Europe 500 years after the fall of the Roman Empire was well past the Roman peak in just about every respect. Stuff like literacy rates and population density

Europe 500 years after the fall of the Roman Empire was well past the Roman peak in just about every respect. Stuff like literacy rates and population density are hard to compare. Yet look at say yields per acre, metallurgy, defensive fortifications, armor, siege weapons, etc and Europe was far more advanced technically. The general population saw a net lifestyle improvement fairly quickly, excluding the direct advantages of being part of a large empire. We tend to think of Math as not recovering for 1,000 years but ditching Roman numerals was a clear advantage that didn’t take nearly as long. So, objectively it’s more complicated. Instead, it’s the myth of the Roman Empire which took a long time to surpass.