He was the eldest of seven children in a Roman Catholic Hungarian noble family Farkas de Kisbarnak, which can trace back their origins to the first half of the 17th century.

His father was Farkas Ferenc de Kisbarnak (1820–1882), administrator of the states of Réde, property of the county Esterházys; his mother was Cecília Hoffmann (1826–1907).

His paternal grandparents were János Farkas de Kisbarnak (1769–1822), state administrator of Súr (property of the Counts Zichys) and Anna Fiber.

His other nephew was Gyula Farkas de Kisbarnak (1894–1958), literary historian, Finno-Ugric linguist, professor of the University of Göttingen.

His family moved around a lot but Farkas attended the gymnasium at Győr (Raab), where he was encouraged towards physics by Ányos Jedlik.

While teaching in a secondary school at Székesfehérvár (Stuhlweissenburg), he read his paper at the Hungarian Academy of Science which was subjected to the critique of Lorand Eotvos.

If the forces in a system are conservative, finding the necessary condition for equilibrium is equivalent to minimizing the potential subject to constraints.

His best-known mathematical paper was ‘Theorie der einfachen Ungleichungen’ published in 1901 where he proved his inequality theorem.

Farkas was among the first to have a modern approach to entropy and derived the Carnot-Clausius principle mathematically fourteen years before Carathéodory.