# MATH NOTES **Ramsey theory** The "R" stands for Ramsey numbers, which look at how large a network (or graph) must be to guarantee that a certain size of interconnected or disconnected relationships must exist. Essentially, it proves that complete chaos is impossible. *If an evil demon threatened to destroy the Earth in two years unless we could tell him the value of R(5,5), our correct response, said Erdös, should be to devote all mankind’s resources to the problem — we could probably solve it in two years. But if the demon instead asked us to tell him the value of R(6,6) — then, said Erdös, we should devote all our resources to finding a way to kill the demon.* - **R(3,3) = 6**: This is the classic "party problem." In any group of six people, you are guaranteed to find either three mutual acquaintances or three mutual strangers. This is easy to prove. - **R(4,4) = 18**: This took significantly more effort to prove, requiring serious mathematical work to pin down the exact number. - **R(5,5) = 43 or 48**: We still do not know the exact number. In 2023, mathematicians made a major breakthrough by narrowing down the bounds, but calculating the exact figure requires checking a nearly infinite number of network combinations. - **R(6,6) = Unknown**: The number of potential configurations you would have to check to find R(6,6) is larger than the number of atoms in the observable universe. No supercomputer we could ever build would have the time or processing power to brute-force it. [Ramsey Numbers: A Problem of Galactic Proportions](https://somacdivad.medium.com/ramsey-numbers-a-problem-of-galactic-proportions-32f1c7a43e9f)