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Jacques Verstraete and Sam Mattheus, researchers at the University of California, San Diego, have made a significant breakthrough in Ramsey theory by solving the r problem, a challenge that has eluded mathematicians for decades.We’ve all been there: staring at a math test with a problem that seems impossible to solve. What if finding the solution to a problem took almost a century? For mathematicians who dabble in Ramsey theory, this is very much the case.
“It’s a fact of nature, an absolute truth,” Verstraete states. “It doesn’t matter what the situation is or which six people you pick — you will find three people who all know each other or three people who all don’t know each other. You may be able to find more, but you are guaranteed that there will be at least three in one clique or the other.”
“Many people have thought about r — it’s been an open problem for over 90 years,” Verstraete said. “But it wasn’t something that was at the forefront of my research. Everybody knows it’s hard and everyone’s tried to figure it out, so unless you have a new idea, you’re not likely to get anywhere.” In 2019, to the delight of the math world, Verstraete and Mubayi used pseudorandom graphs to solve r. However, Verstraete struggled to build a pseudorandom graph that could help solve r.
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