What was Isaac Newton's view of the Trinity?

John Byl, in his article "Newton and the Trinity", paints a clear picture that Newton was non-trinitarian. Newton's published works do not contain clear statements of this nature. In his private notebooks however, some of which were not examined completely until the mid 20th century, Newton committed a significant amount of effort to criticizing the Church's trinitarian doctrines. Byl writes:

In one notebook it is clear that, already in the early 1670's, Newton was absorbed by the doctrine of the Trinity. On this topic he studied extensively not only the Bible, but also much of the Church Fathers. Newton traced the doctrine of the trinity back to Athanasius (298- 373); he became convinced that before Athanasius the Church had no trinitarian doctrine. In the early 4th century Athanasius was opposed by Arius (256-336), who affirmed that God the Father had primacy over Christ. In 325 the Council of Nicea condemned as heretical the views of Arius. Thus, as viewed by Newton, Athanasius triumphed over Arius in imposing the false doctrine of the trinity on Christianity.

Newton further asserted that, in order to support trinitarianism, the Church deliberately corrupted the Bible by modifying crucial texts. For example, Newton claimed that the well-known words of I John 5:7 (”there are three that bear record in heaven, the father, the Word and the Holy Ghost: and these three are one”) were not in the original, pre-4th century Bible (Newton, it seems, was not a King James only man). Newton writes that “the Fathers…preferred to desert the Scriptures than not to condemn Arius”. Soon thereafter a universal corruption of Christianity followed the central corruption of doctrine: in the 4th century trinitarianism fouled every element of Christianity.

Newton's anti-trinitarianism is evident also in his interpretation of Revelation. According to Newton, the seventh seal began in the year 380, when trinitarianism was officially ratified at the Council of Constantinople. The great apostasy was not Romanism, but trinitarianism, “the false infernal religion”, to quote Newton's own words.

Economist John Maynard Keynes obtained a significant amount of Newton's unpublished works in 1936 due to his interest in Newton's alchemical (occult) studies. Newton wrote vastly on alchemy, which should be considered a philosophy in it's own right and not merely a proto-science. As a proto-science, it is more akin to a proto-psychology than a proto-chemistry, as is the common opinion (I'm happy to elucidate in chat or in the comments), and Newton was interested in the considerable discussion in the alchemical corpus on God, the human soul, and matter, as Newton, even in his published works, considered his work on physics to be an expression of worship toward the Creator and a revelation of his divine arcitecture. Newton is considered by many biographers to have been a deist, and not necessarily Christian, and so Newton's writings on Christianity should be considered in alchemical or deist context and not primarily in that of Christianity. Indeed, his commentary on Christian doctrine appears to be predominantly critical.

Among the previously unpublished work obtained by Keynes is a list of twelve points stated by Newton on the relation between the Father, Son, and Spirit. Chief differences of Newton's perspective in comparison with both Catholic and Protestant doctrine is that Christ is not human or endowed with a human soul (8), and that the relationship between the persons of the trinity is like that of the saints, that they are distinct beings in agreement with one another (12). In the list, Newton made an entry for a 13th point which he left blank.

1. The word God is nowhere in the scriptures used to signify more than one of the three persons at once.
2. The word God put absolutely without restriction to the Son or Holy Ghost doth always signify the Father from one end of the scriptures to the other.
3. Whenever it is said in the scriptures that there is but one God, it is meant the Father.
4. When, after some heretics had taken Christ for a mere man and others for the supreme God, St John in his Gospel endeavoured to state his nature so that men might have from thence a right apprehension of him and avoid those heresies and to that end calls him the word or logos: we must suppose that he intended that term in the sense that it was taken in the world before he used it when in like manner applied to an intelligent being. For if the Apostles had not used words as they found them how could they expect to have been rightly understood. Now the term logos before St John wrote, was generally used in the sense of the Platonists, when applied to an intelligent being and the Arians understood it in the same sense, and therefore theirs is the true sense of St John.
5. The Son in several places confesseth his dependence on the will of the Father.
6. The Son confesseth the Father greater, then calls him his God etc.
7. The Son acknowledgeth the original prescience of all future things to be in the Father only.
8. There is nowhere mention of a human soul in our Saviour besides the word, by the meditation of which the word should be incarnate. But the word itself was made flesh and took upon him the form of a servant.
9. It was the son of God which He sent into the world and not a human soul that suffered for us. If there had been such a human soul in our Saviour, it would have been a thing of too great consequence to have been wholly omitted by the Apostles.
10. It is a proper epithet of the Father to be called almighty. For by God almighty we always understand the Father. Yet this is not to limit the power of the Son. For he doth whatsoever he seeth the Father do; but to acknowledge that all power is originally in the Father and that the Son hath power in him but what he derives from the Father, for he professes that of himself he can do nothing.
11. The Son in all things submits his will to the will of the Father, which could be unreasonable if he were equal to the Father.
12. The union between him and the Father he interprets to be like that of the saints with one another. That is in agreement of will and counsel.

Some points, esp. 5, 6, and 11, support the claim that Newton was a subordinationist, and the Roman Catholic Church and many protestant denominations strictly reject that teaching. Newton also names the Arians as having a proper notion of the Logos in point 4, while Arianism is also considered heretical by The Roman Catholic Church and many protestant denominations. Byl summarizes Newton's heretical points:

He explicitly declares only the Father to be supreme; the Son is a separate being, different from the Father both in substance and in nature; Christ is not truly God but is the so-called Word and Wisdom made flesh, divine to be sure, but only so far as divinity is communicated by the Father.

Even so, what Newton actually believed is disputed among those who study his life and writings. While Keynan maintains that he was an Arian and John Byl counts him as a non-trinitarian, James Hanson concludes in a 1996 article in Biblical Astronomer that Newton's positions are not far from the modern mainstream:

In my reading of what Newton himself wrote, and by analyzing the claims of his biographer detractors, I find Newton to be a Bible-believing Christian who would be comfortable attending my small semi-rural blue-collar Baptist church.