What can be said about ajata? David Godman has brought together a few quotes, from Papaji (H.W.L. Poonja) and Ramana Maharshi (Bhagavan).

First, David’s comments (Gaupada was the teacher of Shankara):

Gaudapada declared “non-creation” to be paramartha,

the final truth, and Bhagavan endorsed this conclusion,

saying that it tallied with his own experience. Papaji too 

sided with Gaudapada on the issue of whether creation “never

happened.”

Ajata, flying in the face of logic, common sense, and everyday

experience, says very clearly that not even an unreal, illusory

projected world has been created. It sticks firmly to the 

position that there is no creation and no causality….

Something can only happen or exist if there is a knower, or

an experiencer, of it. If there is no seer of the world, the world

itself is not there, and never was…

This is what certain masters have said on this topic, and I can

add that they have all said this on the basis of their own

direct experience of the Self.

And among the things said about ajata by Papaji:

I have to accept Gaudapada’s teaching. And that

teaching is “Nothing ever existed at all”…. If the

ultimate reality is perfect in itself, then the act of

creation can never be predicated on it… As a

result, the whole world becomes illusory and non-

existent. The world never did exist...

You can see the world as real…or, like the

Buddha, you can say that it is not there at all…. 

It is the names and forms that never existed….   

Absolute non-manifestation is the only Truth….

That place is my real home. It is where I always

am. One can say this with authority only when one

abides in that ultimate place where nothing has ever

happened.

And Ramana explains that ajata cannot be pictured by anyone who cannot envision total emptiness:

…they are told, ‘God first created such and such a

 thing, out off such and such an element, and then 

something else, and so forth. That alone will satisfy 

this class. Their mind is otherwise not satisfied, and 

they ask themselves, ‘How can all geography, all maps, all

sciences, stars, planets and the rules governing or     

relating to them, and all knowledge, be totally untrue?’

To such it is best to say, ‘Yes. God created all this and 

so you see it’. All these are only to suit the capacity of the 

learner….One who is established in the Self sees 

this [ajata] by his knowledge of reality.

The understanding of ajata is at least as old as the Upanishads, but becomes clear to those who are most steeped in advaita.

What can be more difficult to comprehend than nothingness?

Even the word commonly used as an alternate—emptiness—suggests something to be (or could be) emptied. In nothingness, there is not even that suggestion. 

Nothing means nothing—and not even something which became nothing. It was (that is, is) nothing from the start; never not ever anything.

The importance of the understanding of ajata is its practicality. In nothing, there are not (nor can ever be) any “problems”.

The Heart Sutra tells us,

all phenomena are emptiness—

they are not born.

In emptiness, there is no consciousness  

no body

and no mind.

There is no form…no origin.

The Dalai Lama tells us,

All phenomena are empty.

Emptiness pervades the whole of reality.

That emptiness is its ultimate nature.

We project onto things a status of existence

which is simply not there.

The understanding of emptiness is one

of the principal factors of the true path.

Such an insight cuts right through the illusion

created by the misaprehensions of grasping

things and events.

And I have written:

In my estimation, any teaching which assists one

to connect with the reality of the sheer emptiness of

their existence—in life or death—is a practical teaching.

Fortunately, we have the capacity to realize, while we

are alive, that ultimately nothing really matters.

Considering that (ultimately nothing really matters),  

how much anguish should we invest in our temporal,

impermanent, “relative” fixations in the meantime?

It is this awareness which is the conscious state of the

thoroughly Self-realized. As a consequence, his attention

is merely on the moment, as one is when witnessing the

unfolding of a dream.

Wherever he looks, and whatever he views, he sees only

impermanence: emptiness—recognizing that he who sees

is no less empty. “His” life, the world, the universe can

cease to be—even to ever have been—at any moment.

This recognition, this awareness, dictates his every

movement—every one of which holds the amusing

“importance” of potentially being his last.

So, he has, in a sense, “Died before one dies,” and his

absence, or non-existence, is as much in his conscious

awareness as is his momentary presence.

In the emptiness after death, there will not even be anything there—as far as you are concerned—to pose such questions as, "Does nothingness exist or not exist?"