In the present paper in the Section 1, we have described some equations concerning the cusp anomalous dimension in the planar limit of N = 4 super Yang-Mills from a Thermodynamic Bethe Antsaz (TBA) system, the Luscher correction at strong coupling and the strong coupling expansion of the function F. In the Section 2, we have described some equations concerning a two-parameter family of Wilson loop operators in N = 4 supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle, principally some equations concerning the one-loop determinants. In the Section 3, we have described some results and equations of the mathematician Ramanujan concerning some definite integrals and an infinite product and some equations concerning the development of derivatives of order n (n positive integer) of various trigonometric functions and divergent series. Thence, we have described some mathematical connections between some equations concerning this Section and the Sections 1 and 2. In the Section 4, we have described some equations concerning the relationship between Yang-Mills theory and gravity and, consequently, the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory including the nonplanar contributions regarding the gauge theory and the gravity amplitudes. In conclusion, in the Appendix A and B, we have described a new possible method of factorization of a number and various mathematical connections with some sectors of Number Theory (Fibonacci's numbers, Lie's numbers, triangular numbers, Phi, Pigreco, etc...).