Who is a Paramahamsa? Answer from Paramahansa-Parivrajaka Upanishad

In this world, very rare is the mendicant monk who is a Paramahamsa. If there is one, he is ever pure.

He alone is the Purusha glorified in the Vedas.

He who is a great man (maha purusha) has his mind resting in me; I too remain in him alone.

He is the ever satisfied.

He is free from the effects of cold and heat, happiness and misery, honor and dishonor.

He puts up with insult and anger.

He is devoid of the six human infirmities – hunger and thirst, sorrow and delusion, old age and death – and is free from the six properties of the body – birth, existence, change, growth, decay and death.

He is without the intervention (i.e. he is not circumscribed by) of elderliness or otherwise.

Excepting the self, he sees nothing else.

Unclad, bowing to none, not uttering ‘svaha’ (as he worships no gods), not uttering ‘svedha’, free from blame or praise, not resorting to mantras and rituals, not meditating on other gods (than the supreme God), free from blame and praise, refraining from aims and their absence, with all the activities ceased, firmly established in consciousness consisting of existence, knowledge and bliss, being conscious of the one supreme bliss, he ever meditates on the Brahma Pranava, that he is Brahman alone, and thus fulfils himself.

Such a one is the Paramahamsa mendicant monk.

Paramahamsa-Parivrajaka Upanishad