Explaining the Mystery of the Trinity
No, the Trinity isn’t mysterious because it insists that 1+1+1=1. But Christians often do find the Trinity mysterious because Christianity does not conform cleanly with philosophical monotheism. Christianity is a monotheistic religion, but its conception of God is caught up in a seemingly irresolvable tension between the oneness of God and the threeness of God. This mystery was pointedly and explicitly articulated first in the Nicene creed, which says that the Son of God “is of one substance with the Father” (ὁμοούσιον τῷ Πατρί).
The real mystery of the Trinity occurs regarding the triune metaphysical schematics of divine existence—that is, it is mysterious how God’s single substance can be metaphysically absolute and yet exist as three persons, and at the same time how God can exist as three distinct persons without compromising the metaphysical characteristics of an essence that is a se—or, of a single essence without source.
The Oneness of God
Traditionally, Christians have posited a doctrine which explains the single essence of God called divine simplicity. Simplicity states, not that God’s existence is a simple-minded matter, but rather that God is not composed of parts. He is not made of love, and holiness, and beauty, and all the divine perfections. Rather, he simply is God, and any attempt to explain distinctions in God are made for the sake of creatures.
In this regard, Reformers made a distinction between archetypal and ectypal theology—that is, theology which is true as God knows it, and theology which is true as humans know it. Humans could not categorically conceive of archetypal theology, because it occurs simultaneously and analytically—that is, it is not composed of a web of syllogisms as human theology must be, but exists as a single, self-contained act of self-knowledge on God’s part.
Therefore, ectypally, we must distinguish between two aspects of divine unity—divine singularitas and simplicitatis. Singularitas refers to the unicity of the divine essence—that there is one essence, and not a compilation of essences; simplicitatis refers more specifically and apophatically to the absence of real distinctions within God. Simplicity has been a way that Christians have philosophically affirmed the metaphysical independence of God from the world.
Because he does not exist “underneath” any philosophical idea—for instance, God is not loving because he must appeal to some abstract principle called “love,” but is love so purely that any creaturely love is merely a derivation and mimification of a divine attribute. The philosophical idea of love explains something divine, rather than God being loving because there is some third realm of philosophical ideas which he didn’t create to which he must conform in order to be who he is. That is not the Christian position—he quite literally is simply himself, and derivatively an  infinite number of attributes when he interfaces with creation.
The Threeness of God
Regarding the threeness of God, the orthodox position has developed to accommodate God’s oneness. In other words, whatever options are available to the tradition must first pass the threshold of divine simplicity—it must not threaten God’s non-composition.
Richard Muller, a church historian teaching at Calvin College, writes in his four volume work Post Reformation Reformed Dogmatics that there are five possible modalities of existence which could classify the three persons of the Trinity. These five modalities could also be called five kinds of distinctions between the persons. The five kinds of distinctions are: (1) rational; (2) formal; (3) virtual; (4) real; and (5) personal (4 and 5 are likely the same). It was the fourth mode, realiter, which was utilized to avoid pitfalls of Sabellianism and tritheism. However, a sub-distinction was required between a major real distinction (distinctio realis maior) and a minor real distinction (distinctio realis minor) in order to avoid attributing separate essences to the persons.
The eastern Orthodox have sought to make a more robust claim about the threeness of God by claiming that the persons are more than subsistences, but are rather energies. Consequently, their strategy which they have conscripted for achieving a doctrine of divine unity is called the doctrine of perichoresis—that the three persons so mutually indwell and exhaust one another that they are functionally one, while yet they are metaphysically individuated. This sort of formulation could not cohere or co-exist with the simplicitist conception of divine unity, because in the Aristotelian framework which has supplied Western Christianity with its concepts would classify those energies as substances, yielding three substances, and therefore tri-theism.
The Mystery of Triunity
Christians often frame the Trinitarian mystery as being stuck between two options—a prioritization of the one or the three. Traditionally, because of the heavy influence of Augustine on the development of Christian orthodoxy between the early church and the Reformation, Western Christianity has leaned toward prioritizing the oneness of God and conceived of the three secondarily, while the eastern Orthodox churches have emphasized the three and formulate softer versions of divine unicity—often lacking divine simplicity altogether.
