Mathematicians can be fascinated by the elegance and beauty of the ideas behind mathematical theories. Mathematical structures are already out there and our goal is to discover them.
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 times of war, secure communication can be the difference between life and death, or even winning or losing a war. The first to patent a rotor machine in Europe was Arthur Scherbius in 1918. Scherbius’ version of the rotor machine became a commercial success, unlike the other patented machines. Scherbius named his machine Enigma.
Recently there has been a breakthrough in the field of algorithms for geometric network problems, concerning the complexity of the Euclidean Travelling Salesman Problem.
At this very moment, the emergent science of DNA self-assembly is giving birth to a new field of mathematics that might be called DNA-mathematics. Cleverly constructed DNA molecules will self-assemble into pre-determined complex structures when placed in solution together.
