Roman scientific achievements are mostly in the areas of medicine and engineering. The Romans invented a lot of new ways to mine for metals like silver and gold and lead. They developed water mills as well for grinding grain. And they were the first people to really use concrete for major building projects. The use of concrete helped them to develop the dome and the barrel vault and the cross vault. They used their vaults to build aqueducts to carry fresh water to towns, and they used their engineering skills to build sewage systems to keep their towns clean and healthy.
Roman subjects in Phoenicia also invented blown glass, and mold-made pottery and oil lamps were also first made in the Roman period.
The Romans didn't do that much work in mathematics, but they did develop their own way of writing numbers.
To find out more about Roman science, check out these books from Amazon.com or from your library:
Science in Ancient Rome, by Jacqueline Harris (1998).