Talmudic Foundations of Mathematics

In this paper, we assume that the mathematicians in proving new significant theorem, such as Fermat’s Last Theorem, deal with combining proof trees on tree forests by using the analogy as an inference metarule. In other words, the real mathematical proofs cannot be formalized as discrete sequences, but they are concurrent and can by formalized as analog processes within a space with some topological properties. For the first time, inference metarules in a topological space were proposed in the Talmud within a general Judaic approach to concurrent or even massive-parallel conclusions. The mathematician does not think sequentially like a logical automaton, but concurrently, also. Hence, we suppose that the proof technique of real mathematics cannot be formalized by discrete methods. It is just a hypothesis of the foundations of mathematics that we can use discrete tools so that mathematics can be reduced to logic. We show in the paper how the mathematical proof can be formalized just by analog computations, not discrete ones.