Tagore: "According to Indian Philosophy there is Brahman, the absolute Truth, which cannot be conceived by the isolation of the individual mind or described by words but can only be realized by completely merging the individual in its infinity. But such a Truth cannot belong to Science. The nature of Truth which we are discussing is an appearance – that is to say, what appears to be true to the human mind and therefore is human, and may be called maya or illusion."
Indian philosophy has long held that there is no individual consciousness, but something encompassing the whole: - Knowledge is just that, knowledge, and it just exists; like numbers, pythagorous theorem etc. - Reality (as consumed by human mind) is result of senses interacting with that knowledge, and producing the illusion of individual. More importantly, it creates "observed knowledge". - The relationships within observed knowledge, which are uncovered by mathematics. Observed knowledge "shadows" the reality, but at no point can we say that observed knowledge is exactly same as reality. - Exactly as we can manipulate the information in computer, the observed knowledge itself can be manipulated. For example, one could add a new "sense" and thus sense the reality in wholly new manner.
So, if anybody says "There is an entity independent of the observed reality, and thus can manipulate it independent of the rules of that reality", then they are merely creating another observed reality.
But then, Indian philosophy further goes ahead and says the consciousness is independent of all this, and therefore, it will forever be creating newer and newer experiences out of the contents of the reality.
So if you identify yourself with brain, all you are saying is that "it is simply not possible to derive any more knowledge other than what senses + mathematics give us".
Instead, if you identify yourself as an entity independent of knowledge itself, then at least there is possibility of finding out if there is an ultimate reality much beyond the brain, and most important, it should "free you" from the bodily limitations.
And hence in India (in particular, the Advaita philosophy) they say, you are "Brahman", i.e. you are yourself God, but you mis-identify yourself as body and brain.
(As an aside, if you come to India, check out the religious channels and listen to Gurus talking there. Most of them convey this very philosophy to its very core!)