Buddhism does not believe in the existence of God whereas Sage Sankara proved the existence of God.+

Buddhism has not proved the truth of Nonduality.  Bhagavan Buddha pointed out the unreality of the world and he told people, they were foolish to cling to it. However, he stopped there. He came nearest to Advaita in speech but not to Advaita fully. 

Buddhism believes in reincarnation. Buddhism does not believe in the existence of Athma. Buddhism does not believe in the existence of God whereas Sage  Sankara proved the existence of Athma and the existence of Brahman or God by declaring Atman is Brahman.

From the standpoint of Athma, reincarnation is an illusion because birth, life, death, and the world are merely an illusion.

Sage Sankara disagrees with Buddhists who say, there is nothing - a nonentity. Sage  Sankara believes there is some reality, even though things are not what they appear to be. If one knows the truth, he will know what to do to find inspiration for action.  The seeker of truth‘s subject is to know what is it that is Real.

Buddhism says: ~ “All things are illusory and nothing exists.  However, Sage Sankara avers that it is not so.  It says that the universe, of course,  is illusory, but there is Brahman (consciousness), that exists forming the very substratum of all things (illusion or universe)”.

In the context of Advaita Vedanta: ~ Jagat (the world) is not different from Brahman; however, Brahman is different from Jagat

It has not been possible to preach Advaitic Truth entirely free from the settings of dualistic weakness it has not been more operative and useful to mankind at large because only a few will be able to grasp and realize it.

'To realize the Advaitic Truth a freer and fuller scope the seeker has to realize the form, time and space are one in essence. And that essence is consciousness. And the Soul, the innermost Self is present in the form of consciousness.   

To realize the Advaitic truth the seeker has to be free from all superstitions and orthodox contaminations. The seeker has to be dedicated to acquiring  Self-knowledge or Brahma Gnana or Atma Gnana alone. 

The point of Bhagwan Buddha is that if God is non-existent, the entire creation including the ‘Self’ is non-existent.  

Sage Sankara wanted to establish the existence of the Brahman. For this purpose, He made the Atman as the Brahman.

Sage Sankara brought out the identity of the ‘Self’ with consciousness and made the Atman the Brahman. Since one will not negate the existence of his Self, he will accept the existence of the Brahman, which is the Athma the Self.  

The Athma is the  Self. The Athma is present in the form of consciousness.  Consciousness is ever-present.  

Without the Athma the world, in which you exist ceases to exist. The Athma is Self-evident. It is not established by extraneous proofs. It is not possible to deny the Athma because it is the very essence of the one who denies it. The Athma is the basis of all kinds of knowledge, presuppositions, and proofs. Athma is everything. Thus, Athma is the ultimate truth or Brahman or God in truth.

The Athma, which is present in the form of consciousness, is real and eternal. The world in which we exist is an illusion created out of the Athma, which is present in the form of consciousness.

That is why Dalai Lama said: ~ Buddhism need not be the best religion, though it is most scientific and religion and inquisitive. But Buddhism has no answer to certain questions like the existence of Atama [Soul] and rebirth. Dali Lama said that as an individual he believes in rebirth as he had come across a few cases of rebirth. Modern science, Dalai Lama hoped would unearth the mystery behind the rebirth. (In DH –dec-212009-Gulbarga) .

Buddhism has no answer to certain questions like the existence of Atama and rebirth.

People who believe in reincarnation and rebirth theories are unaware that their belief is based on the waking entity is the false self within the false experience. 

The waking entity itself is a false self within the false experience, it means the present experience of birth, life, death and the world is a falsehood. 

Thus, whatever is seen, known, believed, and experienced as the waking entity is bound to be falsehood because the Soul, the Self, which is present in the form of consciousness. 

The Soul, the Self is unborn and eternal because it is birthless and deathless. Therefore, the rebirth and reincarnation theory based on the false Self is bound to be a falsehood.

Accepting rebirth and reincarnation theory as reality is accepting the false self (waking entity or ego) as the real Self and the false experience (waking) as a reality. Self-realization is impossible 

if one accepts the present waking entity as the real Self because the Self is neither the waking entity nor the Self is a dream entity but the Self is the unborn Soul, which witnesses the coming and going of the three states.

The three states are impermanent, but the Soul or consciousness, which is the witness of the three states, is permanent and eternal. 

In Advaitic reality, the three states are one in essence. And that essence is consciousness. Therefore, there is no second thing exists other than consciousness. Thus, consciousness (Soul) is second to none.

A deeper self-search reveals that the waking experience is an illusion. It means the present experience of birth, life, death and the world is an illusion. 

Thus, the reincarnation theory based on the false self within the false experience is bound to be a falsehood. When the waking entity is not the Self then whatever theories are based on the waking entity imagined theory.

This imagined theory based on the waking entity or ego is for that lower mindset that is incapable of grasping the ultimate truth or Brahman.

People who are caught up in the idea of reincarnation and rebirth theories are not qualified for Self-Knowledge or Brahma Gnana or Atma Gnana because they accepted the duality as reality. Birth implies duality and from the standpoint of the Soul, the  

Remember:~

Reincarnation is based on ignorance.  Reincarnation is a religious fable based on the birth entity (ego).   The experience of birth, life, death, and the world is a reality only from the dualistic perspective.

From a nondualistic perspective, there is really no reincarnation at all, either now or before. Nor will there be any hereafter. This is the truth.

Religion propagates reincarnation happens to the individual Soul after the death of the body. Some claim that the Soul goes to heaven or hell while others claim that it is reincarnated in a new body.

Reincarnation theories are based on the imagination based on the birth entity. The birth entity is the false self within the illusory world (dualistic world).  

The religion is dualistic because the religion holds the experience of birth, life, death and the world as a reality.  The religion holds the Soul as an individual and the Soul is within the body.  All the religious and yogic theories are based on the individual Self

From the non-dualistic perspective, the reincarnation theories collapse. From the standpoint of the Soul, the Self, there is no birth or death, no heaven or hell, and no reincarnation.

Religious people who are unable to assimilate the truth, which is beyond form, time, and space, think that reincarnation is true. If one imagines on the base of the ego (birth entity) then he would imagine he would new body and a new life in the new world.

Once one realizes the ‘Self’ is not the ‘I’ but ‘Self’ is the Soul then the ‘I’ ceases to be a reality and the unreality of the experience of the birth, life, death, and the world is exposed.  

All theories about birth, life death, the world, and reincarnation belong to the dualistic illusion.  

Remember:~

The Self is birthless therefore it is deathless. The one which is born lives and dies within the world (waking) is not the Self.  The idea of reincarnation is based on the birth entity (waking entity or ego) which lives and dies within the illusory world (waking).   

The Self is the one which witnesses the coming and going, of the dual (waking or dream) nondual (deep sleep) experiences. When the experience of birth, life, and death takes place in the illusion, then recantation also is part of the same illusion.

The dream becomes unreal when the waking takes place. Similarly, the waking becomes unreal when wisdom dawns. Wisdom dawns when the Soul,   Self, consciously remains awake in its formless nondual nature.  

When the substance and the witness of the three states are one in essence and that essence is consciousness, then what value is there for the universe in, which the experience of birth, life, death and reincarnation happen. 

Even you take reincarnation as a reality, reincarnation happens within the world, which is an illusion, from the standpoint of the unborn Soul, the  Self.  From the standpoint of the unborn Soul, the  Self,  the world in which we are born is merely an illusion.     ~ Santthosh Kumaar