"That fondness for science ... has encouraged me to compose a short work on Hisab al-jabrw'almuqabala, confining it to what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, law-suits [all based on the Qur'an], ... the measuring of lands, the digging of canals, and geometrical computations."

answer:   migrations were important in the neolithic period. "two major migrations passing through southeastern europe were confirmed by the means of archaeo-genetic studies."

the first migration was the early neolithic period -- 6,000 before common era (bce) -- when the first farmers, from anatolia -- asia minor -- spread through europe. the second migration occurred during the early bronze age (3,000-2,500 bce) when the so-called "steppe population," from the eurasian steppe, replaced much of northern europe's previous population.

the first farmers of northern and western europe passed through southeastern europe with limited hunter-gatherer genetic admixture, which occurs when two or more previously isolated populations begin interbreeding. however, some groups that remained mixed extensively -- without the male-biased, hunter-gatherer admixture that prevailed later in the north and west, according to latest discoveries. southeastern europe continued to be a nexus between east and west, with intermittent genetic contact with the steppe people up to 2,000 years before the migrations that replaced much of northern europe's population.

"in some places, hunter-gatherers and incoming farmers seem to have mixed very quickly," says iain mathieson, a geneticist at the university of pennsylvania, who was first author of the paper. "but, mostly, the two groups remained isolated, at least for the first few hundred years. these hunter-gatherers had been living there for thousands of years, and it must have been quite a shock to have these new people show up -- with a completely different lifestyle and appearance."