The East Roman Empire survived until 30 years before Columbus reached America.
The Roman Empire is one of the greatest to ever spread across the Earth. It is certainly one of the best known and remains massively influential until this day. Modern roads are based on the size of ancient Roman roads. As a result, everything that is transported by road, including modern missiles, is based on the size of Roman roads.
For all its influence, Rome is seen as ancient history. The last of the Roman Empire, however, did not truly fall until much later than is normally imagined. The Western Roman Empire fell centuries before the Eastern Roman Empire, so the fall of Rome was, technically, long ago. That said, the Eastern Roman Empire held out around the rim of the Mediterranean until the Siege of Trebizond in 1461. Just over 30 years later, Christopher Columbus landed in the West Indies. So, living Romans would have heard about the discovery of the New World.