Math to replace s-boxes - Good or bad idea?
The S-boxes in quite many encryption algorithms (for example, in AES) have been already built with math (the AES S-box is an inversion function in $GF(256)$ plus an affine transformation). The lookup tables exist solely to ease the implementation. In fact, modern Intel/AMD CPU are already equipped with AES round function instructions, so the tables are not needed at all.

When people design new S-boxes, the first question to answer is Why? and the next one is What properties do they have compared to the existing ones?. Until there are reasonable answers, the proposals are not used and even not being analyzed.