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.
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.
