Most people think that history is all about reading important events in the form of a story or narrative. Rarely do they associate the study of history with mathematics or any quantitative methodologies. Perhaps this is so because most contemporary historical resources, be they in the form of a book or journal article, appear to be qualitative at least. But will the study of history become more math-intensive or quantitative?
One important innovation in 21 century is the use of DNA analysis for historical and pre-historical research. Here is the book which lists some recent achievements: Nicholas Wade, Before the dawn. Discovery of the lost history of our ancestors, Penguin Press, NY 2006.
It is mostly about pre-history, but there are some amazing examples from history as well. (For example it was established that Jefferson had children from one of his slaves. An example from pre-history: it was possible to establish when people started to use cloth, by analyzing the DNA of lice:-). DNA analysis is certainly a quantitative method using many results of various exact sciences.
There are also several archeological dating methods based on exact sciences, but they were known since 20 century. The things like astronomy, chemistry and geophysics (climate history, for example) which are also exact sciences were used even earlier.