Equidecomposability of polyhedra: a solution of Hilbert's third problem in Kraków before ICM 1900 (Q1670966)

The authors show that Hilbert's third problem had in fact been solved by Ludwik Antoni Birkenmajer in his entry to a prize competition organised by the Kraków Academy of Sciences in 1884. He was awarded the prize, but never published his solution. The authors have found and examined it, and find it to be correct. He used a different method to the one found later and entirely independently by Max Dehn that is usually taken to provide the first solution to Hilbert's problem. A short biography of Birkenmajer is also provided.