Mahavakias - the great statements are procedures from jnana yoga, part of the traditional nondualist yoga practice.
It is understood similarly but a little differently in Advaita Vedanta and in Kashmir's nondualist Shivaism.
Kashmirian Shivaism integrates life as a spiritual path, it does not consider it an illusion.
Shivaism affirms its value of reality (being formed by the mind of the Supreme Being) but specifies its great "defect".
Namely, the fact that life is fleeting.
"Neither this nor this"
It is the statement of denial, nothing that is external is real (Advaita Vedanta) or - nothing is non-tantaling (Abheda)
"I am Brahman"
We know that we are the individual immortal Self Atman, but here it emphasizes a supreme truth: All of us, each of us, we are God or the only Supreme Being.
"You're the One"
i.e. "you, the being, or, above all, the man in front of me, you, even you are the Supreme Being, whoever you are or whatever you are".
"Allthese things (outer) are Brahman"
This mahavakias pushes understanding even further, even things, i.e. anything in the Universe are brahman or the Supreme Being.
"Atman and Brahman are identical"
I mean, the Individual Supreme Self and the Supreme Being are One.
" Brahman is the supreme wisdom" is one of the 9 Mahavakias – the great claims.
"Brahmanis One without a second (like Him)"
In the universe there can be no two omnipotent and perfectly free beings because the omnipotence of one would limit the omnipotence of the other.
"Brahmanis real, the world is unreal"
or, more correctly, from a Abheda's perspective
"Brahman is eternal, the world is fleeting"
all 8 Mahavakias - the great claims
"Thereis an essential identity between man,
the outside world
and Brahman (God or Supreme Being)"
" Man, the outside world and God are essentially identical "
These are great claims or nondualistic maxims from Advaita Vedanta.
On them we can reflect or even meditate, to help us intuit their reality in our hearts.
It is not enough to repeat them mechanically (much less repeat them in Sanskrit).
The important thing is to seek to truly realize their significance.
Even their mere knowledge, however, can help us when we have an inner search, when we seek to achieve the Self or tend to fully identify with the Supreme Self Atman.
What is Atma Vichara?
What is not Atma Vichara?
It doesn't have efficiency just by simply repeating the question. It is possible to repeat this question all your life without progressing!
Even the mere repetition of these "maxims" or Universal Truths expressed in words can make our description of these truths more familiar.
And when the true inner search takes place, even if we no longer think about statements, they help our spiritual intuition to realize the final declic.
It is preferable to repeat the Mahavakias - the great statements in both Sanskrit and Romanian.
Then, when the Romanian meaning is clear to us, we can sometimes repeat them only in Sanskrit.
We seek to savor their meaning in our mother tongue and we tend to the reality they express.