Hilbert's third problem

The third of Hilbert's problems presented in 1900 was the first to be solved. The problem asks the following:

Given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces which can be reassembled to yield the second?

Based on earlier writings by Carl Friedrich Gauss, David Hilbert conjectured that this was not always possible. His student Max Dehn confirmed the conjecture with a counterexample.

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