Since the dawn of history (and certainly before) people have bickered, even battled, over the fair distribution of resources—for example, the division of estates, disputed territories and the spoils of war.
Figure 1. Babylonian Talmud contains the earliest (second century A.D.) record of what mathematicians now call a fair-division problem. Fair division seeks to divide resources in a way that produces maximum satisfaction among all parties. In the talmudic example shown in Hebrew above (original, or Mishna, text highlighted in tan), a man dies owing 100, 200 and 300 zuz to claimants A, B and C, respectively. The solution, shown at right, is not always proportional: If his estate is worth 100 zuz, then each claimant is given equal shares of 100/3 each; if his estate is worth 200 zuz, then A gets 50, and B and C each get 75; and if the estate is worth 300 zuz, then A receives 50, B 100 and C 150. This unusual (to modern sensibilities) approach actually anticipates the "nucleolus" solution, one of many fair-division problems solved by mathematicians in the past 50 years.
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