Feynman diagrams is the standard tool of theoretical physics usually associated with the analytic approach. I will argue that diagrammatic expansions are also an ideal numerical tool with enormous and yet to be explored potential for solving interacting many-body systems. The current scheme is based on direct simulation of Feynman diagrams for the proper self-energy up to some high order. Though the original series based on bare propagators are sign-alternating and often divergent one can determine the answer behind them by using two strategies (separately or together): (i) using proper series re-summation techniques, and
(ii) introducing renormalized propagators which are defined in terms of the simulated proper self-energy, i.e. making the entire scheme self-consistent. The first results for the Fermi-Hubbard model at U/t=4 and away from half-filling prove that this approach is working.