Did Arianism survive as Islam?

Islam is as opposed to Arianism as it is to orthodox Christian teaching on the person of Christ and his relationship with God. That is why Islam makes no distinction between modern-day Arians (such as the Jehovah’s Witnesses) and the bulk of Christian denominations that eschew Arianism. They all believe in God as “Father” and as Christ as “the Son of God” which, to Muslims, is the sin of “shirk” – ascribing ‘partners’ to God. However, once we grasp what Arius actually taught on this subject, we are in a better position to have meaningful dialogue with those who reject the Christian Trinity doctrine.

Arius was the presbyter whose doctrine of the co-eternity of the Logos (the Word who became the man, Jesus) caused the Council of Nicaea in 325 A.D. A reading of John’s gospel, the first chapter, is vital to know the significance of the one named as ‘the Word’ who ‘became flesh’ - the man, Jesus Christ. Arius believed there was a time when the Logos did not exist. When the Bible spoke of the Father 'begetting' the Son, Arius said that was a synonym for 'creating'; the perfect creature through whom all other things were made.

Arius's theology was that Christ did not possess deity by nature but developed into it by virtue of his constant and growing moral unity with God - he furnished the perfect example of commitment to the good and to God. Such a view hardly differs from the teaching of Adoptionism.

Arius's view of Christ is that God created him to be mediator, as in the Neoplatonic concept of the Logos. His ideas helped the 'conversion' of countless pagans during Constantine's era as they sharply reduced the clash between Christianity and pagan philosophical monotheism. Interestingly, Arius was ready to pray to Jesus and give him relative worship. When a creature is worshipped as ‘a god’, not the same God as the Father, then Christian monotheism has been violated. That is why Christianity has always maintained that Christ was never created – never had a starting point in time – that the one Being of God subsists in the three uncreated, co-equal ‘persons’ of the Father, the Son, and the Holy Spirit. All Catholics, Orthodox and Protestants agree on this, but Arians (and their modern-day counterparts) disagree.

That is why the step of saying this creature was the supreme archangel, Michael, naturally follows from the initial claim that the Son was created. The logic is that if the Father only created one creature, who was to be supreme in heaven, that would have to be the first angel who was superior to all other angels. However, the theological work of Tertullian (A.D. 160 - 230) gave the basis for refuting Arius, and his theology was accepted a century before Arius came along with his! Modern-day Arians, such as the Jehovah's Witnesses (who say Jesus is the Archangel, Michael) never admit that Trinitarian beliefs were expressed as sound theology a century before Arius.

I have gleaned that from the massive book, Heresies and Orthodoxy in the History of the Church by Harold O.J. Brown, pp 108-117 (Hendrickson/Baker 1998). It gives an excellent explanation on such historical matters as they relate to Christian theology.

This serves to show that Islam is not influenced by Arianism, rejecting it just as much as they do orthodoxly Christian teaching that also rejects Arianism.

Muslims are not Arians

They do not believe God became a man.

They do not believe Jesus to be God.

They also do not believe that the Holy Spirit is a separate God from the Father.

They do not give religious praise to Jesus, for they only give such to God.

They believe Jesus is the Son of God, or in this case, Allah.

They believe God was the one to send Jesus.

They also believe in the Shema Yisrael/Command/Prayer like today's Christians/Jews, only to them it is seen in the Sura [surah]-112 (Al-Tawhid or Monotheism) in the Qu'ran unlike Arians who show a total disregard for it:

• Arabic: قُلْ هُوَ اللَّهُ أَحَدٌ‎ - Qul Huwa 'Llāhu ʾAḥad ("Say, He
  is Allah the One")

• Hebrew: :שְׁמַע יִשְׂרָאֵל יהוה אֱלֹהֵינוּ יהוה אֶחָד‬ - Sh'ma
  Yisra'el YHVH Eloheinu YHVH Eḥad

Note: The words "أَحَدٌ" in Arabic is identical to the word "אֶחָד‬" in Hebrew.

Islam is based on Arianism and originated from Arian's teachings according to the Qur'an and tradition. Nowhere in the Qur'an affirms that Jesus was the son of god. However, it calls Jesus the son of Mary. This is in conformance with Bahira's Arianism teachings. Indeed, Bahira was the teacher and guide to young Muhammad. Then, the Jews intervened in two different time periods; during Muhammad's time and after his death. What we see as Islamic Jihadis, is as a result of mixture of Arianism and orthodox teachings of Judaism.

Like @curiousdannii pointed out in his comment, Arian influences do not equal an Arian viewpoint or verbatim parroting. In Qur'anic teaching, worship or veneration of anything besides God is strictly forbidden, or haram. This helps define what a Muslim (or a Christian or Jew or Sabean for that matter) can be and cannot be.

"Say: 'O People of the Scripture! Come to an agreement between us and you: that we shall worship none but Allah, and that we shall ascribe no partner unto him, and that none of us shall take others for lords beside Allah.' And if they turn away, then say, 'bear witness that we are they who have surrendered unto him [Muslims].'"

^{— Surat al-Imran 3:64}

Here the authors sought to separate the wheat from the chaff in terms of who is and is not submissive to God's will; they understood that a polytheist couldn't care less about their al'Ilah, and they also knew that Catholics venerated saints (take others for lords)and placed Jesus at the right hand of God (ascribing a partner to God). Such a practice was unacceptable to them, and it was here that the line was drawn in the sand.

According to Arian schools of thought, worship of the Logos/the only-begotten Son was not rejected in favor of a strictly monotheistic faith. Arius' initial issue was not with worship of Jesus, but with semantics over what exactly the terms 'only-begotten' and 'one substance' implied. One faction believed that Christ was of one-substance, and that the Logos had not been created by the Father. Arius' followers instead posited that in eternity past, the Father created a lesser divinity through whom the creation would arise and would act as our reflection of the deity, meaning that the Logos was technically a created being.

"But we say and believe and have taught, and do teach, that the Son is not unbegotten, nor in any way part of the unbegotten; and that he does not derive his subsistence from any matter; but that by his own will and counsel he has subsisted before time and ages as perfect as God, only-begotten and unchangeable, and that before he was begotten, or created, or purposed, or established, he was not."

^{— Arius of Alexandria's Letter to Eusebius of Nicomedia (circa AD 300)}

Here you can see that Islamic perspectives on God are very much distinct from Arianism, perhaps more compatible with the Adoptionism that was popular in early Christianity or Paul Samosatene's theology.