( the abstract) Subject: Mathematical Scientific Paper. Scope: Abstract Algebra and Quantum field theory and general relativity Achieved Result to discuss: Complete model to describe a mathematical universe. It gives me great pleasure to discuss/ present a different and unique perspective to describe a complete model for a mathematical universe. Tracing the trail of previous mathematicians, and tracking the history of mathematics and physics , I have reached to amazing results considering quaternions and primes . As a sub ring of quaternions with some properties defined on it, can amazingly work as a model to describe a mathematical universe capable of realizing itself ,where a distribution of mater on three-dimension space changes while a fourth dimension changes ,capturing the universe as one wave of probability of quantum fields interacting together. And the most important is not knowing where we are in that ring captures exactly the universe as a wave of probability collapsing to smaller probability moment after moment as the act of observation occurs. In the third part, how this mathematical universe realizes itself and how the act of observation happens is captured using the same model Later in the fourth part it will be clear how after choosing the correct functions one can show that this model captures to somehow the stander model of particles the strong and weak and the electromagnetic forces are captured and the quarks and leptons are captured. later in the fifth part it will be shown that this model captures the maxim speed and time dilation and the relation between mass and energy !(coming soon) moreover there will be a way to capture gravity and dark matter and dark energy ! (coming soon) Author: Amgad Ahmed Abdelmaksod Ali Mohamed Younes. gloryyxp4@yahoo.com , Researcher GRE Math 2021