The theory of Maximal SuperSymmetry in four dimensions known as N = 4 SUSY considered to be the ’harmonic oscillator of the 21st century’. It is the conformal field theory in the famous ADS5/CFT4 correspondence conjecture known as the primary example of one of the most fascinating ideas - the Gauge-gravity duality. It is widely believed that N = 4 SUSY is exactly solvable at least in the planar limit what will make it the first gauge theory in four dimensions to be solved exactly. By ’solve’ we mean here to find all anomalous dimensions of all operators of the theory for any value of the gauge coupling which are nothing but equal to the energy levels in the ADS side if the conjecture is correct. Solving N = 4 SUSY will serve as a point of departure in the understanding of other gauge theories with QCD being the most important one. Intensive research in the last decade has resulted in the discovery of surprising structures and symmetries in N = 4 SUSY such as Integrability, Dual Superconfrmal Symmetry and the principle of maximal transcendentality. Without such discoveries the great progress in confirming the above conjecture and finding important quantities like the correlation functions would have been hard or even impossible to achieve. Direct gauge theory perturbative computations would have not been sufficient. Recently, relying on integrability ,crossing symmetry and maximal transcendentality Beisert,Eden and Staudacher found the asymptotic spectrum of the planar N = 4 SUSY to any order in the weak coupling expansion. Until their seminal work it was only known up to the three loops order! This may signify that there is some structure in the perturbative expansion of gauge theory which is waiting to be revealed. Borrowing ideas from different branches such as Statistical physics, combinatorics, Graph theory and approximation theory we suggest an Ansatz which reveal such structure in the aforementioned expansion with implication not only to the asymptotic spectrum. * This work has been done under the supervision of Prof. Marek Karliner.