Our namesake – Bolyai Farkas

Bolyai Farkas

Bolyai Farkas

9 February 1775 – 20 November 1856

Bolya – Târgu Mureș

“Truth must be sought, and whoever seeks it will find it.”

— Bolyai Farkas
Occupation

Mathematician, physicist, playwright

Chair

Târgu Mureș, 1804–1856

Friend

Carl Friedrich Gauss

Son

Bolyai János (1802–1860)

Main work

Tentamen (1832)

Languages

8 languages: Hungarian, Latin, Romanian, German, French, English, Italian, Hebrew

The school's namesake

Mathematician · Physicist · Playwright · Poet · Inventor · Teacher

Bolyai Farkas is one of the most versatile figures in the history of Hungarian science. A mathematician who studied the foundations of geometry; a physicist who designed stoves; a playwright who published five tragedies; a poet who wrote verse in Latin, German and Hungarian; and a teacher who shaped the young people of Târgu Mureș (Marosvásárhely) for nearly half a century. He was the lifelong friend of Carl Friedrich Gauss and the father of Bolyai János, the creator of non-Euclidean geometry.

Family and childhood

He was born on 9 February 1775 in Bolya, near Sibiu (Nagyszeben). His father, Bolyai Gáspár (1732–1804), came from an impoverished noble family. His mother, Pávai Vajna Krisztina, brought a modest dowry into the family. He also had a younger brother, Antal (1779–1845).

Until the age of six he was taught at home by his father, who recognised his son's extraordinary talent. Even then the little boy showed an outstanding gift for mental arithmetic – he is said to have worked out the square and cube roots of 14-digit numbers in his head.

His studies

In 1781, at the age of six, he enrolled at the famous College of Nagyenyed (Aiud), where his teachers quickly recognised his outstanding talent. He spoke Latin and Romanian fluently and proved to be an extraordinary mental calculator. Later he also learnt Greek, Hebrew, French, Italian, English and German – in all, he spoke eight languages.

Besides mathematics, he also showed outstanding talent in drawing and music. He was considered a child prodigy, especially because of his rapid progress in arithmetic and languages.

Gauss and the university years

In 1796 he went to the University of Jena and then moved on to Göttingen, where he met Carl Friedrich Gauss – the greatest mathematician of the age. Their friendship is one of the most remarkable relationships in the history of mathematics.

Their correspondence lasted for decades and is one of the most important documents in the history of mathematics. Gauss's letters were full of metaphors, similes, rhetorical questions and exclamations.

His marriage and his son, János

On 28 September 1801 he married Árkosi Benkő Zsuzsanna, the daughter of a surgeon and teacher in Cluj (Kolozsvár). At the end of 1802 their son, Bolyai János, was born; he later became world-famous as one of the creators of non-Euclidean geometry.

Farkas directed his son's mathematical education himself – he chose his teachers, and when they had nothing new left to teach the boy, he continued the teaching himself.

The Târgu Mureș years – 47 years of teaching

On 22 January 1804 he took up the chair of mathematics, physics and chemistry at the Reformed College of Târgu Mureș. He taught there until he retired in 1851 – for nearly half a century. He was a pioneer in teaching mathematics as a science in its own right, rather than as part of philosophy.

Although his salary was modest, he took on extra work: he wrote and published plays, ran the college tavern, and designed tiled stoves and stove parts. His teaching creed was that students must be taught to think, not merely made to learn formulas by rote.

A true polymath

Extraordinary talents in one person – from mathematics to music

Mental calculator

Worked out the roots of 14-digit numbers in his head

8 languages

Hungarian, Latin, Romanian, German, French, English, Italian, Hebrew

Musician

Outstanding musical talent; he played the violin and the piano

Draughtsman

Exceptional drawing skills, technical illustrations

Playwright

5 tragedies + 1 comedy, published in Sibiu in 1817

Poet

Poems in Latin, German and Hungarian – under the title Szívhangok (Voices of the Heart)

Inventor

A stove invention that spread all over Transylvania

Aphorist

~1700 aphorisms on courage, love and wisdom
1775

Birth

Born on 9 February in Bolya, near Sibiu (Nagyszeben). His father, Bolyai Gáspár, came from an impoverished noble family.
1781

College of Nagyenyed

At the age of six he enrols at the famous College of Nagyenyed (Aiud). He speaks Latin and Romanian fluently and is an extraordinary mental calculator. He is considered a child prodigy.
1796

Jena and Göttingen

He studies at the universities of Jena and then Göttingen. Here he meets Carl Friedrich Gauss – the beginning of a lifelong friendship.
1801

Marriage

On 28 September he marries Árkosi Benkő Zsuzsanna, the daughter of a surgeon and teacher in Cluj (Kolozsvár).
1802

Birth of Bolyai János

In December his son János is born, who later becomes world-famous as one of the creators of non-Euclidean geometry.
1804

Appointed teacher

On 22 January he takes up the chair of mathematics, physics and chemistry at the Reformed College of Târgu Mureș. He teaches there until he retires in 1851 – for 47 years.
1817

Five tragedies published

His plays are published in Sibiu: Pausanias, Mohamed, Kemény Simon, The Triumph of Virtue and The Triumph of Love.
1830

Az arithmetika eleje

His first major mathematical work is published, containing original and independent research results.
1832

Tentamen published

His main work: a systematic foundation of geometry, arithmetic, algebra and analysis. Some 1,000 pages summing up 30 years of research. His son's Appendix also appears in it.
1854

His last works

Az arithmetikának, geometriának és physicának eleje (Elements of Arithmetic, Geometry and Physics) is published – his last great summarising work.
1855

Jelentés – a farewell letter

He writes his own farewell letter and will under the title Jelentés (Report). He writes elegies in memory of friends and family members who have passed away.
1856

Death

He died in Târgu Mureș on 20 November, at the age of 81. The high school took his name in 1956.

