Maya is an important category in explaining the philosophy of Śankara (pronounced as Shankara). For him Maya is not pure illusion. It is a cross of the real and the unreal. It is neither existent nor non-existent nor both. It is not existent as the only one that exists is Brahman nor is it non-existent as it is responsible for the appearance of the Brahman as the world. It is called superimposition, like a shell being mistaken as silver. And when right knowledge arises this error vanishes. This relation between shell and silver is neither that of identity nor of difference nor of both. It is unique and is known as non-difference ( tadatmya). Thus, when right knowledge dawns, which is realisation of the oneness of jiva with the Paramatman, Maya vanishes.
Śankara emphasizes the phenomenal point of view that the world is real as long as true knowledge does not dawn. It is not an illusion. It is a practical reality. In his book A Critical Survey of Indian Philosophy (Motilal Banarsidas; 1983), Chandradhar Sharma writes, " He who imagines that Shankara's position means complete denial of this world, of this souls, of action, of philosophy, of religion and even of God, may know anything but Shankara Vedanta."
Just as it is said that Hegel is a born foe of Mysticism, Madhvacarya (b. 1197) may be said to be a born foe of Sankara. Madhva is the champion of dvaita (unqualified dualism) as much as Sankara is the champion of advaita (non-dualism). His hatred for Advaita is so great that he called Advaitins 'deceitful demons. For Madhva there is a real difference between God and the world; whereas for Sankara the difference is appearance, subjectively different, and not real as in the sense of being ontologically different.
In his book Victory of Reason by Rodney Stark quoted the very distinguished Joseph Needham, Oxford historian of Science, to conclude that the failure of the Chinese to develop science was due to their religion, to the inability of Chinese intellectuals to believe in the existence of laws of nature because the conception of a divine celestial lawgiver imposing ordinances on non-human Nature never developed. Quoting Needham he continued, " The Taoists, indeed, would have scorned such an idea as being to naive for the subtlety and complexity of the universe as they intuited it." I believe it's not just the Taoist, the Advaita Vedantins as well would have scorned such an idea. Chandradhar Sharma noted, " Shankara... gave the final death-blow to Buddhistic philosophy", and after this we saw the rise of Advaita Vedanta into prominence among Indian religious scholars. And within Sankara's non-dualism there is no scope to recognize the 'lawgiver imposing ordinances on non-human Nature" because the concept of the difference between Creator and creation never fully developed.
I do think that Madhva's philosophy would provide a far better philosophical ground than Sankara's for science and moral philosophy to flourish in India. Christianity and Islam have such distinction between God and the world and would be equally fertile for scientific advancement. However, for the Hindus I believe the answer to human flourishing does not lie in Advaita Vedanta. Madhvacarya's Dvaita is perhaps a very viable alternative philosophy that needs further engagement.