Final answer:
The Romans significantly influenced engineering, law, and government, but their contributions to education were less original and therefore did not have as much influence on the Western world.
Step-by-step explanation:
The ancient Romans left a profound mark on Western civilization, influencing various aspects such as engineering, law, government, and language. Through their innovations in infrastructure—such as roads, bridges, aqueducts, and efficient urban planning—Romans connected and shaped their vast empire. They also set precedents in governmental structure with the Roman Republic serving as a model for later systems, featuring balanced branches of power. Moreover, Roman law forms the bedrock of the legal systems in many Western countries.
When it comes to the category in which Rome did not significantly influence the Western world, the answer is education. The Roman educational system was heavily based on that of the Greeks, and while the Romans did adopt and expand on some aspects, their contributions to the field of education were not as original or influential as their accomplishments in other areas. Thus, education is the domain where Rome's influence is less apparent compared to their profound impacts on engineering, law, and government.