Computer scientists are abuzz over a fast new algorithm for solving one of the central problems in the field. (January 15, 2017, update: On January 4, Babai retracted his claim that the new algorithm ...

Abstract Let 𝑝 be an odd prime such that the Greenberg conjecture holds for the maximal real cyclotomic subfield 𝕂₁ of ℚ[𝜁𝑝]. Let 𝐴𝑛 = (𝐶(𝕂𝑛))𝑝 be the 𝑝-part of the class group of 𝕂𝑛, the ...

If someone asks you to determine whether two objects are the same, it might seem like a trivial request. In most everyday cases, a quick glance is enough for you to render an accurate judgment. But in ...

The Nature Index 2025 Research Leaders — previously known as Annual Tables — reveal the leading institutions and countries/territories in the natural and health sciences, according to their output in ...