It explicated the first finite procedure to produce an envy-free division of a cake among any positive integer number of players.
In 2016, Aziz and Mackenzie discovered a protocol that is even bounded by the number of players; for more details, see here.
In 1988, prior to the discovery of the BTP, Sol Garfunkel contended that the problem solved by the theorem, namely n-person envy-free cake-cutting, was among the most important problems in 20th century mathematics.
[2] The BTP was discovered by Steven Brams and Alan D. Taylor.
It was first published in the January 1995 issue of American Mathematical Monthly,[3] and later in 1996 in the authors' book.
[4] Brams and Taylor hold a joint US patent from 1999 related to the BTP.
If we want to make sure that Alice gets an IA over a specific player (e.g. Bob), then a much more complicated procedure is required.
This might take an unbounded time – depending on the exact valuations of Alice and Bob.