"Revolutionary Breakthrough: Mathematicians Push the Limits of the Coloring Problem"
Mathematicians have made a breakthrough in the coloring problem, which involves determining how much of an infinite plane can be colored while ensuring that no two colored points are exactly one unit of distance apart. After decades of research, a team of mathematicians from the Budapest University of Technology and Economics, the Hungarian Academy of Sciences, and other institutions used machine learning models and optimization techniques to prove that no more than 24.7% of the plane can be colored without unit-distance pairs, breaking the previous upper bound set by Paul Erdős. The researchers are now focusing on determining the chromatic number of the plane, which represents the minimum number of colors needed to completely cover the plane while avoiding unit-distance pairs.