Are quantitative or mathematical methods becoming more dominant in the 21st century historical research?
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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.
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Source: stackoverflow.com
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