I was recently involved in a debate on when science began. To avoid any personal bias, I turned to the Britannica Guide to the 100 Most Influential Scientists of All Time (2010), as a quick reference.
That list begins with the ancient Greeks Hippocrates (c. 460–375 BC) and Aristotle (384–322 BC), who were not really scientists in the modern sense. With the Persian Ibn Sina (980–1037) and the Englishman Roger Bacon (c. 1220–1292), however, we begin to get people thinking a little like modern scientists. As I have previously pointed out, the basics of the scientific method were established by Dante’s time, with development accelerating in Europe after the Fourth (Italian) Renaissance.
The bar chart above plots the 100 scientists by their century of death (many of those represented by the last bar are still alive, of course, and some scientists who will take their place in the last bar are not yet born). There is probably a significant bias towards modern scientists here, but (as shown) the data nevertheless fit an exponential growth beginning in the 12th century. This is consistent with the historical record. Science, it seems, began around the 1100s, with an influx of ideas from the Muslim world. But what made the Europe of that time (the early Gothic) such fruitful soil for science?
The Gothic Cathedral of Bourges, begun c. 1195, finished c. 1230
Update: see also Why did Science begin?