"There exists the icon of the Trinity by St Andrei Rublev; therefore, God exists."  These words by Pavel Florensky, 20th century Russian Orthodox priest, theologian, and victim of Stalin's gulags, sum up well what many people feel instinctively when they gaze upon the world's most popular icon.  Its  popularity stems from the mystery of its subject matter as well as the skill of the monk who wrote it (icons are "written", not painted).  Sadly, we know very little about the life of Andrei Rublev, though that's probably how he would want it.  He was born sometime around 1360, spent much of his boyhood in the great Holy Trinity monastery, became a monk at Moscow's Andronikov monastery, but returned temporarily to Holy Trinity where he created his masterpiece.  He reposed on this day in 1430.  He was declared a saint by the Russian Orthodox Church in 1988 and several years ago was included in the liturgical calendar of the Episcopal Church. 

Below is an Orthodox liturgical prayer, a collect from the Book of Common Prayer, and an excerpt from Fr Gabriel Bunge's The Rublev Trinity:  The Icon of the Trinity by the Monk-Painter Andrei Rublev (2007, St Vladimir's Seminary Press), p 88.

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Troparion Tone 3
Shining with the rays of divine light,
O venerable Andrei,
You knew Christ the wisdom and power of God.
By means of the image of the Holy Trinity
You preached to all the world the Holy Trinity in unity.
And we with amazement and joy, cry out to you:
As you have boldness before the Most Holy Trinity
Pray that the Uncreated Light
May illumine our souls!

Book of Common Prayer
Holy God, we bless you for the gift of your monk and icon writer Andrei Rublev, who, inspired by the Holy Spirit, provided a window into heaven for generations to come, revealing the majesty and mystery of the holy and blessed Trinity; who lives and reigns through ages of ages.  Amen.

Bunge
Despite his modifications, Rublev was not at all original.  Rather, his genius consisted in advancing the ancient iconographic tradition of his Church to a depth and transparent clarity that had never been attained before or even later, even in the most exact copies.  This is the place where the personality of the painter enters permanently into his work.  The ancient sources about the monk Andrei draw attention to his great humility, which more than his artistic genius led not only to the canonization of his Troitsa [Trinity icon] at the synod of 1551, but also to his official glorification as a saint in 1988 as part of the celebrations of the millenium of Russian Christianity.

For without a deeply rooted humility, a complete renunciation of all worldly ambition before the sublimity of the mystery that he served as a painter, Rublev would never have been able to paint his Trinity.  Not once did he set his name as icon painter to his work.