Seal of the Matha
The seal shows a swan above the sentence Brahmaiva satyam. The image has been adapted from the offical seal of the Sringeri matha, which shows a swan on a lotus, above the Yajurveda Mahavakya, Aham Brahmasmi. Swan figures come from traditional Hindu symbolism, and can be found in oil-lamps used in temples and at shrines in people's homes. Swan and lotus motifs are also found in seals of other advaita institutions.
The swan has a special association with Advaita Vedanta. The swan is called Hamsa in Sanskrit. The highest monks in the advaita order are called Paramahamsas - the great swans. The Sringeri Sankaracharyas are Paramahamsa Parivrajakas. The word Hamsa is a variation of so'ham: I am He, which conveys the basic teaching of the yajurveda mahavakya, "Aham Brahmasmi". There are other equivalences between the swan and the monk, that make the swan a particularly apt symbol for advaita The swan stays in water, but its feathers do not get wet. Similarly, the monk must live in the world, yet remain unaffected by life's ups and downs.
The lotus also has similar connotations. Lotus leaves stay on the surface of the water, but do not absorb water. The flower is a symbol of divinity immanent in the waters of creation, and reminds us of Brahman's immanence in the universe. It is a thing of beauty even though it grows out of the mud. Lotus petals are found in various yantras like the well-known Sriyantra. The lotus and the swan are associated with the Universal Goddess in Her aspect as Sarasvati, the Goddess of Wisdom. The lotus is Her seat and the swan is Her vehicle. Lotuses also adorn the hands of Goddesses Lakshmi and Uma.
In India, the swan is also mythically credited with the ability to separate milk from water. Similarly, the advaitin strives to discriminate the eternal Atman from the non-eternal world. The Atman is immanent in the world, just like milk mixed with water, but It can never be truly realized without the nitya-anitya-vastu viveka that is essential to the monk. The swan is thus a symbol for the jivanmukta, who is liberated while yet alive in this world, by virtue of having realized Brahman.