Buddhist do not believe in the existence of the Athma. Buddhist believe in emptiness and they fail to realize the emptiness is the nature of the Athma.+

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)

The Upanishads have the answer to the existence of the Atama.

Brihadaranyaka Upanishad: ~ Brahman (God in truth) is in the form of the Athma, and it is indeed Athma itself.

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.

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, Advaita 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).

Advaita is very different from Buddhism. Advaita regards consciousness as permanent and all-pervading while Buddhists regard it as momentary. Madhyamikas regard that a non-existent entity can appear in perception like it does in the snake in the rope illusion.

Buddhism has not proved the truth of Nonduality because Buddhists do not believe in the existence of the Athma. Buddhist believe in emptiness and they fail to realize that emptiness is the nature of the Athma. 

Bhagavan Buddha pointed out the unreality of the world, and Advaitic Sages agree. Bhagavan Buddha told people they were foolish to cling to it. But he stopped there. He came nearest to Vedanta in speech but not to Vedanta fully.

Only when we independently search for the truth without religion and its doctrine then we will be able to realize the truth beyond form, time, and space.

Unless one exercises his Buddhi--reason--there is no chance of getting the ultimate truth or Brahman.   

Buddhism is not Bhagavan Buddha's wisdom because Bhagavan Buddha's wisdom is lost in diverse Buddhist theories. Bhagavan Buddha is not the founder of Buddhism because Bhagavan  Buddha rejected religion, the religious idea of God, and the scriptures.

Advatic wisdom does not belong to neither   Buddhism nor Hinduism because Advatic wisdom is pure spirituality. Buddhism and Hinduism are based on form, time, and space whereas Advatic wisdom is based on the Athma (Spirit), which formless, timeless, and spaceless existence. 

Remember:~

You cannot live without the physical world; it is the basis of your life, so it must be the starting point of your inquiry. Things, not imaginations, must be the truth seeker's material.

Without knowing the nature of the world in which you exist, it is impossible to know the truth, which is beyond form, time, and space. What is the use of trying to find our inner Self before we understand the world, which confronts us?  You have to realize the fact that, this world that confronts you is also consciousness. 

If you do not make his induction from facts from the world before you, then you are only drawing on your imaginations. By saying the  ‘Self’ is like this, or like that." but it will be only your imagination.

You must inquire into the nature of the ‘I’ i.e. matter. Second, he must inquire into the nature of the Soul, the innermost Self. To say the world in which you exist as an illusion without first examining them and inquiring into them thoroughly is to delude yourself.

This world is common to all of us, therefore you must begin our inquiry with it and not avoid it. It is only after you have inquired into the nature of the objective world, that you should inquire into who is the knower. If, however,  you inquire into the knower before the inquiry into the world in which you exist, then it is mere mysticism.

‘What is this world?’ must precede ‘What is this I? in the Atmic path.

Look at everything in its essence because in everything there is consciousness.  You should not avoid them, do not shut your eyes to the world in which you exist; do not shut yourself away from the world which is as much consciousness, as anywhere else.

Those who are weak and those who are not sharp enough to grasp the truth beyond the form, time, and space advise others to be non-observant and to withdraw.  Soulcentric reasoning will help, not hinder your pursuit of truth.  There is no need to run away from worldly life in ascetic fear or shyness of them.

The yogi shuts his eyes against the world and then has the temerity to declare that he knows the world to be Brahman! Because he has not inquired into the world in which he exists, he knows nothing.  Yoga cannot remove ignorance. It is only a step. It removes obstructions.

Sage Sankara definitely says: ~ Yoga is not the means of liberation. (pages 132-133 of his commentary on Brihadaranyakopanishad).

In Sutra Bashya and Manduka: ~ Samadhi and sleep are identical.

Brihad Upanishad does not advocate Samadhi.

Self-knowledge or Brahma Gnana or Atma Gnana cannot come if anything is left out. The whole universe must be included. For only when all is known can all be known to be but ideation. Hence,  yogis blotting all out in Samadhi cannot lead to Gnana.:~Santthosh Kumaar