Science is a body of empirical, theoretical, and practical knowledge about the natural world, produced by a global community of researchers making use of scientific methods, which emphasize the observation, experimentation and explanation of real world phenomena. Given the dual status of science as objective knowledge and as a human construct, good historiography of science draws on the historical methods of both intellectual history and social history. While empirical investigations of the natural world have been described since antiquity, and scientific methods have been employed since the Middle Ages, the dawn of modern science is generally traced back to the early modern period, during what is known as the Scientific Revolution of the 16th and 17th centuries. Scientific methods are considered to be so fundamental to modern science that some—especially philosophers of science and practicing scientists—consider earlier inquiries into nature to be pre-scientific. Traditionally, historians of science have defined science sufficiently broadly to include those inquiries.
The area of study known as the history of mathematics is primarily an investigation into the origin of new discoveries in mathematics. To a lesser extent it isan investigation into the standard mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. One striking feature of the history of ancient and medieval mathematics is that bursts of mathematical development were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 16th century, new mathematical developments, interacting with new scientific discoveries, were made at an ever increasing pace, and this continues to the present day.
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