The notion of product ciphers is due to Shannon.
Nobody knows how to prove mathematically that a product cipher is completely secure.
For example, the cipher must be nonlinear, and it must produce ciphertext which functionally depends on every bit of the plaintext and the key. It was shown that at least 5 iterations of DES are required to guarantee such a dependence. The nonlinearity of a product cipher reduces to a careful design of these S-boxes.