Skim through some of the ancient literature, Vitruvius, Archimedes, Ptolemy, and you will quickly come to appreciate that the ancients excelled in both engineering and mathematics. Roman construction materials were manufactured to an Imperial standard. Construction methods reflected an understanding of physics.
The arithmetic used by the Egyptians, Greeks and Romans was derived from the Babylonian sexigesimal counting system. This system, in turn, derived from an ancient finger counting technique, and can still be recognized in applications which use 12,60,or 360 divisions of a whole. By the time of the Romans, finger counting techniques had reached the point where surprisingly complex mathematics could be worked out using "digital" techniques. The Romans also used a device called a counting table, similar in concept to an abacus, to extend the range and complexity of their calculations.
The concept of zero, one of the keys to modern mathematics, seems to have taken seed in many places and times. But it wasn't until the middle ages that it was generally accepted in Europe. Whether the Romans understood zero is a matter of some question.
Trigonometry was well advanced by Roman times, and was probably the "highest math" practiced by engineers. They were pretty good at using trig for surveying: water tunnels were dug from both ends, often extending many hundreds of feet underground, and meeting within a small margin of error. Newton was far in the future, as was calculus.
Good reading on this topic, as Drawoh pointed out, is L Sprague De Camp's book on ancient engineers. Also check out Vitruvius's "Ten Books on Architecture", and George Ifrah's books, "From One to Zero", "Universal History of Computing", and "Universal History of Numbers".