Were all Ainur made at the Beginning?

Question

The Ainulindalë says that the Ainur were created at the beginning of time, and seemingly all at once. Were there any of their order, Valar or Maiar, who were "born" later? I can find a reference to one Maia who fell in love with an Elf, but her children seem to be counted as Elves, not Maiar.

I've often heard the pantheon of Middle Earth described as a mix of monotheistic and polytheistic traditions, as though the One God of Christianity were to create the Greek Pantheon. The Valar certainly seem similar to Greek/Norse gods, even dividing up the world into "spheres of influence" and residing in a mythical, but theoretically geographical, location (like Mt Olympus).

But one thing that polytheistic pantheons did all the time was have children. Athena born from Zeus, Thor born to Odin, etc. Did the Valar or Maiar ever conceive of successive generations? Or were they all, every one of them, created at the Beginning?

Answer 1

There was Eru, the One, who in Arda is called Iluvatar; and he made first the Ainur, the Holy Ones, that were the offspring of his thought, and they were with him before aught else was made. (Ainulindale)

There's absolutely nothing in Tolkien's writings to suggest that any Ainur were made at any other time - in fact there is a further reference to "all the Ainur" later in the Ainulindale. Since the Ainulindale is feigned to be a later work by Elvish sages, it must be assumed that "all the Ainur" still holds for that later time too.

Here I give the title page of Ainulindale D (published in Morgoth's Ring) to establish it's status as a later work:

Ainulindale
The Music of the Ainur
This was made by Rumil of Tuna in the Elder Days. It is here written as it was spoken in Eressea to AElfwine by Pengolod the Sage. To it are added the further words that Pengolod spoke at that time concerning the Valar, the Eldar and the Atani; of which more is said hereafter

Regarding the offspring of an Ainu and an Elf or Man, at the end of the 1937 Silmarillion we have Manwe saying the following:

Now all those who have the blood of mortal Men, in whatever part, great or small, are mortal, unless other doom be granted to them

This can conjecturally be generalized to a rule that all offspring of a union between a greater being and a lesser being are held to belong to the species of the lesser being; but like I said - conjecture. However, the evidence (of Luthien being counted among the Eldar) fits the conjecture.

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Update: 1st March 2015

Footnote 53 to the Shibboleth of Feanor (History of Middle-earth 12) has this to say about Melian:

Melian alone of all those spirits assumed a bodily form, not only as a raiment but as a permanent habitation in form and powers like to the bodies of the Elves.

This is of course very late writing and other parts of it are in disharmony with more developed concepts elsewhere, but if we accept it then it's definitive: when Melian took her "worldly body" she became, to all intents and purposes, an Elf.

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There is, however, one interesting case of one of the people of the Valar who was not created at the beginning, and that's Turin Turambar. The Second Prophecy of Mandos (not in the published Silmarillion, but given most fully in HoME 5) ends with:

But of Men in that day the prophecy of Mandos doth not speak, and no Man it names, save Turin only, and to him a place is given among the sons of the Valar.

This idea was never actually abandoned by Tolkien himself, but was editorially removed from the published Silmarillion based on conflicting text elsewhere.

The use of the phrase "sons of the Valar" is significant here, and it relates to an older conception, that of the "children of the Valar"; here I'll quote from Annals of Valinor in HoME 5 (note that it's important to distinguish between Valar and Ainur: the Valar are a subset of the Ainur):

And with them also were later numbered their children, begotten in the world, but of divine race, who were many and fair; these are the Valarindi.

This conception was abandoned during revisions to the Silmarillion after LotR was completed, but it certainly did exist in the earlier versions of the mythology.

Answer 2

The LOTR Wikia states

The Ainur, the Holy Ones (singular Ainu, meaning Holy One; Quenya; IPA: [ˈaɪnur]) were the first and mightiest beings created by Eru Ilúvatar in the depths of time before the beginning of the World. The 'order' of the Valar and Maiar, made before Eä.

This technically means that it was the Eru first and then the Ainur before the beginning of the universe, if you consider the beginning of "the world" the universe but not necessarily the beginning of time itself.

From what I understand there were only 14 main Valar, 15 if you had included Melkor. These were known as the Lords and Queens of the Valar, there being eight lords and seven queens.

The Maiar is hard to put a number on

The wikia from here states http://lotr.wikia.com/wiki/Maiar

The Maiar (Quenya, singular Maia) were spirits that descended to Arda to help the Valar shape the World. They were supposed to be numerous, yet not many were named. Their chiefs were Eönwë, banner-bearer and herald of Manwë, and Ilmarë, the handmaid of Varda.

This would suggest that there are a multitude of Maiar but it's unknown how many there were... it also states some of the Maiar here

Though less powerful than the Valar, the Maiar were powerful nonetheless, and included Melian, Sauron, Olórin (later known as Gandalf) and the other Istari, the Balrogs, and many others. A Maia would often associate himself with a particular Vala. For example, Ossë and Uinen, powers of the oceans, served under Ulmo, while Curumo (later known as Saruman), served Aulë the Smith. Sauron also served Aulë before he was corrupted by Melkor.

Also in many of the polytheistic pantheons there were usually first beings whom then birthed the rest.. for instance as far as I remember the Greek Pantheon was Uranus was the one who mated with Gaia and had the children such as Cronos, which in turn had Zeus later on. In LOTR Eru is the one who created the rest. From what I gather this means that he birthed all of the Valar and Maiar.