Adi Shankaracharya is believed to be incarnation of Lord Shiva. What are views of Gaudiya Vaishnavism on Adi Shankaracharya?
According to Sri Chaitanya Charitamrita, Sri Chaitanyadeva quoted the slokas of Padma-Purana ( CC 2/6/162-164)
Sri Krishna's order to Shiva : " Swaagamaih kalpitastawamcha janaan madbimukhaan kuru" -- make peole distarcted from me by creating your own inaginary paths.
Shiva's statement in Padma-Purana to Devi : Mayavaadam asat shaastram prachchannam baudhdham uchchyate/ Maya eva bihitam devi kalau brahmana-murtina// -- Mayavaad is a false doctrine which is buddhism in disguise. I have preached this in Kaliyuga taking a brahmin form."
The above provides the view of the Gaudiya Vaishnavas on Adi Sankaracharya as mentioned in the Sri Sri Chaitanya Charitamrita.
Gaudiya Vaishnavas accept Adi Shankara to be an incarnation of Shiva. However, they believe that like Buddha, Adi Shankara was born to deviate the people in Kali-Yuga from the path of the Vedas.
This is what Jiva Goswami states in his "Sri Tattva Sandarbha" regarding Adi Shankara:
atha yad eva kaivalyam apy atikramya bhakti-sukha-vyaharadi-lingena-nija matasyapy upari viraj amanartham matva yad apauruseyam vedanta-vyakhyanam bhayad acalayataiva sankaravatarataya prasiddhena vaksyamana-sva-gopanadi hetuka-bhagavad-ajna-pravartitadvaya-vadenapi etan-matra-varnita-visva-rupa- darsana-krta-vrajesvari-vismaya-sri vraja-kumari-vasana-cauryadikam govindastakadau varnayata tata-sthi-bhuya nija-vacah-saphalyaya sprstam iti.
Sankaracarya, known to be an incarnation of Lord Sankara, considered the message of Srimad-Bhagavatam far superior to his own conception of merging with the Supreme, in as much as it reveals the pleasure pastimes of pure devotion and other special truths. Because the Personality of Godhead wanted to hide Himself and accomplish other purposes, Sankaracarya on His order promulgated the philosophy of Oneness, which we will discuss later on. Nonetheless Sankaracarya was anxious not to disturb the Bhagavatam, the original authorless commentary on the Vedanta. By depicting in his Govindastaka and other works events described only by the Bhagavatam — such as the Queen of Vraja's amazement at seeing the total form of the universe and Krsna's stealing the clothes of the unmarried girls of Vraja — he kept himself at a respectful distance and merely touched the Bhagavatam to assure the success of his own words. (Sri Tattva Sandarbha 23.3)