# Gyula Farkas

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### Brief Biography

Gyula (Julius) Farkas was a famous Hungarian mathematician and theoretical physicist, whose name is best known to optimizers and OR specialists because of his theory of linear inequalities. He also obtained fundamental results in analytical mechanics in that he gave necessary condition for the equilibrium of a mechanical system, where the states are constrained by inequalities. These results earned him the place of a forerunner of modern optimization theory. His biographical data, mentioned below, are taken from his autobiography.

Gyula Farkas was born on March 28, 1847, in the village of Sárosd, Fejér County, western Hungary. His father was the manager of a nearby estate. Gyula was the first of seven children. The family soon moved to Réde, Veszprém County, where Gyula’s father became the manager of an Esterházy estate. After a few years, they moved to the city of Gyõr, where Gyula joined the high school of the Benedictine fathers. He graduated in 1866. During the high school years in Gyõr, his interest turned to music and he published three papers in the nationwide periodical: Music Theory.

After graduation he was admitted to the University of Pest (Buda and Pest were united only in 1873 to form the city of Budapest), where he started to study law. He was also admitted to the music academy but considered himself less talented than other students and gave up studies in music. He was, however, an excellent pianist and later on, while serving as a high school teacher, gave public piano concerts. He also had to cut short his studies in law because his father went bankrupt. Farkas became a private tutor in well-to-do families first in the countryside, and then in Pest. Not long afterwards, he was able to continue his university studies, but he abandoned law and studied physics and chemistry. He had excellent professors, one of whom was the Benedictine monk Ányos Jedlik, the first inventor of the dynamo, and Farkas decided to pursue a career in science. He finished his studies in 1870 and became a high school teacher in physics and chemistry in the city of Székesfehérvár. Finishing studies and obtaining a teacher’s diploma were two different things. One was able to start to teach and obtain the diploma later. That was the case with Farkas.

Four years later, Count Geiza Batthyány invited Farkas to tutor his three talented children in high school studies at his estate, and the position was accepted. The Count was generous and established a physics laboratory for him. The family traveled a lot, accompanied by the tutor, primarily in Italy and France. While in Paris, Farkas seized the opportunity and published three mathematical papers in the widely read Comptes Rendus. In 1876, after taking the exam, he obtained his high school teacher’s diploma in mathematics and physics. Meanwhile the Batthyány children graduated from high school and in 1880, Farkas moved to Budapest. Soon he acquired a Ph.D. in mathematics and a few years later he became ‘privatdozent’ at the University of Budapest. His habilitation script or thesis was about complex functions and quaternions. He taught there until 1887. Being a privatdozent meant a professorship without salary. However, Farkas was able to devote himself entirely to science because Count Batthyány generously continued to support him.

After the 1848-49 Hungarian uprising against the Hapsburg rule, which was suppressed by the aid of the Russian army, Hungary fell under lawless Hapsburg dictatorship. That lasted until the Compromise between Austria and Hungary in 1867, when the Austro-Hungarian Empire was established. In the year of 1872, a new university was founded, in the city of Kolozsvár, which was named after Franz Joseph I, already the crowned king of Hungary. In 1886, the university nominated Farkas to the position of professor of mathematical physics, and a year later he obtained it as an extraordinarius (professor without tenure). In 1888 he became an ordinarius and kept the position for 27 years, until 1915.

He was Dean twice and in the academic year 1907-1908 he was president of the university. In the year of 1892, he represented the university at Padova during the Galilei anniversary celebration. He became doctor honoris causa of the University of Padova. His scientific reputation increased in his home country and abroad as well. One of the signs that showed this was the discussion of his results in hydrodynamics and thermodynamics in the second volume of the book ‘Mathematische Physik’, published in 1896, by the Göttingen professor Voigt. At that time, however, in part due to the Galilei celebration, his interest turned to analytical mechanics. This research led to his best known scientific achievements.

In 1894, he gave mathematical formulation to the mechanical principle of Fourier, stated in 1798, and developed a theory of linear inequalities that he needed to derive the necessary condition of the equilibrium of a mechanical system. He published the results in subsequent papers between 1894 and 1901. The mechanical principle of Courtivron, stated in 1747, was given mathematical form by Lagrange, in 1788. In that theory the mechanical system was constrained by equalities. The novelty in Fourier’s and Farkas’ work was the use of inequality constraints, where the former theory is a special case. If the forces form a conservative system, i.e., there exists potential, then finding necessary condition to equilibrium is the same as minimizing the potential subject to constraints. This was the way Farkas arrived at the formulation of the necessary condition of optimality of nonlinear programming, in an analytical mechanical framework. He needed his linear inequality theorem for the same purpose as the authors of the KKT theorem needed it.

There is no constraint qualification, however, in Farkas’ work; the mathematical rigor in his physical papers was at the same level as in other contemporary papers on physics. His mathematical papers, the best known of which, ‘Theorie der einfachen Ungleichungen’, published in 1901, where he proved his inequality theorem, among others, were rigorously written. Farkas also contributed fundamental results in thermodynamics. He was the first to approach in a modern form the entropy concept of thermodynamics and derived mathematically the Carnot-Clausius principle, fourteen years earlier than Carathéodory.

Acknowledging his scientific results, in 1898, the Hungarian Academy of sciences elected Farkas to be a corresponding member and a full member in 1914. In 1915 his glaucoma forced him to retire. He moved to Budapest and continued to work and publish until 1926. He died on December 26, 1930.

Today it is well-known that Farkas contributed fundamental results to science. Less known is the fact that he was an extraordinary man with noble personal qualities and efficient talent in organization. He was somewhat reserved but he thought highly of professional and human qualities and helped those whom he considered worthy of it. He did not seek popularity and this was one of the reasons why he was highly respected both inside and outside the university. His words had been decisive. The picture that we can form of his character becomes more complete if we quote from his obituary that appeared in a nationwide newspaper after his death: ‘His colleagues, who knew him more closely, enthusiastically admired him; his students adored him.’ He invited to the University of Kolozsvár quite a few of those mathematicians, who later on laid the foundation of the twentieth century Hungarian mathematical school.

To commemorate him, the János Bolyai Mathematical Society of Hungary created a Farkas Prize in 1974, to honor young Hungarian mathematicians for excellence in applied mathematics. Recently, the Gyula Farkas Society of the Trasylvanian Hungarian mathematicians decided to present its members with the Farkas plaquette (created by the artist Kinga Széchenyi), for their excellent results in science and teaching. The INFORMS Farkas prize is a worldwide recognition of its recipients for their scientific results in optimization. At the same time it focuses the attention of all those working in operations research and management science on the great man and scientist Gyula Farkas.