The Brams–Taylor theorem is a result in fair division

Fair division

Fair division, also known as the cake-cutting problem, is the problem of dividing a resource in such a way that all recipients believe that they have received a fair amount...

 discovered by Steven Brams

Steven Brams

Steven J. Brams is a game theorist and political scientist at the New York University Department of Politics. Brams is best known for using the techniques of game theory and public choice to research voting systems and fair division. He is one of the independent discoverers of approval voting...

 and Alan D. Taylor

Alan D. Taylor

Alan Dana Taylor is a mathematician who, with Steven Brams, solved the problem of envy-free fair division for an arbitrary number of people with the Brams–Taylor procedure.Taylor received his Ph.D...

. First published in the January 1995 issue of American Mathematical Monthly

American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is currently published 10 times each year by the Mathematical Association of America....

, it explicated the first finite procedure to produce an envy-free

Envy-free

In mathematical sociology and especially game theory, envy-free is a property of certain fair division algorithms for a divisible heterogeneous good over which different players may have different preferences....

 division of an infinitely divisible good among any positive integer number of players. Prior to the discovery of this theorem, Sol Garfunkel

Sol Garfunkel

Solomon "Sol" Garfunkel is an American mathematician who has focused his career on mathematics education and is best known for his mathematical television series For All Practical Purposes....

 contended that the problem solved by the theorem, namely the n-person cake cutting problem, was among the most important problems in 20th century mathematics.