Pathanjali Siddhar:

To the noblest of Sages, Patanjali, who gave Yoga for serenity of mind, grammar for purity of speech, and medicine for the health of the body, I prostrate with folded hands. To this white Patanjali, who has a human form, holding conch, disc and sword and having a thousand heads, I bow.

Sri Pathanjali is considered the first siddhar. The information on Pathanjali is available only in Purana's. Pathanjali is considered as a form / incarnation of Adiseshan (the snake associated with Lord Vishnu). Lord Vishnu sleeps over Adiseshan.

Once, Lord Vishnu saw the Siva Thandava (the divine dance of Lord Siva) and got extremely happy. Adisheshan could not bear the weight of Lord Vishnu in such a state. So, when Adiseshan informed Lord Vishnu of his difficulty, He was told about the Siva Thandava. Adiseshan also wanted to see the Siva thandava. So he did penance and Lord Siva appeared before him and granted his wish to see the divine dance.

Lord Siva told him that he and Viyakramabathar would see his dance in the southern city of Thillai. Thillai is the other name of Chidambaram and it houses the famous Nataraja temple (please refer to the note below for details about the dance of Lord Siva).

Hence, Adisesha came to Thillai in South India and performed poojas for Lord Siva along with Viyakramabathar. Eventually, both of them witnessed the Siva Thandava. Afterwards, Pathanjali (Adisesha) stayed in Thillai forests for a long time. He wanted to teach his script (Vyagarana Suthiram) to his disciples in the thousand-pillar structure in Thillai. However, Pathanjali was afraid that Himself being the form of Adisesha, his disciples would be burnt when they come near his breath.

Hence, he arranged for a partition between himself and his disciples. He taught his disciples sitting behind the partition. Sixty students (disciples) were learning under him. The students were very much impressed with their master and were anxious to see his face.
Once, a student got very apprehensive and pulled the partition to see the face of the master. All the students were burnt at the same instant.

However, one of the students, Kaubathar did not attend the lecture on that day due to an external work. On seeing his fellow students being burnt to ashes, Kaubathar was terrified. Pathanjali changed his form and pacified his student. Pathanjali was very happy that one of his disciples is alive and he taught all the skills to his disciple, Kaubathar. Kaubathar's disciple is Govinda Bhawat Badal, who is also considered as the Guru of Adi Sankaracharya.

There are varied schools of thought that the Pathanjali who wrote "Maha Bashyam" in North India is different from the Pathanjali who wrote "Gyana Sutra" in Tamil. As siddhars have been known to live for ages, the period of the life of Pathanjali and the exact duration of his life can not be known.

Moreover, there are no definitive texts available about Pathanjali. Both Pathanjali and Viyakramabathar had lived in Tamil Nadu in a period where siddhars had also lived there. Both of them had observed the divine dance of Lord Siva at Thillai in Tamil Nadu. Both of them attained their Samadhi at Rameswaram in Tamil Nadu. Hence the argument that Pathanjali could not have written texts in Tamil could not be true.

About Siva Thandava (as given in templenet):

The dance of bliss, or the Ananda Tandavam of Siva is said to symbolize the five divine acts of creation, sustenance, dissolution, concealment and bestowment of grace. The dance of Shiva has been frozen in metal and held in worships in Nataraja Sabhas, in virtually all of the Saivite temples in Tamilnadu.

Five of the foremost Sabhas (Pancha Sabhai) are at Chidmbaram (Kanaka Sabhai the hall of gold), Madurai (Rajata Sabhai the hall of Silver), Tiruvalangadu near Chennai (Ratnasabhai the hall of rubies), Tirunelveli (Tamirasabhai the hall of copper) and Kutralam near Tirunelveli (Chitrasabhai the hall of pictures).

Other dance halls of significance are Adri Sabhai (the Himalayas), Aadi Chitsabhai (Tiruvenkaadu near Chidambaram) and Perur Kanakasabhai (Patteeswarar temple at Perur near Coimbatore).