Across the religious traditions that are today encompassed by the terms ‘Islam’ and ‘Hinduism’, a recurring motif is that the originative cause of the world is also the spiritual breath animating its return to its singular root. In this paper, I venture into the relatively unexplored terrain of a Hindu-Muslim comparative inquiry into the intimate presence of the divine reality to the finite world. More specifically, I offer a comparative analysis of the conception of the infinite in the worldviews of two major philosopher-poets of the Indian subcontinent – Muhammad Iqbal (1877-1938) and Rabindranath Tagore (1861-1941). I argue that both Iqbal and Tagore, drawing on their distinctive religio-cultural inheritances, set forth the relation between the finite and the infinite as non-contrastive, wherein the infinite stands not as a reifiable item in a cosmic inventory but as the ever-creative and sustaining ground of all that there is. In short, I will highlight their distinctive ways of articulating two poles of a fundamental paradox – the infinite encircles the finite and the finite recapitulates the infinite. Building on this motif of God-human ‘encirclement’, I will develop some of the implications of their cosmologies for their visions of human becoming – an existential undertaking that is, for both figures, firmly rooted in, and dynamically oriented to, the boundless divine reality. By analysing this logic of the infinite in their writings, I will suggest that conceptual inquiries in a Hindu-Muslim comparative key can yield a much richer theological harvest than what may be initially expected while ploughing through their scriptural fields.