Optimization

Samkhya is one of the six schools of classical Indian philosophy. Sage Kapila is traditionally considered as the founder of the Samkhya school. It is regarded as one of the oldest philosophical systems in India. Samkhya was one of the six orthodox systems (astika, those systems that recognize vedic authority) of Hindu philosophy. The major text of this Vedic school is the extant Samkhya Karika. There are no purely Sankhya schools existing today in Hinduism, but its influence is felt in the Yoga and Vedanta schools.
Samkhya is an enumerationist philosophy that is strongly dualist. Samkhya philosophy regards the universe as consisting of two realities: Purusha (consciousness) and Prakriti (phenomenal realm of matter). They are the experiencer and the experienced, not unlike the res cogitans and res extensa of René Descartes. Prakriti further bifurcates into animate and inanimate realms. On the other hand, Purusha separates out into countless Jivas or individual units of consciousness as souls which fuse into the mind and body of the animate branch of Prakriti.

Purusha|Prakriti|
Consciousness( Self)|Phenomenal realm of matter|
Experiencer|Experienced|
Separates out into countless Jiva or individual units of consciousness which fuse into the mind and body of the animate branch of Prakriti|Bifurcates into animate and inanimate realms|
Passivity|Dynamism |

There are differences between Sankhya and Western forms of dualism. In the West, the fundamental distinction is between mind and body. In Samkhya, however, it is between the self (as Purusha) and matter (Prakriti).
Epistemology:
According to the Sankhya school, all knowledge is possible through three pramanas (means of valid knowledge) -

1. Pratyaksha or Drishtam - direct sense perception,
2. Anumana - logical inference and
3. Sabda or Aptavacana - verbal testimony.

Sankhya cites two kinds of perceptions: Indeterminate (nirvikalpa) perceptions and determinate (savikalpa) perceptions.

Nirvikalpa: