This philosophy was established by Sripad Sankaracarya, in order to refute Buddhistic doctrine.
The Mayavadis believe that the Supreme Truth is brahman or spiritual energy which is unlimited, without form, qualities, or activity. According to Mayavada philosophy, all living entities are one with brahman, but at present, are covered by illusion, and therefore temporarily seperated from brahman. When the illusion is gone, the living entity becomes again one with the brahman and loses its identity.
The main idea is that everything is God, meaning that you too are God but somehow or other you forgot that you were God.
Out of this perspective, the Mayavadis neither accept the form nor the personality of Krsna as absolute but as creation of maya. Therefore, Sri Caitanya Mahaprabhu called the Mayavadis the biggest offenders of Krsna.
Mayavada-philosophy is also spread under the name "Vedanta-philosophy". The majority of all western philosophers (if they are not dogmatic followers of the Bible) who are studying Indian culture and philosophy also fall into this category because they do not differentiate between the higher, spiritual energy, and the lower, material energy. They do not have a proper understanding of the transcendent nature of God.
Since people in general do not have sufficient information about the transcendental form of God, they are easily influenced by Mayavada philosophy. Whenever we meet people who accept the Vedas we will find that it is not so difficult to establish the Personality of Godhead on the basis of sastra. Since the majority of people are neither interested in any proofs from the sastra and don't recognize sastra as such, we have to establish Vaisnava philosophy on the basis of logic. There are some fatal defects in Mayavada philosophy which we should be able to recognize when confronted with it or otherwise have to deal with the subject:
1. Since we possess individuality, it is not logical that our ultimate source doesn't possess individuality. Since we can normally observe that personality is superior to an impersonal energy, we can conclude that personality is superior to impersonal energy. Since the Vedanta sutra explains that the Absolute Truth is the source of all existence, it must also be the source of personality and possess personality.
2. The Mayavadis say that the brahman is manifested in a personal form in this material world. How can something personal be manifested from something impersonal? Where do we have an experience of such a phenomena? Lord Krsna explains in Bg 7:24 that this theory is extremely illogical and indicates a lack of intelligence.
3. It is said that brahman is unchangeable. How then can it split into different living entities within the material world? And why should it do that? In Bhagavad-gita, Lord Krsna explains (15:7) that the living entities are eternal parts and parcels of the Supreme and states than individuality is an eternal principle (Bg 2:12).
4. If we were all God, why is there so much suffering and ignorance in the world? Also, if we say that we are God but just temporarily covered by illusion, then illusion would be more powerful than God, which doesn't make any sense.
5. The speculation that Krsna's body is material clearly indicates a complete misunderstanding regarding the transcendental appearance and nature of Krsna. Krsna's body does not consist of matter and contains unlimited, varied energies and attracts even liberated personalities, who are free from material attachments. (SB 1.7.10)
6. Reality according to Mayavada philosophy is beyond material form and duality. But they are erring in the premise that there is no spiritual form or variety. The negation of these facts is a materialistic concept and doesn't provide us any information about spiritual reality.
7. The desire to become one with God is called the "last snare of maya". Because the Mayavadis got frustrated with their attempt to become the supreme enjoyer in this material world, they want to become one with the Supreme. This desire is illusory because the soul is by constitution Krsna's servant. The Srimad Bhagavatam(10:2:32) explains that the misconception of the impersonalists is caused by an impure intelligence and that consequently their realizations are not ultimate and they are thus forced to fall down again to the material platform.
8. The material world is not false ("brahma satyam, jagan mithya" is one of their favourite slogans)/ because the material world originates in the Absolute Truth, it is real but temporary. However, the belief that the material world is permanent is false-in other words the material world is real but temporary.