*Result*: The Secret of Ramsey Numbers: A new order forms out of randomness.

Title:
The Secret of Ramsey Numbers: A new order forms out of randomness.
Authors:
Edwards, Chris1 (AUTHOR) chris@chrised.com
Source:
Communications of the ACM. Jan2025, Vol. 68 Issue 1, p11-13. 3p.
Database:
Business Source Premier

*Further Information*

*This paper discusses recent advancements in Ramsey theory, focusing on breakthrough work by Sam Mattheus, a postdoctoral researcher at Vrije University in Brussels and Jacques Verstraete, a professor of mathematics at the University of California at San Diego, in determining bounds for off-diagonal Ramsey numbers, specifically 𝑟 ( 4 , 𝑡 ) r(4,t). Utilizing a novel combination of pseudorandom graph structures and finite geometry, their approach has resolved longstanding challenges and spurred new collaborations across mathematical fields, including coding theory and algebraic geometry. These developments underscore the potential of Ramsey theory to drive innovation in mathematics and theoretical computer science, offering new tools and techniques with broad implications for combinatorics and complexity theory.*