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ancient · c. 200 CE
A cryptic rule in the Mishnah for splitting a bankrupt estate baffled scholars for two thousand years, until two mathematicians in 1985 discovered it was a solution concept from cooperative game theory all along.
Facts reviewed 2026-07-11.
The Mishnah, compiled around 200 CE, is the foundational text of rabbinic law, a distillation of centuries of legal reasoning. One passage addresses how to divide the estate of a man who dies owing three creditors more than he owns, and it prescribes divisions that, for centuries, no one could reconcile with any consistent principle.
When the total claims equal the estate, the rule looks proportional. But in other cases it prescribes an equal split, and in still others something stranger. Generations of Talmudic scholars treated the numbers as either inconsistent or dependent on lost reasoning.
The sages were not doing arithmetic for its own sake. They were encoding a theory of fair division under conflicting claims, one that behaves differently depending on how scarce the estate is relative to the debts. In tight cases it protects the smallest claimant; in loose ones it approaches proportionality. The rule embodies a coherent sense of equity that its authors could apply but never formalized.