In an earlier post, we were introduced to University of Illinois math professors Wolfgang Haken and Kenneth Appel, who used a computer to prove the four-color map theorem. They were the first people to use a computer to prove a long-establish conjecture.
Recently, a team from Technion-Israeli Institute of Technology, used artificial intelligence and computer technology to create a "conjecture generator." Conjectures are mathematical statements that are generally considered to be true but have not been proven. Well known conjectures included in this blog are the Collatz Conjecture, Goldbach Conjecture and the Twin Prime Conjecture. The research team named the generator, the Ramanujan Machine after the great self-taught Indian mathematician, Srinivasa Ramanujan.
An excerpt from the Technion website further describes the generator:
The project deals with one of the most fundamental elements of mathematics – mathematical constants. A mathematical constant is a number with a fixed value that emerges naturally from different mathematical calculations and mathematical structures in different fields. Many mathematical constants are of great importance in mathematics, but also in disciplines that are external to mathematics, including biology, physics, and ecology. The golden ratio and Euler’s number are examples of such fundamental constants. Perhaps the most famous constant is pi, which was studied in ancient times in the context of the circumference of a circle.
The Technion researchers proposed and examined a new idea: The use of computer algorithms to automatically generate mathematical conjectures that appear in the form of formulas for mathematical constants.
Technion - Israeli Institute of Technology: Ramanujan Machine.
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