The popular charge is that 1+1+1=3, not 1. But that's not what Christians have ever claimed. The Trinity is not "three Gods are one God" or "three persons are one person" — that would be a contradiction.
The actual doctrine
One God in essence (ousia — what God is); three Persons (hypostases — who God is). Different categories. The Father is not the Son; the Son is not the Spirit; yet each is fully God, sharing one undivided divine nature.
Analogies all break down (water/ice/steam is modalism; three men sharing humanity is tritheism). The doctrine is its own category, hammered out at Nicaea (325) and Constantinople (381) precisely to refuse easier reductions.
Why this matters
If God is eternally Father-Son-Spirit, then God is eternally love, not just becoming loving when he made the world. The Trinity means relationship is woven into the deepest fabric of reality. "God is love" (1 John 4:8) requires plurality of Persons in unity.
The Orthodox lens
The Cappadocian Fathers — Basil, Gregory of Nazianzus, Gregory of Nyssa — gave us the language. St. Gregory the Theologian: "No sooner do I conceive of the One than I am illumined by the splendor of the Three; no sooner do I distinguish them than I am carried back to the One."
Andrei Rublev's icon of the Trinity (the three angels at Mamre) shows the truth visually: three Persons in perfect, self-giving communion, with a fourth place at the table — open to you.
A pastoral word
If you can't fully grasp the Trinity, welcome — neither could the Fathers, and they said so. We worship a God big enough to be mysterious. The point isn't to comprehend; it's to be drawn into the love that the Father, Son, and Spirit have shared from eternity.