What did the Romans ever do for maths? Very little
Despite advances in many areas, Romans were happy with mathematical rules-of-thumb
A Roman abacus. But what did the Romans really do for mathematics?
The ancient Romans developed many new techniques for engineering and architecture. The citizens of Rome enjoyed fountains, public baths, central heating, underground sewage systems and public toilets. All right, but apart from sanitation, medicine, education, irrigation, roads and aqueducts, what did the Romans ever do for maths?
It might be thought that the great Roman works of engineering and architecture required advanced mathematical understanding and achievement. However, this is a false view. The reality is that, in relation to mathematics, the Roman contribution amounted to essentially nothing.
The Romans were disinterested in speculative or logical investigation. They regularly applied simple mathematics to solve practical problems. They also needed elementary arithmetic for surveying and for managing trade and taxes, but they were satisfied with rules-of-thumb that called for little in the way of understanding of the great body of theoretical Greek scholarship.
Any educated person asked to name a mathematician of the ancient world would have no difficulty. Certainly Pythagoras, Euclid and Archimedes are universally familiar, even to people without any knowledge of their work. But they are all Greek. The Wikipedia list of Greek mathematicians names nearly 100 ancient mathematicians from the Hellenic world. There is no corresponding list for ancient Rome.
Greek mathematicians continued under the rule of the Roman Republic and later in the days of the Empire, but there were no noteworthy native Roman mathematicians. There is not a single name from the Roman Empire worthy to stand alongside the great mathematicians of Greece.
Roman engineers and military technologists were interested only in simple mathematics that was essential for solving practical problems. Curiously, they took little interest in Greek trigonometry, which could have been of great value in surveying, engineering and astronomy. They were oblivious to the beauties of theoretical mathematics and geometry that were so highly valued by the Greeks.
The creation of the Roman calendar organised by Julius Caesar, which included a leap day every four years in a 365-day annual cycle, involved some tricky mathematics. But it was a Greek astronomer, Sosigenes of Alexandria, who carried out the design. His scheme stood for 1,500 years until it was replaced by the Gregorian calendar used in modern times.
Boethius, a philosopher and statesman who lived around the end of the Empire, has been described as one of the foremost mathematicians of ancient Rome, but this says little. He wrote textbooks on the four mathematical branches of the liberal arts, but they were no more than elementary summaries of earlier Greek classics.
His Geometry comprised only statements of the simpler theorems of Euclid’s Elements, without any proofs. His works on Arithmetic, Astronomy and Music were little better. Nevertheless, these books had widespread influence and were used extensively in medieval monastic schools, including the Irish monasteries. Cassiodorus and Isidore of Seville, contemporaries of Boethius, also wrote mathematics books, but neither contributed anything original.
During the Second Punic War, the city of Syracuse was besieged by the Romans. The great geometer Archimedes, who lived there, invented ingenious war machines to hurl stones, hooks to smash the Roman ships and mirrors to set fire to them. Alas, when the city was sacked in 212 BC, Archimedes was slain by a Roman soldier. The murder of Archimedes was perhaps the most profound impact of the Roman civilization on mathematics.