Fair Share: 111 Problems from Ahmes to Aumann

American businessman, John Landgraf stated: “I hope that most of us believe that we actually would all benefit from living in a more equitable society. If that's not happening, we're squandering human potential.” For the world to be fair, one needs to know how to divide. Without the mathematics of division, humankind cannot function…

Marie Antoinette, Queen of France (infamously) said “If people have no bread, let them eat cake,” and while Ahmes ― the scribe of the Rhind Mathematical Papyrus ― dealt with loaves of bread, prosperous people in the twentieth century dealt with cake division, although bread is also uniformly available. You’ll be surprised, but there are at least four books and over 200 scientific (not gastronomical!) papers on cake division. Those authors were not overly concerned with obesity, one can guess, but whether distributing loaves, cakes, chores, or dividends, one needs to master division.

Isaac Elishakoff serves as a Distinguished Research Professor at the Florida Atlantic University (FAU), in Boca Raton, Florida, USA. He has authored 18 books and over 590 scientific papers. He was awarded the Worcester Reed Warner Medal by the American Society of Mechanical Engineers in 2016, the Blaise Pascal Medal by the European Academy of Sciences in 2021, and the FAU President’s Award for Career Achievement in 2023.