Greatest Empire

[Smartboy]

From the world historical point of view, which is the greatest empire - British? Roman? Greek? Inca? or Mongols?

[kidpacific]

None of the above. The Persian Empire under Cyrus the Great was nearly 30% larger than the one one under the Roman, Alexander the Great. Likewise, Cyrus was more tolerant than the Roman tradition, and in fact established that leadership mentality which the Romans later adopted. In terms of wealth, surprise surprise the Inca's probably had the greatest purchasing power of any of the empires you list but I am not certain that it was greater than Cyrus's Persia since he ruled the greatest percentage of mankind that has ever been beneath one empire. Incan silver however was so central to the world economy that some of Southern China's coinage was made with silver mined by the Inca's. The legacy of silver from South America came back to haunt China in the 19th century causing a huge depression and leading to revolution that ultimately led to downfall of the Qing in 1911.

[kidpacific]

Your question is about which was the greatest empire, not the wealthiest or biggest, so I must again return to Cyrus. He was the first world leader to make education a national objective and he believed in building libraries (something Alexander the Great later copied). He incorporated the culture positivies from all the peoples beneath him and created one of the most peaceful, productive empires of all time. All of the empires you list except the Incas are defined by mighty battles and a manifest destiny type of mandate. The British are perhaps the most lucid example-- English is the most widespread language isn't it? It was not uncommon however, for tribes and peoples to rejoice when Cyrus took them into his empire (with no armed conflict at all), for his empire was far more comfortable than the ones they had previously been in.
It is interesting that History preserves the legacy of Alexander more than it does of Cyrus, but then again humility was not among Alexander's repertoire, as it was hubris that caused him to get pneumonia and drop dead in the middle of central Asia.