His work in mathematics

His main field of interest was the foundations of geometry and the parallel postulate. Gauss acknowledged his "honest striving for independence and thoroughness".

Tentamen

1832 · Main work

A rigorous and systematic foundation of geometry, arithmetic, algebra and analysis. A work of some 1,000 pages summing up 30 years of research. His son Bolyai János's famous Appendix was first published in this work.
Gauss spoke appreciatively of the work, highlighting Bolyai's "honest striving for independence and thoroughness".

Az arithmetika eleje

1830 · Arithmetic

A work on arithmetic containing original and independent research results. The basis of a reform of mathematics teaching, in which Bolyai approached the fundamental questions of number theory with his own methods.
Later, in 1850, a version "for beginners" was also published: "Az arithmetika eleje kezdőknek" (Elements of Arithmetic for Beginners).

Summarising work

1854 · Last great work

"Az arithmetikának, geometriának és physicának eleje" (Elements of Arithmetic, Geometry and Physics) — his last great summarising work, which treats the foundations of arithmetic, geometry and physics as a single system. A work with a teaching purpose but scholarly standards.

Stove invention

A practical scientist

Besides mathematics, he was also a practical inventor: he designed improved heating and cooking stoves, which won wide recognition all over Transylvania. Designing and building tiled stoves also gave him extra income on top of his modest salary at the college.

His literary work

Bolyai Farkas was not only a mathematician but also a prolific man of letters. He wrote plays, poems and aphorisms — leaving behind some 1,700 wise sayings in all.

His plays

Five of his tragedies were published in Sibiu in 1817:

  • Pausanias, or the Victim of Ambition
  • Mohamed, or the Triumph of Glory over Love
  • Kemény Simon, or the Victim of Patriotism
  • The Triumph of Virtue over Love
  • The Triumph of Love over Virtue

He also wrote a comedy — A párizsi per (The Paris Lawsuit) —, which contains a Shakespeare-like line about the dilemma of marriage.

His poems

His poems were published under the title Szívhangok (Voices of the Heart); he wrote them in three languages: Latin, German and Hungarian.

He was particularly fond of elegies — moving poems in a short, concise form, written on the deaths of his friends and family members.

In 1855–56 he also wrote his own farewell letter and will, under the title "Jelentés" (Report), which is at once a personal confession and a literary work.

~1700 Aphorisms

Bolyai Farkas left behind some 1,700 aphorisms and sayings on the great questions of life:

CourageLoveHopeHonourTimeFaithFreedomWisdomYouthOld age

His aphorisms reflect the polymath's wisdom, humour and deep understanding of people. Many regard him as one of the forerunners of Hungarian aphoristic literature.

Quotations from Bolyai Farkas

“Truth must be sought, and whoever seeks it will find it.”

Aphorism

“To marry or not to marry? — that is the question.”

From his comedy A párizsi per (The Paris Lawsuit)

“Science is the only treasure that we keep even when we share it.”

An aphorism about knowledge

“Friendship is more important even than mathematics, for the most beautiful equation of the human soul is the one written by two understanding hearts.”

From his correspondence

Father and son — in the service of science

The relationship between Bolyai Farkas and his son, Bolyai János, is one of the most remarkable father–son relationships in the history of science. Farkas directed his son's mathematical education himself, chose his teachers, and when they had nothing new left to show him, he continued the teaching himself.

Guided by his father, János set out to study the fundamental questions of geometry and in the end created non-Euclidean geometry — which fundamentally changed humanity's understanding of space.

Farkas was his son's only true understander and supporter at a time when the world did not yet grasp the significance of János's discoveries. Their mutual respect and love for each other is the most beautiful human story in mathematics and science.

BF

Bolyai Farkas

1775–1856

father – son
BJ

Bolyai János

1802–1860

The most important father-and-son pair in the history of mathematics. The father studied the foundations of geometry — the son solved the problem.

Why does our school bear his name?

The high school in Târgu Mureș took the name of Bolyai Farkas in 1956, honouring the memory of the great mathematician and teacher. But the choice of name goes far beyond remembrance.

Bolyai Farkas embodies everything our school stands for: a passion for knowledge, versatility, the courage to innovate and commitment to the community. He was a polymath in the noblest sense of the word — a mathematician who also wrote plays; a teacher who also built stoves; a scholar who also thought in aphorisms.

During his half-century as a teacher, generations grew up under his guidance, among them his own son, who became one of the most famous mathematicians in the world. Bolyai Farkas's intellectual legacy still pervades the life of the school today: the values of knowledge, perseverance, high standards and an open mind are the cornerstones of the school.

“Knowledge is the only treasure that we keep even when we share it.”

The spirit of Bolyai Farkas lives on within the walls of the Bolyai today.

Discover the school's history

Discover the centuries-old past, traditions and values of the Bolyai Farkas Theoretical High School.