The period of history known as THE DARK AGES spans from 475 AD (fall of the Roman Empire) to 1200 AD when Universities started forming.
During this time, material conditions deteriorated so much that people had to concentrate all their efforts on daily survival and science became stagnant.
However, there are 2 common misunderstandings related to this period:
1. Everybody thought again that the Earth was flat or had the shape of a chest, and knowledge of a spherical Earth was lost completely, only to be recovered when Columbus discovered America. But this is not true. The idea of a round Earth was never lost among scholars and among the cult circles, small as they became in the darkest of the dark ages.
2. Science and scientists were persecuted by law. This is also untrue. The claim has to do with the Theodosian and Justinian code, from 400 and 500 AD respectively. But the articles in these "codexes" or laws banished superstition and divination, activities which were known at the time by the Latin name "MATHEMATICA", because of the complicated calculations astrologers had to make in order to get their horoscopes.
On the other hand, the social situation had deteriorated to such an extent that Roman Empire ruling class had a strong will to get rid of threats of war from outside by the barbarians, but also from division in the inside because of the abundant heresies (Nestorians, Arians, Priscillians... ). This situation caused pagan science to suffer consequences similar to persecution: academies and schools were closed, scholars were banished, informers thrived; but there was never a formally written law against science.
Science during the dark ages was stagnant: annotators, commentators, translators, no advance. Preserving and transmitting knowledge in monasteries and a few reduced circles. Material conditions didn't allow for more.
Ignorance extended widely among society, especially the popular classes, but it doesn't follow from that, that everybody thought the Earth was flat again.
Science wasn't persecuted by law, but material conditions and human weaknesses created an atmosphere that crushed pagan science.
Initial rejection of pagan science for the reasons explained, turned later into acceptance by the very church fathers, from Augustine of Hippo (354-430AD) who concentrated in resolving contradiction conflicts with scripture in a process that lasted until the end of the period, when Aristotle (V century BC) was finally admitted into Christian lore, thanks to the works of Albertus Magnus (1193-1280) and Thomas Aquinas (1225-1274).