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Numa was a Sabine, and a contemporary of Romulus. When Romulus died, the people of Rome were little more than a disputatious rabble, still divided along the tribal divide between Romans and Sabines. However, they had suffered enough under the last tyrannical years of Romulus' reign that they made an effort to find a moderate ruler who could unite the city's warring factions, and bring stability to Rome. They decided to hold a vote between two nominees: a Sabine nominated by the Romans and a Roman preferred by the Sabines. Numa, a Sabine, won the vote and - after some initial reluctance - became the second king of Rome. 

Numa was an unusual ancient king in that he was a scholar and mystic, rather than a warrior and conqueror. Numa did not add any territory to Rome's dominion. What he did was set Roman culture on a path towards greatness. He did this by instituting many of Rome's religious practices and festivals, which he saw as providing a means to impress upon the Roman masses a sense of wonder and awe for the universe. Plutarch claims that Numa was a disciple of Pythagorus (of Theorem fame), a belief apparently widespread in Rome, but unlikely as the two men lived a century apart. While Pythagorus is known now as a mathematician, he was known to the ancients as a mystic and philosopher whose innovations in geometry were directed more towards a religious end than a scientific one.

A prime example of this is the story of Numa's creation of the vestal virgins. Plutarch writes that they were among the most essential elements of Roman religious practice because they were tasked with keeping the vestal flame lit. For the Romans, fire (read: the sun) was the essence of life, and the vestal flame was a symbol of pure holy fire. Numa lit the vestal flame using a technique derived from the Pythagorean Theorem. The flame itself was kept in a circular room with the flame in the center, and the circular walls representing the manner in which the Earth circled the fire/sun. The basic mysteries of Roman religion were thus dependent on their knowledge of astronomy and geometry. 

Plutarch also credits Numa with instituting the 12-month, 365-day calendar. Before Numa, the Romans had used  a 10-month calendar, devised by Romulus, which began in March and ended in December, with two blank months in between. (this was apparently a typical characteristic of ancient calendars, which were used primarily to regulate the growing season) Numa created the months of January and February, and then instituted the practice of beginning the year in January. Numa's calendar wasn't perfect - the solar and lunar cycles eventually became decoupled from each other, requiring further tinkering, for example. However, it was an improvement over what came before, and was the basis for the calendar we know today. 

To quell the endless fighting between the Romans and Sabines, Numa divided the Romans into divisions based on their employment, creating guilds for the various occupations. This reduced violence in the city by causing people to focus on business rivalries, rather than blood rivalries. To alleviate the overcrowding and underemployment resulting from the large numbers of poor people within Rome's walls, Numa divided Rome's rural areas and assigned each of the urban poor to lots. His idea was to put people to work and improve their character through the bracing life of a farmer, who must remain attuned to the seasons, the weather, and the vagaries of nature. 

These were Numa's major innovations. He was also a benevolent ruler whom the Romans admired for his sense of justice, and for the peace that he brought with him during his reign. At his death, Numa asked that he be buried in one casket, and his writings and mathematic works be buried next to him in a second casket. The Romans did so. generations later, the Romans inadvertently dug the caskets up. The one containing Numa was empty, but the Romans found voluminous writings in the other. These writings were burned with the Roman leaders believing that the Roman people should not see their contents. Such was life in the ancient world, where the learning of one generation was easily lost by the carelessness of its successors.