Indeed, although there is a bit of mythos surrounding the
  rediscovery. The BBC rendering of history still clings to old
  notions of dark/middle ages, even though that's discarded by
  historians now. The knowledge stayed intact elsewhere, but
  Europe _was_ in a crap state for a few hundred years. The
  beginnings of Scholasticism in the 11th century started to see a
  shift though. The start of the University system, with the
  assistance of the writings they had of aristotle and especially
  improved with 11th century commentaries. However, a HUGE boost
  came about during the Council of Florence in the mid 1400s. It
  completely failed in its aims to reunite the Eastern Churches
  and the Latin Church, who had gone her own way a few centuries
  before that, HOWEVER, the Byzantines, likely in a compassionate
  move, brought along a scholar named Gemistus Pletho along with
  others scholars, to help re-introduce the classics of Byzantine
  thought to an intellectually needy West, which they quickly
  translated from Greek into Latin and vulgar tongues and began
  teaching in their existing University system (which was already
  300 years old by then), bringing about a popularization of
  humanism and other thoughts to a new generation of students.
  Byzantium was struggling and it was only a few years later that
  it fell completely to Mehmet II, marking the end of an era for
  one intellectual culture yet thanks to the last-minute transfer
  of knowledge, brought about the start of another. Had Byzantium
  not falling to a "let's wipe out everything and do it right this
  time" mindset (which was new to Islamic education and began the
  start of the Ottoman empire), it's very likely that the East and
  West would've been able to join together in this new revolution,
  the old educating the new in an ongoing basis. But alas, all the
  West had were some books given right at the end of the Eastern
  Roman Empire and we've done the best we can with them ever
  since, shaping the course of Europe for centuries to come. We're
  still picking up the historical pieces and some of our
  misreadings of history have yet to be improved, but I think a
  lot of that has to do with an England-centric view of history
  that we've inherited since the 19th century.