“The profound study of nature is the most fertile source of mathematical discoveries.” — Joseph Fourier
In the course of studying the benign overfitting phenomenon, I not only developed the Feature Space Decomposition method, which refines one of the most fundamental techniques in mathematical statistics, but also discovered several intriguing phenomena in the geometric aspects of functional analysis—for example, that the isometric version of the Dvoretzky–Milman theorem for ellipsoids can hold under probability measures that are far from Gaussian. In fact, in the study of benign overfitting, there are additional new phenomena arising from geometric functional analysis, such as Milman's M*-estimate for random affine subspaces—a result first proven by Wang et al., though they did not present it in a way that highlights its significance to the GAFA community. In the future, I also plan to further investigate additional mathematical phenomena underlying benign overfitting, which may be connected to geometry of random polytopes.