The problem is that if you give to small a metaphysical due to the three, you risk becoming a modalist. If you give to small a metaphysical due to the one, you risk becoming a tritheist. Both are heresies. Both contradict the creeds and Scripture.
There exists, then, in the orthodox Trinitarian formulation, a sliding scale which represents what has so far been an insurmountable paradox for Christianity. The stronger one’s formulation of divine unicity and simplicity, the more the Christian doctrine of God is able to accumulate credibility and integrity as a truly monotheistic religion. By strongly formulating God’s unicity and simplicity, Christian theologians resolve what is mysterious about the Trinity, but risk denying sufficient metaphysical status to the three persons to which the Scriptures and the creeds testify.
The stronger one’s formulation of divine threeness, the greater weight is given to the theological uniqueness of Triniterian monotheism. This solution, codified mainly by the Eastern Orthodox, solves the Trinitarian mystery by resolving to settle for a weaker definition of divine unity that dispenses with the notion of a simple divine substance. In this case, God could still be conceived as having aseity, but there wouldn’t remain a philosophical way of articulating the metaphysics of that aseity.
This is what is mysterious about the Trinity—the sliding scale of prioritizing the oneness of God in terms of his simplicity, which protects his aseity and the credibility of Christian monotheism but risks modalism, and the threeness of God, which protects the identity and existence of the three persons, but risks tri-theism.
The doctrine of simplicity doesn’t allow Christian theologians to posit any metaphysical quiddity or quality to the divine persons per se, but the tradition compels simplicitists to do so. Simplicitists would wrangle with me on this point, but the point is that in the typical Western construal, God is more one than he is three—even if that doesn’t make its way into a formulated account, the three are functionally minimized in the Augustinian tradition.
The doctrine of the Trinity conflicts with purist accounts of the divine essence that want to posit radical versions of non-compositeness about God’s essence. Of course, the problem is that simplicitists want to claim that the metaphysical quality of each divine person isn’t of the sort that compromises the integrity of divine simplicity—but if simplicity is the absolute absence of metaphysical composition and therefore real distinction, then the three persons cannot have real and idiosyncratic metaphysical properties which characterize them each as persons, even if they do share an essence.
Critics of Christianity often point to the Trinity as an example of the logical incoherence of Christianity. But, with all Christian mystery, it is a necessary aspect of theological work. Just as a sailor can’t see what’s beyond the horizon, a theologian can’t conceive theologically too far beyond his historical moment. This is why the articulation of theological truth has become better every century since the resurrection—even while errors multiply along with the truth: theological mystery will always exist because the science itself deals with an object that is unlike any other scientific object; he exists independently and archetypally, and we know him ectypally.
The problem with those who criticize Christianity from the outside is that they are unable to genuinely make a distinction between Creator and creature. Because they are unable to make this distinction, they are unable to accept the premise of revelation. And because they are unable to accept the premise of revelation, they are unable to conceive of the existence of the only evidence you have for God’s triunity—his speech about himself. And so, when someone critiques Christianity because it is irrational, using the Trinity as an example, your response can be simple: “Your argument is this: ‘I don’t accept the Trinity because I don’t accept the Trinity.’ And this, I already know.”
 For a detailed delineation of this concept, see Paul Maxwell, “The Formulation of Thomistic Simplicity: Mapping Aquinas’s Method for Configuring God’s Essence,” JETS 57, no. 2 (2014): 371-403 (available as a chapter in this book).
 See Willem J. van Asselt, “The Fundamental Meaning of Theology: Archetypal and Ectypal Theology in Seventeenth-Century Reformed Thought,” WTJ 64 (2002): 329-335.
 Richard A. Muller, Post-Reformation Reformed Dogmatics, 4 vols. (Grand Rapids: Baker, 2003), 4:192–93.
 See Francis Turretin, Institutes of Elenctic Theology, vol. 1 (ed. James T. Dennison; trans. George Musgrave Giger; Phillipsburg: P&R, 1992), 3.7.1.
 For a Reformed conception of this concept, see Lane G. Tipton, “The Function of Perichoresis and the Divine Incomprehensibility,” WTJ 64 (2002): 289-306.