## Department of Mathematics and Statistics

#### Resources

##### Main Campus
###### University Hall

Second Floor Rm 2040
419.530.2568
419.530.4720 Fax

The University of Toledo
Dept of Math and Statistics
University Hall 2nd Floor Suite
2925 W. Bancroft Street
Toledo, OH 43606

## Delta X/Pi Mu Epsilon 2016 Combined Meeting

You and your guests are cordially invited to attend a joint meeting of Delta X, a mathematics student interest organization at the University of Toledo, and the Ohio Gamma Chapter of Pi Mu Epsilon, a national mathematics honor society, which will have an initiation ceremony for new members. Anyone interested in mathematics is welcome to attend. Dress is casual.

The speaker at the Initiation Ceremony (held Wednesday evening, November 2, 2016) will be Professor Alessandro Arsie, Department of Mathematics and Statistics, University of Toledo.

November 2, 2016 (Wednesday, 7:30pm in FH 2100)

Alessandro Arsie (University of Toledo)

A mathematical puzzle from the Talmud

Abstract: A man dies leaving an estate that is too small to pay all his debts. How should the estate be divided among his creditors? The Talmud, a compendium of Jewish law dating back to 1800 years ago gives the following teaching.

There are three creditors, creditor 1 is owed 100, creditor 2 is owed 200 and creditor 3 is owed 300. The Talmud (Tractate Ketubot 93a) says:

• if the estate of the man who died is 100, then each creditor gets 33 and 1/3;
• if the estate of the man who died is 200, then creditor 1 gets 50 and creditors 2 and 3 both get 75;
• if the estate of the man who died is 300, then creditor 1 gets 50, creditor 2 gets 100 and creditor 3 gets 150.

What algorithm is the Talmud using? People have been trying to answer this for 1500 years and there were famous Jewish scholars, like Maimonides who thought that this example did not make any sense. Naturally, as in any legal system, the answer must be based on the system's principles.

The problem was finally solved in the 1980's by Robert Aumann (PhD in Mathematics, 1955 and Nobel Prize in Economics in 2005, also a religious Jew) and by Michael Maschler. Later, Marek Kaminski showed how the solution can be constructed using a hydrodynamic analogy!

I will explain their ingenious solution and its relation to game theory (as time permits), with some other mathematical algorithms that appear in the Talmud. Within the framework of Jewish culture, the solution provides insight into the moral question of what creditors are owed when they can't be paid in full.

Congratulations to the new initiates of Pi Mu Epsilon.

For further details contact:

• Dr. Ivie Stein Jr., Department of Mathematics and Statistics,
• EMAIL: Ivie.Stein@utoledo.edu.
• PHONE: (419) 530-2994 (voice mail)
• Department Phones: (419) 530-2568, 530-2232.

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