows. Suppose some liquid is poured over a porous material. Will the liquid be able to make its way from hole to hole and reach the bottom?
In mathematics it is almost impossible not to encounter the name of Paul Erdős. Much of his work centered around discrete mathematics, cracking many previously unsolved problems in the field.