As shown by Gödel and other mathematicians, foundational problems of classical mathematics (CM) arise because this theory involves the entire infinite set of natural numbers. Therefore, CM must be modified in some way. A problem discussed in a wide literature is how mathematics should be treated: (1) as a purely abstract discipline, independent of nature; or (2) as a discipline that must ultimately describe nature. Most physicists accept only viewpoint (2), while many mathematicians and philosophers adopt viewpoint (1). However, currently approach (1) did not solve the problem of how CM should be modified, and quantum theory (QT) is considered to be the most general theory for describing nature. Therefore, CM must be modified so that it correctly describes QT. As shown in our publications, finite mathematics (FM) satisfies this condition. It involves a finite ring $R_p=(0, 1, ...p-1)$ where addition, subtraction, and multiplication are performed modulo $p$. FM does not contain any foundational problems and is a more general theory than CM: the latter is a degenerate special case of the former in the limit $ptoinfty$. The purpose of this paper is to provide a brief overview of our results to make them understandable to a wide audience of mathematicians and physicists.