Even Hilbert, however, could not foresee how mathematics would grow in the 20th century.  There were more and more mathematicians, more and more journals, more and more professional societies.  The phenomenal growth that had begun in the 1800s [sic] continued, with mathematical knowledge doubling every twenty years or so.  More original mathematics has been produced after astronauts first walked on the moon than there had been in all previous history.  In fact, it is estimated that 95% of the mathematics known today has been produced since 1900.  Hundreds of periodicals published all over the world devote a major share of their space to mathematics.  Each year the abstracting journal Mathematical Reviews publishes many thousand synopses of recent articles containing new results.  The 20th century (and perhaps this new century, as well) is justifiably called the “golden age of mathematics.”

Quantity alone, however, is not the key to the unique position the current era occupies in mathematical history.  Beneath this astounding proliferation of knowledge, there is a fundamental trend toward unity.  The basis for this unity is abstraction.  This conceptual unity has led in two directions.  On the one hand, new, more abstract subfields of mathematics have emerged to become established ares of research in their own right.  On the other, researchers working on truly big classical problems, such as Fermat’s Last Theorem or Hilbert’s twenty-three problems, have become increasingly adept at using new techniques from one area of mathematics to answer old questions in another.  As a result, the 20th century has been a time when many old questions were finally answered and many new questions have come to the fore.

–– Math through the Ages (A Gentle History for Teachers and Others)” by William P Berlinghoff and Fernando Q Gouvêa pages 53-54


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