BIOGRAPHY OF NON EUCLIDIAN FIGURES

1.     Carl Friedrich Gauss

Carl Friedrich Gauss (1777-1855) is considered to be the greatest German mathematician of the nineteenth century. His discoveries and writings influenced and left a lasting mark in the areas of number theory, astronomy, geodesy, and physics, particularly the study of electromagnetism.

Gauss was born in Brunswick, Germany, on April 30, 1777, to poor, working-class parents. His father labored as a gardener and brick-layer and was regarded as an upright, honest man. However, he was a harsh parent who discouraged his young son from attending school, with expectations that he would follow one of the family trades. Luckily, Gauss' mother and uncle, Friedrich, recognized Carl's genius early on and knew that he must develop this gifted intelligence with education.

At the age of fourteen, Gauss was able to continue his education with the help of Carl Wilhelm Ferdinand, Duke of Brunswick. After meeting Gauss, the Duke was so impressed by the gifted student with the photographic memory that he pledged his financial support to help him continue his studies at Caroline College. At the end of his college years, Gauss made a tremendous discovery that, up to this time, mathematicians had believed was impossible. He found that a regular polygon with 17 sides could be drawn using just a compass and straight edge. Gauss was so happy about and proud of his discovery that he gave up his intention to study languages and turned to mathematics.

Gauss' next discovery was in a totally different area of mathematics. In 1801, astronomers had discovered what they thought was a planet, which they named Ceres. They eventually lost sight of Ceres but their observations were communicated to Gauss. He then calculated its exact position, so that it was easily rediscovered. He also worked on a new method for determining the orbits of new asteroids. Eventually these discoveries led to Gauss' appointment as professor of mathematics and director of the observatory at Gottingen, where he remained in his official position until his death on February 23, 1855.

Carl Friedrich Gauss, though he devoted his life to mathematics, kept his ideas, problems, and solutions in private diaries. He refused to publish theories that were not finished and perfect. Still, he is considered, along with Archimedes and Newton, to be one of the three greatest mathematicians who ever lived. 

2.  Janos Bolyai

János Bolyai,  (born December 15, 1802, Kolozsvár, Hungary [now Cluj, Romania]—died January 27, 1860, Marosvásárhely, Hungary [now Târgu Mureş, Romania]), Hungarian mathematician and one of the founders of non-Euclidean geometry— a geometry that differs from geometry in its definition of parallel lines. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world.

By the age of 13, Bolyai had mastered calculus and analytic mechanics under the tutelage of his father, the mathematician Farkas Bolyai. He also became an accomplished violinist at an early age and later was renowned as a superb swordsman. He studied at the Royal Engineering College in Vienna (1818–22) and served in the army engineering corps (1822–33).

The elder Bolyai’s preoccupation with proving  Euclid’s parallel axiom infected his son, and, despite his father’s warnings, János persisted in his own search for a solution. In the early 1820s he concluded that a proof was probably impossible and began developing a geometry that did not depend on Euclid’s axiom.

Although Bolyai continued his mathematical studies, the importance of his work was unrecognized in his lifetime. In addition to work on his non-Euclidean geometry, he developed a geometric concept   pairs of real numbers.

3. Lobachevsky

Nikolay Ivanovich Lobachevsky is born in Nizhniy Novgorod on November 20, 1792, in the family of a poor petty officer.

When Nikolay gets 9, his mother brings him to Kazan and arranges Nikolay together with his two brothers to attend a grammar school for free. Since that time life and work of future star of mathematics takes place in the city of Kazan.

Seven years of nearly prison regime in the university do not crush recalcitrant spirits of Lobachevsky, now a professor. He reads courses in mathematics and physics, heads department of physics, teaches geodesy and astronomy, being responsible for observatory. Later he becomes the dean of the faculty of physics and mathematics. Nikolay Ivanovich’s creativity results in writing two school-books for grammar schools – “Geometry” comes off the press in 1823 and “Algebra” in 1825. Both school-books are not approved due to some revolutionary changes Nikolay Ivanovich has suggested to make in traditional science. He starts experiencing problems with the university’s curator.

However, Lobachevsky keeps working on formulating geometry’s bases and finally makes a brilliant discovery, which results in absolutely new geometry. The mathematician makes a report about his discovery – he calls it “Imaginary Geometry” – at his faculty. He wants to know what his colleagues think about his discovery and asks to publish his work in “Scientific Notes” of the faculty. However, no comments followed, and later the manuscript of his discovery is lost.

In 1827 Nikolay Ivanovich Lobachevsky becomes a rector of Kazan University and dedicates following 19 years to the university, making it flourish. He manages to introduce new educational standards, his reign results in library, astronomical and magnetic observatories, dissecting room, physical and chemical laboratories. His ideas are so revolutionary and future-oriented that brilliant scientists of his time fail to foresee their significance. However, misunderstanding and, sometimes, open humiliation, cannot force Nikolay Ivanovich to stop his studies. Several years of hard work result in “Geometrical studies of theory of parallels”, summarizing his ideas and published in German language in 1840. Lobachevsky doesn’t receive a single positive report, except a prediction of one professor that sooner or later Lobachevsky’s theory would find its admirers.

4. Bernhard Riemann

Bernhard Riemann (1826-1866) was the son of a poor country minister in northern Germany. He studied the works of Euler and Legendre while he was still in secondary school. It is said that he mastered Legendre's treatise on Theory of Numbers in less than a week! Riemann was shy and modest and was probably unaware of his own extraordinary abilities. In fact he went to the University of Gottingen (when he was nineteen) to study theology and (hence) become a minister himself. Fortunately before it was too late he realized his mistake and with the permission of his father switched to MATHEMATICS. The presence of the legendary C.F.Gauss made Gottingen the center of the mathematical world. But Gauss was remote and unapproachable, so after a while Riemann switched to University of Berlin. Once there he learned a great deal from Dirichlet and Jacobi. Two years later he returned to Gottingen, where he obtained his doctor's degree in 1851.

Riemann had a short life and published comparatively little, but his works permanently altered the course of mathematics in analysis, geometry and number theory. His first published paper was his celebrated dissertation of 1851 on the general theory of functions of a complex variable. Riemann's fundamental aim here was to free the concept of an analytic function from any dependence on explicit expressions such as power series, and to concentrate instead on general principles and geometric ideas. In doing so he used/created concepts such as Cauchy-Riemann equations, Riemann surfaces etc. Gauss was rarely enthusiastic about achievements of his contemporaries, but in his official report to the faculty he warmly praised Riemann's work: "The dissertation submitted by Herr Riemann offers convincing evidence of the author's thorough and penetrating investigations in those parts of the subject treated in the dissertation, of a creative, active, truly mathematical mind, and of a gloriously fertile originality."