It is often said that the Roman Empire reached its greatest extent in the final years of Trajan, who was emperor from 98 to 117. As far as I know, the French philosopher Montesquieu already said so at the beginning of the eighteenth century. Two centuries later, Mussolini ordered maps of several stages of the Roman expansion to be made (the last one being the Fascist Empire); the map of the empire’s greatest extent under Trajan is still visible at the Via dei fori imperiali. In 2007, a Dutch schoolbook repeated that under Trajan, the Roman Empire reached its greatest extent. Everybody seems to know this – but it’s not the full truth.
What is true, is that Trajan added Dacia (modern Rumania) and Arabia Petraea (modern Jordan) to the Roman Empire. He also invaded Iraq, in 114. At first, the Roman armies were successful and reached the Persian Gulf, and in 115, victory was declared. Armenia and Mesopotamia were added to the empire, which at this moment indeed reached its greatest extent at this moment. However, almost immediately, revolts broke out, and 116 saw several rounds of inconclusive fighting. Trajan himself headed back toward Rome, but died on the way, and his successor Hadrian abandoned all conquests east of the Euphrates.
For about twenty-five months, the Romans claimed to control Armenia and Mesopotamia. It is misleading to say that this was the moment of the greatest extent of the Roman Empire. We must be looking for something more solid, more lasting. We can find it during the reign of Septimius Severus (198-211), who conquered much land between the Euphrates and Tigris, which the Romans never gave up, until they lost it to the Muslims, more than four centuries later.
In 201-202, Severus added several oases in the Libyan desert to the Roman Empire; several forts were built to ensure that Roman presence would be lasting. The desert between these forts was irrigated and developed. This project is called the Limes Tripolitanus. This was to remain loyal to Rome until the Vandals took over, more than two centuries later.
Septimius Severus added even more to the Empire. There was a small correction of the border near the Danube, and in 208, he tried to conquer Scotland. At some stage, he could rightfully boast to have expanded the empire in all directions. But to be honest, the occupation of Scotland is identical to the conquest of Iraq: it was Roman in name only. Severus’ son and successor Caracalla recalled the troops from Scotland. So 208-211 does not really count as the moment of Rome’s greatest territorial extent. 202 is a better candidate.