The central and defining mystery of mainstream Christianity is the Trinity, which postulates one God subsisting in three coequal, coeternal, and different Persons—the Father, the Son, and the Holy Spirit. Though most churches accept it as a basic fact, this article argues that the doctrine is formally inconsistent and makes it nonsensical when subjected to the standards of mathematical and logical inquiry. This analysis will proceed by first formalising the Trinitarian claims as a set of logical propositions based on creedal statements, primarily the Athanasian Creed. Subsequently, it will apply fundamental axioms of identity, arithmetic, and elementary set theory to demonstrate the doctrine's internal inconsistency. The paper will scrutinise common theological defences—such as the distinction between ‘person’ and ‘essence,’ the appeal to divine mystery, and the use of analogy—and argue that they fail to resolve the underlying logical paradox. Instead, these defences are shown to be either special pleading, evasions of the logical problem, or collapses into recognised heresies like Modalism or Tritheism. This paper contrasts the Trinitarian model with strict monotheistic systems like Judaism and Islam, concluding that affirming the Trinity costs the abandonment of the law of non-contradiction, undermining its philosophical tenability.