MIT博士生Alex Cohen成功证明了分形不确定性原理在所有高维空间中的成立，将这一原理从一维扩展至更高维度 [1]。这项成果已发表在2025年《数学年刊》上 [1]，揭示了量子波与经典波在混沌环境下的根本差异：量子波无法被困在分形路径上，而是会不断扩散逃逸 [1]。
分形不确定性原理表述为：若在分形集上叠加波，结果曲线不能同时具有分形特征；反之亦然 [1]。这一基础数学工具已被应用于研究混沌系统中的波传播行为 [1]。2016年，Semyon Dyatlov与Jean Bourgain首次在一维情况下证明了该原理 [1]。Cohen在2023年5月在线发布了自己的高维证明 [1]，其工作随后被Kim与Nicholas Miller利用于2025年扩展双曲空间中的相关结果 [1]。数学家Bourgain在2018年底去世前留下的未发表笔记为Cohen的研究提供了关键启发 [1]。
Cohen已获得纽约大学的助理教授职位 [1]。
MIT doctoral student Alex Cohen has extended the fractal uncertainty principle to higher dimensions, resolving a longstanding open question in mathematical physics.[1] The principle states that when a wave is superimposed on a fractal set, the resulting curve cannot simultaneously exhibit fractal characteristics; the inverse relationship also holds.[1] Cohen's proof reveals a fundamental distinction between quantum and classical particles under chaotic conditions: quantum waves cannot be confined to fractal trajectories but will instead diffuse and escape.[1]
Cohen published his findings in the Annals of Mathematics in 2025, building on earlier work by Semyon Dyatlov and Jean Bourgain, who established the principle in one dimension in 2016.[1] The researcher first released his proof online in May 2023, drawing critical inspiration from unpublished notes left by Bourgain before his death in late 2018.[1] Subsequently, researchers Kim and Nicholas Miller applied Cohen's higher-dimensional framework to extend results in hyperbolic spaces in 2025.[1] The work has already found application as a fundamental mathematical tool for studying wave propagation behavior in chaotic systems.[1] At age 25, Cohen secured a position as an assistant professor at New York University.[1]