Epilog

Summary

In a very real sense, the history of the world prior to the world wars could be treated as a collection of individual regional histories: the history of Asia, the history of the Americas, the history of Europe, and so on. Occasionally one region might influence another: the Mongol invasion of Europe; the scientific accomplishments of the Islamic states; European imperialism in the Far East. But the effects were either brief (the Mongol Empire virtually vanished within a generation), limited (European colonies in China were mainly limited to the coastal regions), or episodic (Islamic mathematics played a formative role in European mathematics, but almost no role after 1600). After World War II, it becomes impossible to treat each region of the world separately. The Soviet invasion of Afghanistan in 1979 led to the creation of the terrorist group that staged the attacks on the World Trade Center in New York City on September 11, 2001. Changes in the lending laws in the United States during the 1980s led to a world-wide financial crisis in 2008. Uncertainty in Middle Eastern affairs causes renewed interest in the resources of sub-Saharan Africa. We can no longer disentangle the history of one part of the globe from another.

Additionally, mathematics has become ever more specialized and in turn requires even more specialized knowledge to understand its applications. The most obvious example is the growth of computerization after World War II, which has led to new fields of mathematical research and new applications of old ideas: fractals, information theory, compression algorithms, operations research, and encryption schemes just to name a few.