Chinese mathematicians have resolved the loose end of a “doomsday hypothesis” that had long puzzled the mathematical community.
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The feat was made possible through major computational methods which could be applied to further problems in the field.
As a result of the breakthrough, the mathematical world finally has proof that manifolds of Kervaire invariant one do exist in dimension 126, ending a decades-long mystery.
The Kervaire invariant is a function that measures whether a smooth framed manifold, or a topological space or shape that can have curvature but locally appears flat, can be converted into a sphere through “surgery,” a concept introduced by American mathematician John Milnor in 1950.
If it can be converted into a sphere, the invariant evaluates to zero. The Kervaire invariant problem seeks to discover dimensions in which the answer is non-zero, or one, meaning they can host strange shapes that do not convert into a sphere.
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The paper, which has not undergone peer review, was written by Wang Guozhen and Lin Weinan from the Fudan University Shanghai Centre for Mathematical Sciences and Xu Zhouli from the University of California Los Angeles (UCLA).