Pakistani Researcher Solves One of the Most Important Maths Problems of 20th Century


Earlier this year, the Institute of Electrical and Electronics Engineering’s (IEEE) published “AI’s 10 to Watch” – a list of 10 people who are doing phenomenal work in the field of artificial intelligence.

A Pakistani researcher Haris Aziz, who had graduated from LUMS, had his name published in this prestigious list for his work in the field related to computational social choice, an intersection between artificial intelligence and economics.

Its seems that was just the beginning of the road for Haris Aziz, who is now back in the news for solving an ‘unsolvable’ mathematical situation.

Haris Aziz and His Work on Game Theory

Who will get the larger share of the profit from a business? Shall it be equally allocated or otherwise? Perhaps its your child ‘s birthday and its time to cut and divide the cake in a way that none of the children gets sad by his/her share? All the answers to such problems involving allocation and conflict-resolution can be given by the field of Mathematics named as “Game theory.”

In 2015, while working on the field of fair allocation, Dr Haris Aziz and PhD student Mr Mackenzie published a solution for envy-free allocation of an object (let’s say a cake) among four agents. The solution could prove to be valid for 4 to 203 cuts of the cake.

Now Dr. Aziz and Mr. Mackenzie have advanced their work & published an algorithm for “any” number of agents!

Their solution has been described as a “major breakthrough” by Professor Steven Brams at New York University, who has worked on such problems for more than 20 years.

“I was convinced that a bounded, envy-free cake-cutting algorithm [did]not exist. So the breakthrough result of Aziz and Mackenzie is nothing short of amazing. It is a beautiful piece of mathematics.” –  Fellow Researcher Ariel Procaccia at Carnegie Mellon University in Pittsburgh.

The paper is yet to be peer reviewed. However, Professor Brams told the Herald that the “results look solid”. Their results can be applied to diverse problems even as complex as conflicts between nations, like the Camp David accords between Egypt and Israel or the Spratlys Island dispute in the South China Sea.

We hope that our new algorithm opens the door for simpler and faster methods of allocation. One day, problems such as allocating access to a telescope among astronomers or the fair distribution of scarce water resources could be made very easy. – Dr. Haris Aziz

This accomplishment will open doors towards further discoveries in the field of mathematics and Artificial Intelligence algorithms.

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