In this work, we solve the main mathematical puzzles of the UMMO file which contains severalthousand postal letters sent since the 1960s addressing many fields such as philosophy, mathematics, human sciences, biology, cosmology, theoretical physics, among others. "The UMMO affair" refers to more than 200 listed documents, representing at least 1300 typed pages (the "Ummite letters"), which are said to have been sent since 1966 to numerous recipients, in particular in Spain and France by editors - the Ummites - claiming to be extraterrestrials on an observation mission on Earth and which have four centuries of technological advance on the terrestrial human technologies. We demonstrate the importance of angular tetravalent logic in mathematics and theorical physics. As an example, we give a proof of Fermat’s last theorem using angular tetravalent logic, as suggested by the Ummites. Then, we will pierce the secrets of the universe always using the tetravalent logic, we will explain the reasoning which proves the existence of a twin universe and we give the mathematical formula for the folding of space-time which separates the two twin universes and finally we explain why the curvature of the universe is necessarily negative.