The point of Bhagavan Buddha is that if God is non-existent, the entire creation including Self is non-existent.+

Bhagavan Buddha: ~ There are only two mistakes one can make along the road to truth: not going all the way... and not starting

Dalai Lama said:~  Buddhism need not be the best religion though it is more 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).

People who argue that Soul does not exist are not aware of the fact that their own existence is dependent on the Soul, which is in the form of consciousness.

One should not conclude because some great thinkers said so or some philosophy says so. Without consciousness, the mind, which is in the form of the universe ceases to exist. Man ceases to exist without the universe. The universe ceases to exist without the Soul, the innermost Self.  The Soul can exist with or without the universe.

The Soul is present in the form of consciousness. Consciousness is the formless substance and the witness of the mind. The mind is present in the form of the universe. The universe appears as waking or dream (duality) and disappears as deep sleep (nonduality.

From the standpoint of the Soul, the Self the birth, life, death, rebirth, and reincarnation theory is part of the dualistic illusion.  Your body cannot reincarnate because it is insentient. 

Bhagavan Buddha: ~ Do not believe in anything merely on the authority of your teachers and elders. 

Sage Sankara opposed the Buddhists only, who misunderstood Bhagavan Buddha and became atheists. According to Sage Sankara meditation always means the critical analysis about the Self to get salvation from worldly tensions. Due to the eccentric ego of the then atheists, Sage Sankara did not go beyond this since the atheists will not accept God beyond themselves. This limitation is not due to limited knowledge of Sage  Sankara but is due to the then-existing situation of the psychology of the surrounding society. 

Even Bhagavan Buddha kept silent about God because the society dealt by Him consisted of Purvamimamsakas, who were strong atheists. Bhagavan Buddha told that everything including the Self is only relatively real (Sunya). This is correct because the Self is a part of the universe, which is relatively real with respect to the absolute unimaginable God. The Bhagavan Buddha stopped at this point because the atheists cannot realize the existence of the unimaginable God indicated through His silence. 

The point of Bhagavan Buddha is that if God is non-existent, the entire creation including Self is non-existent. Sage Sankara wanted to establish the existence of the Brahman. For this purpose, He made the Atman as Brahman. He brought out the identity of the Self with the 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 Atman or Soul, the innermost Self. Both Bhagavan Buddha and Sage Sankara kept silent about the absolute unimaginable God. The same philosophy was dealt with by them from different angles in different situations.

Even in Buddhism: - Buddhist teaching has itself become a kind of interactive and Self-evolving process, much like its idea of pratityasamutpada. However, the end goal is still Nirvana, which is an experience ultimately beyond all concepts and language, even beyond the Buddhist teachings. In the end, even the attachment to the Dharma, the Buddhist teaching, must be dropped like all other attachments. The tradition compares the teaching to a raft upon which one crosses a swift river to get to the other side; once one is on the far shore; there is no longer any need to carry the raft. The far shore is Nirvana, and it is also said that when one arrives, one can see quite clearly that there was never any river at all.

Chandogya Upanishad: ~ One who meditates upon and realizes the 'Self' discovers that everything in the cosmos-- energy and space, fire and water, name and form, birth and death, mind and will, word and deed, mantrams and meditation--all come from the Self.

Sage  Goudpada: ~ To establish the truth of Non-duality by sheer reasoning alone. He begins by defining "What is real?" "What is unreal?" etc, because that is the right way to discuss or teach. People must first know what they are talking about. (Manduka Karika)

Buddhism and its relationship with Science is like that of water and wine, one cannot say there is no water in wine, but when you drink it, it would not be the water but wine... thus Einstein’s view is water in wine because modern science does not believe in the matter but in this religion, everything is the matter only"

Sage Sankara says you must first know what is before you. If you cannot know that, what else can you know or understand? If you give up the external world in your inquiry, you cannot get the whole truth.

Emptiness is the nature of the Soul, which is present in the form of consciousness. Emptiness is the fullness of consciousness without the division of form, time, and space.

For proof of God's creation of the world, you have to go back to a time when there was no world. Since this is impossible, there is no proof of creation. Hence Bhagavan Buddha kept silent. Hence four schools of Buddhism sprang up later which varied from realism to emptiness claiming to interpret his silence. 

We have one key from Sage Sankara to be applied to every statement or assertion or speculations: It is “Is this true?” “Where is the proof?” Opinions belong to scholasticism, not to Advaitic truth. Advaita has no use for opinions.

