One of the first theorems in the field of mathematics combinatorialthat of Ramsey, It was formulated in 1928 by the British Frank Plumpton Ramsey, but it was not published until 1930, after his death. Several researchers have tried to advance the “upper limit” of the problem over the past 88 years. But it’s only recently that the feat has been achieved, by a team during the Summer Program of the Institute of Pure and Applied Mathematics (IMPA).

The group is made up of British Robert Morris (IMPA) and Simon Griffiths (associate professor at PUC-Rio), by the Canadian Julien Sahasrabudheassistant professor at the University of Cambridge, England and by the Brazilian Marcelo Campos (Doctor by IMPA). they congregate since 2018 to explore the problem.

After many studies, scientists have arrived at a new algorithm who is able to improve theorem limit In Ramsey. Since 1935, this is the most significant advance in the region. In a statement, The fields explain :

“The social network represents what in mathematics is called a graph”. “For us, what matters is the connection between the points of a graph. We are looking for the type of structure where all points are connected or none are connected”.

difficult task

However, according to Galileo, finding this structure is not easy, mainly because the interconnected pairs are determined “almost” randomly. the British mathematician William Timothy Gowerswinner of Fields Medal 1998, praised the band through a series of tweets.

Basically, all combinatorics researchers have tried to answer this question, myself included. Gowers. “I think it’s fair to say that this is one of the top two or three open problems in extreme combinatorics, or maybe even the best.”