Fair cake-cutting (or, less imaginatively, 'fair division') is a branch of mathematics that deals with resources allocation. The aim is to divide resources such that all parties involved feel that they have received a 'fair share'. Various methods have been proposed to deal with this task. The simplest is the 'Divider-Chooser' method, in which one person divides the resources into two parts of equal value, and then the other person chooses. For more than two parties, the procedure becomes more complex. Some schemes prove effective in dividing up estates, and others work well for splitting territory. Fair cake-cutting has even been use to resolve conflict in the Middle East. There is still much work being carried out on designing a computer algorithm to efficiently generate optimal cake-cutting scenarios.
Bonus:
Speaking of tricky math problems, David Hilbert introduced a list of 23 problems at a conference of Paris in 1900. At the time, none of them were solved, and they were all considered crucial stepping stones in the progression of mathematics. At present, 9 have been definitively solved, another 9 have been 'partially solved', and an additional 2 have been deemed unsolvable on account of ambiguity in their phrasing. That leaves three unsolved.
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