I've heard that by the Vedic doctrine of MAYA, everything that we see around is an illusion. Thus, by this doctrine, the sun, the moon, the billions of stars in the night sky as well as mountains, oceans, volcanoes, plants, animals, mushrooms, etc., etc. (i.e. in a word, the entire Universe) are Nonexistent. As far as I know, Adi Shankara interpreted it thus as well. Nevertheless, Vivekananda claimed that MAYA means Neither truth Nor falsehood. This gave rise to great confusion. MAYA= Not truth= Not falsehood means truth= falsehood. It's an absurdity. A day must be either a Rainy day or a Non-Rainy day. It canNot be both a Rainy day and a Non-Rainy day, can it be?
In the 20th verse of Brahmajnanavalimala, Adi Shankara says.
ब्रह्म सत्यं जगन्मिथ्या जीवो ब्रह्मैव नापरः । अनेन वेद्यं सच्छास्त्रमिति वेदान्तडिण्डिमः ॥ २०॥
Brahma Satyam Jagan Mithya Jivo Brahmaiva Na Aparah
Brahman (the Absolute) is alone real; the world is mithya; Jiva is non-different from Brahman.
Mithya actually means it is not sat or asat.
Shankara in Brahma Sutra Bhasya I.1.2 defines sat as that is available at all times (trikalaabaadhyami) including dreams and deep sleep. Thus Only Brahman is sat.
asat is used to mean unfitness to appear as existent (tuccham) on any locus. For example: hare’s horn or unicorns.
jagat is not real like Brahman, because it is subject to time/space/change but it is also not asat. However, jagat is mithya, which is neither sat nor asat.
To give you an example how it can be both. Take the case of the rope being mistaken as a snake. When the rope is not perceived, only snake is perceived and when the rope is perceived, no snake is perceived. Thus, when the world is viewed as separate from Brahman, it is false and when the world is viewed as same as Brahman, it is sat.
Maya has two Shaktis - Avarana and Vishepa Shakti. Avarna Shakti means veiling power, which does not allow you to realize Brahman. Viskshapa Shakti means projecting power, which projects the universe and the body.