Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.
Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite.
Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now.
For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.
John Priscu’s search for life that thrives under ice took him to subglacial lakes at the South Pole. Now he has his eye on Mars and Europa.
Einstein’s equations describe three canonical configurations of space-time. Now one of these three — important in the study of quantum gravity — has been shown to be inherently unstable.
For the first time, physicists have calculated exactly what kind of singularity lies at the center of a realistic black hole.
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