We study the problem of estimating the mean of a distribution in high\ndimensions when either the samples are adversarially corrupted or the\ndistribution is heavy-tailed. Recent developments in robust statistics have\nestablished efficient and (near) optimal procedures for both settings. However,\nthe algorithms developed on each side tend to be sophisticated and do not\ndirectly transfer to the other, with many of them having ad-hoc or complicated\nanalyses.\n In this paper, we provide a meta-problem and a duality theorem that lead to a\nnew unified view on robust and heavy-tailed mean estimation in high dimensions.\nWe show that the meta-problem can be solved either by a variant of the Filter\nalgorithm from the recent literature on robust estimation or by the quantum\nentropy scoring scheme (QUE), due to Dong, Hopkins and Li (NeurIPS '19). By\nleveraging our duality theorem, these results translate into simple and\nefficient algorithms for both robust and heavy-tailed settings. Furthermore,\nthe QUE-based procedure has run-time that matches the fastest known algorithms\non both fronts.\n Our analysis of Filter is through the classic regret bound of the\nmultiplicative weights update method. This connection allows us to avoid the\ntechnical complications in previous works and improve upon the run-time\nanalysis of a gradient-descent-based algorithm for robust mean estimation by\nCheng, Diakonikolas, Ge and Soltanolkotabi (ICML '20).\n