I believe that Boethius is considered essentially the last light of classical civilization in the West. Certainly not the creative genius of the earlier Greeks and even the Romans of 500 years earlier, his works helped transmit their ideas to thinkers of the medeival period, when many of the earlier works were lost, at least for a time. Of course, thinkers such as King Alfred, and the leaders of the Carolingian court, 3 and 4 centuries after Boethius, still considered that they lived in 'Romania', in the wider sense, the lands of Roman civilization.
People in later times said that these people lived in the 'Dark Ages', and they were well aware of their reduced level of culture. But their writings, and that of Boethius before them, contributed to the continuation of the conception of classical civilization until its revival in the Renaissance. Their continuing influence helped pave the way for this later revival of high culture.