By Swami Harshananda
Ajātivāda literally means ‘doctrine of non-origination’.
Creation of the world is one of the fundamental problems invariably discussed in the philosophical systems. In whichever way a system posits the basic reality, as one or many, from which the world has evolved, logical and ontological difficulties can never be avoided. Gauḍapāda, the guru of Śankara’s preceptor, and the famous author of the Kārikās on the Māndukya Upanisad has successfully tackled this problem by denying the problem itself!
Gauḍapāda, one of the earliest writers on Advaita Vedānta, takes the view that Brāhman or Ātman alone is the only reality that exists and hence neither the world nor the jīva (individual self) ever comes into being. Since Brāhman has no birth (jāti = birth or origination) nor modification, his doctrine is termed ajātivāda. Brāhman alone is real. Anyone who sees the world of duality as existing and tries to discover its origination from Brāhman is trying to ‘see the footprints of the birds in the sky’. 
Gauḍapāda establishes his ajātivāda on the bases of the arguments on the śrutis as well as logic and reasoning. He admits that the Upaniṣads have described creation but avers that they have never declared it to be real. The main purport of such statements is to emphasize the non-dual Reality behind this apparent diversity.
After successfully countering the arguments of all other schools and establishing his ajātivāda, Gauḍapāda goes to the extent of denying even ajāti! Since the very concept of an external world which includes the revealed scriptures, is an illusion, even the theory of ajāti established on the basis of such scriptures and logic, is an illusion! From the highest standpoint, the Atman is not aja (unborn) also. He is beyond all relative descriptions and hence defies all such attempts.
- The Concise Encyclopedia of Hinduism, Swami Harshananda, Ram Krishna Math, Bangalore