Clearly we are making a huge jump here from the Greeks to the so called scholasticism. This is of course to ignore major schools that followed Aristotle such as neoplatoism & stoicism. It is to ignore Roman philosophy and falsely it implies that nothing much happened for hundreds of years. Indeed the same can be said for the medieval period itself. This was widely regarded as an insignificant interlude between the Greeks and the so called moderns. Scholasticism was normally taken to describe a sterile philosophy written in bad Latin and above all subservient to the theology of popery. Today's scholars are more interested in the medieval period without prejudgement.
Various dates are given for the origins of this philosophy. Today's history of medieval philosophy tend to start with St Augastine (354 - 430 AD). However Augastine belonged very closely to the worlds of Greece and Rome (particularly the Stoics and neoplatonic schools) and he put that knowledge to work in the illustration of fundamental concepts such as those of God, eternity, good & evil, and creation.
Another approach to the origins of medieval philosophy is that of Hagel who located the transition from antiquity to the middle ages in 529 AD when a decree from the Emperor Justinian (a Christian) closed the platonic academy an Athens and sealed "the downfall of physical establishment of pagan philosophy" (note this academy had a history of over a thousand years.) In that same year (529 AD) the first Benedictine abbey was established. And so we see the beginnings of a shift in intellectual life from places like platonic academy to the cloisters of Christian monasteries.
Like St Augastine the medieval thinkers philosophised because they wished to understand Christianity. Indeed the first great philosopher of the middle ages, St Anselm of Canterbury (1033 - 1109 AD) was deeply influenced by Augastine and St Tomas Aquinas (1224/5 - 1274) referred to Augustine more often than any other church authority.
The high point of scholasticism in the 13th century, centred around people like Albertus Magnus and Tomas Aquinas. By the 14th century we have the decline and disintegration of scholasticism.
The aim was to achieve the "whole attainable truth" consistent, however, with the teachings of Christianity. In this connection a pivotal 6th century scholar was Boethius who wrote a book called "The Consolation of Philosophy". However his reputation as one of the founders of scholasticism refers to the last sentence of an important work on the Holy Trinity: "as far as you are able, join faith to reason.". For centuries this was to become the foundation of scholasticism, various expressions (e.g. revelation, authority, tradition) could be used in place of "faith". But from the beginning thought was concerned with this potentially explosive encounter between faith and reason, or subjectivity and objectivity, or what is accepted and what is subject to proof. Eventually this was to lead to the rationalistic conviction that there cannot be anything that exceeds the power of human reason to comprehend even the mysteries of divine revelation. To be sure the great thinkers of scholasticism, in spite of there ephatic affirmation of faith and reason, consistently rejected any such rationalistic claim. But it must be admitted the possibility of rationality being emphasised at the expense of faith.
Anselm had practically unlimited confidence in the power of human reason to illuminate even the mysteries of Christian faith, indeed, his famous phrase "Fides quaerens intellectum" (faith seeking understanding) is a perfect description of the philosophy of the Christian west written throughout the middle ages. Christianity they clamed was not incompatible with what can be demonstrated by reason. The doctrine of "double truth" associated with Averroes of Spain (12th century) which declares that 'truth of faith can be incompatible of truths sanctioned' by reason made very little impact upon thinkers of the Christian west.
And then came an upheaval that would shake this emphasis on a faith / reason balance to its foundations. At the start of the period the works of Aristotle where on the whole unknown. Gradually more of his writings reached the Christian west from the Muslim world accompanied by profound and learned commentaries, particularly by Avicenna and Averroses. Aristotle became the philosopher to which every philosopher and theologian had to react.
The crucial question became not if Christianity and philosophy were compatible, but if Christianity and the teachings of Aristotle where compatible.
Albertus Magnus was the first (13th century) to accept the challenge of Aristotle's philosophy. He devised new methodological principles e.g. "there can be no philosophy about concrete things" and "in such matters only experience can provide certainty". Reason had acquired a new meaning, implying now the capacity to grasp the reality that human beings encounter. From now on it was no longer a matter of "joining faith and reason" but of making sense of the multiplying stock of natural knowledge of the individual and the universe. It was his pupil Tomas Aquinus who thought of a system, that was intellectually consistent, to unite the bible and Aristotle (i.e. the affirmation of natural reality as a whole including the body and the mind). Towards the end of his life he went back to seek more consistent understanding of creation and createdness. Secularism was growing and theologies became more mistrustful of the capacities of natural reason.
For Aquinus faith presupposes and needs natural knowledge of the world and at times an error concerning the creation leads us also from the truth of faith. Yet he admitted that not only do human beings not know what God is, but they do not know the essence of things either. Aquinus did not succeed in bridging the faith / reason gulf.
After he left Paris 1272 and after his death in 1274 the gulf became much more radical; and in 1277 the archbishop of Paris formally condemned a list of sentences, some of them close to what Tomas himself has allegedly, or really taught. Instead of free disputes among individuals organised "schools" now began to form and mutual distrust began to develop between theology and philosophy. However it is not until the next generation that the principle "join faith with reason" was repudiated.
The concept of "freedom" became important, particularly with an important Franciscan Duns Scotus in the 14th century. Scotus used freedom with reference to God who alone had absolute freedom. It was therefore futile to attempt to link faith with speculative reason. Faith is one thing and knowledge is an altogether different matter, and conjunction of the two is neither meaningfully possible nor even desirable. Faith and reason, which had been linked for thousands of years, where in the process of separating. And with that separation came the end of Medieval scholasticism.