ChatGPT Meets Elchanan Mossel's Dice Problem

Nov 11, 2023 ·

The article discusses Elchanan Mossel's Dice Problem, which has been a difficult problem in mathematics for over 20 years. It involves the question of how many dice need to be rolled to guarantee that the sum of the faces is greater than 7.

Elchanan Mossel proved that the answer is 3 dice. He then studied the same problem but with different constraints and found that the answer was typically higher than 3. This led to a more general version of the problem, involving various types of dice with different numbers of sides.

Mossel then asked a more difficult version of the problem: given a set of dice with any number of sides, what is the minimum number of rolls required to guarantee that the sum of all faces is greater than 7? After extensive research, he concluded that the answer can be determined by solving a system of linear equations.

Notably, OpenAI recently announced that they trained their ChatGPT language model on the Dice Problem, as part of a larger effort to teach machines to reason mathematically. The machine was able to understand the problem, infer the general equation that Mossel solved, and produce an accurate answer. This is a major milestone in artificial intelligence and machine learning, as machines are now starting to understand and solve mathematical problems.

The article also mentions some of the potential applications of ChatGPT and similar language models. These include education, where the model could be used to teach students about complex math, as well as Artificial General Intelligence (AGI), which would involve teaching machines to reason like humans. In addition, the technology can be used for medical diagnosis, helping doctors to accurately diagnose illnesses.

In conclusion, Elchanan Mossel's Dice Problem has proven to be an incredibly challenging problem, requiring immense amounts of research and thought. However, OpenAI's recent breakthrough with ChatGPT has enabled machines to understand and solve the problem, leading to exciting possibilities in both education and Artificial General Intelligence.