As Joseph Fourier wrote in Théorie analytique de la chaleur (The Analytical Theory of Heat): 

“The profound study of nature is the most fertile source of mathematical discoveries.” 

Together with my advisor, Guillaume Lecué, I have been studying the phenomenon of benign overfitting and discovered Feature Space Decomposition (FSD) method. FSD is a mathematical method for analyzing the population excess risk of an estimator. I developed this method to improve the most fundamental proof technique in mathematical statistics — the  uniform convergence argument — in order to prove the phenomenon of  benign overfitting and to answer the most basic question in supervised learning theory.  

I have successfully applied it to the study of spectral methods, which serves as an illustration of the power of this approach.