Kapila is the avatar of Vishnu described as the sage who propounded the Samkhya school of philosophy.
In the Bhagavata Purana, Kapila is presented as the son of Kardama and Devahuti and as a divine teacher who explains spiritual knowledge to his mother. His teaching distinguishes conscious spirit, or purusha, from primordial nature, or prakriti. This analytical framework became central to Samkhya thought and later influenced Yoga philosophy.
Kapila is also described in several Puranic traditions as an incarnation of Vishnu, although the historical Kapila and the theological figure may reflect layers of tradition. Scholars also caution that the name Kapila appears in accounts of more than one sage, and the surviving Samkhya Sutra cannot be securely dated to his lifetime.
A common mix-up is with Patanjali, who systematized Yoga, or Vyasa, who is associated with commentaries and epic literature. In this question, the distinctive combination of Vishnu avatar and Samkhya points to Kapila.