By discriminating between the dual (waking or dream) and non-dual (deep sleep) experiences and realize the existence of the formless witness of the coming and going of the three states.   The Soul, the  Self is the formless witness of the coming and going of the three states (witnessed).

From the standpoint of the Soul, the innermost Self, the three states are nonexistent as reality because the witness and the witnessed are one in essence. That essence is the Soul, which is present in the form of consciousness. Thus, the consciousness is real and all else is unreal.

The Soul, the  Self is beyond form, time, and space.  The Soul, which is present in the form of consciousness, is the very form of existence, though one would find it difficult to understand because of the intoxication of the illusory duality.

This formless non-dual Soul is beyond the mind.   The Soul, the Self is never subject to any change by any cause, but the waking is subject to change as deep sleep or dream, and when this is realized then one becomes aware of the fact that the subject and object are one in essence.

The difference between mind (universe) and Soul (consciousness) is only when one considers the waking entity (ego or you) as the Self.

From the ultimate standpoint, there is no second thing that exists other than Soul or consciousness because the formless substance and witness of the mind or universe is consciousness.   The mind and Soul are one in essence. 

Remember:~ 

Buddhism has not proved the truth of Non-duality.  There is no doubt Bhagavan Buddha pointed out the unreality of the world. Bhagavan Buddha told people they were foolish to cling to it. But he stopped there. Bhagavan Buddha came nearest to Advaita in speech but not to Advaita fully.

The distinction between Sage Sankara’s Advaita and Vijnanavadin Buddhism is that the former is mentalism i.e. mind is the real, whereas the latter is idealism, i.e. ideas are real. Advaitins follow the former.

Buddhism did not graduate its teaching to suit people of varying grades; hence its failure to affect society in Asia.

Sage Sankara opposed the Buddhists only, who misunderstood Bhagavan Buddha and became atheists. 

According to Sage Sankara meditation always means the critical analysis about the Self to get salvation from worldly tensions. Due to the eccentric ego of the then atheists, Sage Sankara did not go beyond this since the atheists will not accept God beyond themselves. This limitation is not due to limited knowledge of Sage Sankara but is due to the then-existing situation of the psychology of the surrounding society. Even Bhagavan Buddha kept silent about God because the society dealt by Him consisted of Purvamimamsakas, who were strong atheists. 

Bhagavan Buddha told that everything including the Self is only relatively real (Sunya). This is correct because the Self is a part of the universe, which is relatively real with respect to the absolute unimaginable God. The Bhagavan Buddha stopped at this point because the atheists cannot realize the existence of the unimaginable God indicated through His silence. 

Bhagavan Buddha as a constructive worker committed an error in failing to give the masses a religion, something tangible they could grasp something materialistic, if symbolic that their limited intellect could take hold of, in addition to his ethics and philosophy. Here Sage Sankara was wiser and gave religion; such as karma and Upasana.--to the ignorant masses, as well as wisdom to those of higher intellect.

The Advaita Sage Sankara' gave religion, rituals, and dogmatic instructions to the populace, but pure philosophy only to the few who could rise to it. Hence the interpretation of his writings by commentators is often confusing because they mix up the two viewpoints. Thus, they may assert that ritual is a means of realizing Brahman, which is absurd.

Bhagavan Buddha's teachings that all life is misery belong to the relative standpoint only. For you cannot form any idea of misery without contrasting it with its opposite, happiness. The two will always go together. Bhagavan Buddha taught the goal of cessation of misery, i.e. peace, but took care not to discuss the ultimate standpoint for then he would have had to go above the heads of the people and tell them that misery itself was only an idea, that peace even was an idea (for it contrasted with peacelessness). That the doctrine he gave out was a limited one, is evident because he inculcated compassion. Why should a Buddhist sage practice pity? There is no reason for it.

Advaita is the next step higher than Buddhism because it gives the missing reason, viz. unity, non-difference from others, and because it explains that it used the concept of removing the sufferings of others, of lifting them up to happiness, only as we use one thorn to pick out another, afterward throw both away. Similarly, Advaita discards both concepts of misery and happiness in the ultimate standpoint of non-duality, which is indescribable.

Buddhists say that a thing exists only for a moment, and if that thing has still got some of the substance from which it was produced, how then can they deny that its cause is continuing in the effect; hence its existence is more than a moment. Vedanta is concerned with whether it is one and the same thing which has come into being or has it come out of nothing.: ~Santthosh Kumaar