Farkas Bolyai

Birth & Early Years

Farkas Bolyai was born into a family of modest means on February 9, 1775 in Bolya, Hungary (which is present day Sibiu, Romania). Although his resources were limited, Bolyai showed promising characteristics from an early age. He was taught by his father until the age of 6 after which he entered a Calvinist school in Nagyszeben. His teachers recognized his promise as a student; particularly in the fields of mathematics and language. As a result of his successes in school, at the age of twelve, Bolyai was taken in by a prominent and extremely wealthy family as a tutor. It was common at the time for members of the lower class, such as Bolyai, to enhance their education and life experiences in this manner. This opportunity is perhaps one of the most important in Bolyai’s life since it brought him into a community of mathematicians who fostered his love of mathematics.

As a Tutor

Upon becoming a tutor to Simon Kemény, both entered a Calvinist college in Kolozsvár in 1790. They spent five years there. In that time, Bolyai took interest in an extensive variety of subjects such as mathematics, science, and writing literature. As the Renaissance swept through all of Europe, Bolyai grew increasingly aware of the importance of reason and reasoning correctly. One of his professors at the college attempted to dissuade him from studying mathematics and suggested that he should rather study religious philosophy. His interests were so wide ranging that upon leaving college, he very seriously considered becoming an actor. Although he was interested in other subjects, Bolyai was always more fascinated by mathematics.

After College

After finishing his five years in Kolozsvár, Bolyai and Simon went abroad on an educational trip. One of the destinations on their journey was Jena. This is where Bolyai first began to study mathematics in a systematic and rigorous manner. After their time in Jenna, the two traveled to Göttingen where Bolyai became acquainted with Gauss. The two would soon become good friends and maintain correspondence for many years. It was in Göttingen that Bolyai became a true mathematician. He was deeply interested in Euclid’s geometric axioms; in particular he became fixated on the independence of Euclid’s Fifth Postulate. Bolyai and Gauss would have much correspondence pertaining to this issue.

Bolyai’s time in Göttingen was beneficial to his development as a mathematician. However, it was also a time of financial difficulty for him as well. Simon had gone back to Hungary and Bolyai was left in Göttingen to support himself. Bolyai was able to return to Hungary in 1799.

Back in Hungary

In 1801, Bolyai married Zsuzanna Benkö and one year later their son János was born. Around that same time, Bolyai began teaching mathematics, physics, and chemistry at a Calvinist college in Marosvásárhely. Although he was reluctant to take the teaching position for several reasons, Bolyai held the position for the remainder of his working life. The college consumed much of his time as he was not paid a tremendous amount for his teaching and thus supplemented his earnings by running a college pub, writing and publishing dramas, and designing tiles and cast-iron stoves. His lack of interest in his position at the college led him to place a great deal of hope in János’ future. Bolyai emphasized mathematics in János’ education even though others had attempted to persuade him to study other subjects.

In 1812, Bolyai’s wife died. Bolyai remarried in 1824 while still teaching at the college. Throughout his years of teaching and attempting to inspire János to partake in the study of mathematics, Bolyai was working on what would become his major contribution to mathematics. He published his work in 1832 and called it the Tetamen.

In it, Bolyai sought to give a rigorous foundation for arithmetic, geometry, algebra, and analysis. He considered arithmetic and geometry to be the building blocks upon which all other mathematics was constructed. Although this work was a major accomplishment for Bolyai, it has been considered to be lacking in originality. It discusses topics such as iterative procedures for finding solutions to algebraic equations, monotonicity, series tests, and the definition of a function to name a few. It has been said that the majority of Bolyai’s original mathematical thinking is contained in the letters that he wrote to Gauss and the correspondence that he had with his son.

Throughout his life, Bolyai had become so fixated on proving the independence of Euclid’s Fifth Postulate that he eventually grew disheartened with each failing endeavor. He even warned his son János not to partake in studying the parallel axiom. In one correspondence to his son he wrote of his feelings for seeking the proof:

Do not try the parallels in that way: I know that way all along, I have measured that bottomless night, and all the light and all the joy of my life went out there.

Although he was never able to prove the independence of Euclid’s Fifth Postulate, Bolyai was able to establish equivalent and seemingly more autonomous versions of the postulate such as:

- No sphere may differ from any other sphere in any property except its size and location.

- Three points which do not lie on the same straight line must lie on a circle.

Fortunately, János did not heed his father’s advice and in 1825 he showed his father his work in what would later be termed non-Euclidean geometry. After a lifelong attempt to conquer Euclid’s Fifth Postulate, Bolyai retired form teaching in 1851 and died five years later on November 20^, 1856. He is primarily remembered as the father of János and for his correspondence with Gauss. However, he should be given due credit for inspiring his son to take up the challenge that he grappled with for so long and for persevering in an area that proved so challenging.

Other Important Contributions

Wallace-Bolyai-Gerwein Theorem: http://www.math.sdu.edu.cn/mathency/math/w/w005.htm

References

http://scienceworld.wolfram.com/biography/BolyaiFarkas.html

http://www.math.wfu.edu/~kuz/Stamps/FBolyai/BolyaiFarkas.html

http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Bolyai_Farkas.html