They never made an overwhelming shift to mathematical / science based civilization. They took over Syracuse with a mandate to keep Archimedes alive, but that failed. Some scholars say the only roman contribution to math was numerals.

Basically they reaped the profits of empire, and fell into the cargo cults of opulent success, abandoning the prior agricultural based common sense by never integrating new ideas in the Aristotelian domains except for to pay homage to the originating culture enough to collect taxes.