Some so-called "primitive mathematics " by ancient mathematicians is trivial, but not banal. My first attempts to reconstruct well - forgotten Plato's periodic perfect numbers in 1998-1999 were are not hopeless and,probably,successful ( article On Plato's periodic perfect numbers published in French Bull.Mathem ,123,1999 ). My new brave step in experimental anthropology is reconstruction of Nicomachus ( of Gerasa ) theory of gnomonic numbers by numerical semantic experiments.It is found that technique of semantic experiments in the ultra complex environment of unsolved mathematical problems - Goldbach conjecture ( additive number theory ) and Riemann hypothesis ( analytic number theory ) could be effective as well. I showed principal simplification for Goldbach conjecture and the new way of understanding of Riemann hypothesis as a consequences of famous Nicomachus theorem. In other words such sort of contemporary problem of number theory ( formulated in XVIII - XIX century ) could be discovered by ancient mathematicians as well.
Some of this results can be used in cryptography and are needed supercomputer - cryptology eprint archive 2010/653
invented human math with its dogma of natural numbers series is , I suppose, rare illusion.It can terminate science in future.
Counter-intuitive alternative mathematics, based on both- solution of Riemann problem of asymptotic distribution of primes and problem of existence of one-way function ( another form of solution of the P vs NP problem ) are discussed in my technical article entitled "Cubic groups " : Cryptology eprint archive 2010/653 .