The press highlights IMPA's progress in Ramsey's Theorem.

The discovery of a new algorithm capable of improving the limit of Ramsey's Theorem, developed at IMPA, was featured on the front page of the newspaper O Globo. this Sunday (7); in Folha de S.Paulo ; in the online edition of Revista Galileu and also in Quanta Magazine .

In Globo, the work of Robert Morris, a researcher at IMPA, Marcelo Campos, who holds a doctorate from IMPA, and researchers Simon Griffiths, from PUC-Rio, and Julian Sahasrabudhe, from Cambridge, had an entire page of the morning newspaper dedicated to the most significant advance in the field in the last 88 years.

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“What is the minimum size a group of people needs to have so that, in a subgroup, everyone knows each other or none of them know each other? In 1935, the Hungarian mathematician Paul Erdős, along with his colleague George Szekeres, formulated a proof that there is a maximum limit to finding a clique of a certain size k, which is 4k (4 raised to the ak). Since the 1930s, however, no mathematician had found a better general rule to establish this limit. Until the work done in Rio (…) finally presented a breakthrough. In a mathematical study that occupies 56 pages of calculations and demonstrations, the scientists offer a formula that slightly reduces the maximum limit for the number k in Ramsey's theorem — in the example above, instead of 4k the solution would be 3.9995k,” explains the report.

Crédito: Jornal O Globo

Crédito: Jornal O Globo

In an interview with O Globo, Robert Morris said the results were a surprise. “When it worked, it was surprising even to us. We were trying to do something more complicated and, following that path, we weren't succeeding. Only later did we find this solution, which is actually much simpler than we were expecting.”

The newspaper also highlighted that the breakthrough was celebrated by mathematicians worldwide, including Timothy Gowers, winner of the Fields Medal, the equivalent of the Nobel Prize in mathematics. Read the full report here.

The Folha de S.Paulo report was published on Saturday (6). The newspaper explained that the 0.005 advance “may stimulate more research with the theorem and have an impact on computer science, an area closely linked to combinatorics.” The report also said that studies involving the problem began in 2018 at IMPA, with Morris, Sahasrabudhe and Griffiths, and that the trio formulated numerous proposals over the years.

Folha de S.Paulo

Marcelo Campos joined the group in 2021. "The scientists held meetings to discuss the problem and, at the beginning of each year, they met in person at IMPA's summer course to spend the weeks in front of a blackboard, using chalk as their weapon," says an excerpt from the report.

Speaking to the newspaper, Campos said that "only now, in 2023, have we found a strategy that really worked," he concluded.

Read the articles from Quanta Magazine and Galileu Magazine here.

Galileu

Quanta Magazine