Nikolai Ivanovich Lobachevsky and His Work
Like many other truly great mathematicians Nikolai Ivanovich Lobachevsky came from a humble background, worked hard to raise himself to be highly renowned and died before the significance of his works could be truly accepted and appreciated. Lobachevsky was a rector and a professor of mathematics at Kazan University for nineteen years, devised a method for finding roots of a polynomial and published a plethora of material on algebra, numerical analysis, astronomy and probability. His most important discovery was the idea of non-Euclidian geometry, the thought of which was met with scorn and derision during his lifetime, but one that would go on to be a cornerstone for our modern understanding of …show more content…
His father was a clerk with a land surveying office, and his mother stayed at home with their three children. However, things took a turn for the worse as Lobachevsky’s father died, presumably of pneumonia, and the family moved in Kazan in 1802. [2] Lobachevsky started to attend a recently opened Gymnasium and in 1807 moved up to a university on a government scholarship. Although originally earning his degree in physics, Lobachevsky was soon influenced by several of the german mathematicians that lectured at the university, in particular Martin Bartel. Bartel was a formidable mathematician in his own right and maintained correspondence with Carl Gauss. In fact many have postulated that Gauss may have pushed Lobachevsky’s research towards exploring the possibility of non-Euclidean geometry, although this seems rather far fetched as the two had never actually corresponded. [3] Lobachevsky became enthralled by mathematics, becoming a professor in the field, and ultimately a rector of the college. He enjoyed a relative fame in the mathematical community, publishing not only in Russia, but also Germany and France and eventually being awarded a medal by Nicolas the second. In 1832 Lobachevsky married Varvara Moiseeva, a woman half his age who went on to bear seven children. Unfortunately living above his means and providing for such a large family wore down Lobachevsky’s fortune as well as his health, and …show more content…
At the time most mathematicians were trying desperately to prove Euclid 's fifth postulate as derived from other axioms. We now know that in fact this can not be done as it must be taken as an axiom to define a Euclidean space. This postulate, reformulated in modern terms, reads as “given a line and a point not on it, one can draw through the point one and only one coplanar line not intersecting the given line.” [8] Meanwhile a different idea occurred to Lobachevsky. Instead of trying to prove the fifth postulate he imagined a system where the fifth postulate was different. Instead of specifying only one line being parallel to the original passing through some point, Lobachevsky imagined a space where infinitely many lines could pass through such a point and be parallel to the first line. Today we call this hyperbolic geometry and can imagine it as a saddle shaped space. [4] This convex space has some fascinating properties, such as all “triangles” having their angles add up to less than 180 degrees. Following some exploration Lobachevsky concluded that his newly devised geometry was in fact consistent with all other postulates in Euclid’s elements. He thus concluded that Euclidean geometry is a specific case and there are other, more general geometries. Although published in 1826 these ideas did not become widely accepted until long after Lobachevsky’s death, around 1868, when
Like many other truly great mathematicians Nikolai Ivanovich Lobachevsky came from a humble background, worked hard to raise himself to be highly renowned and died before the significance of his works could be truly accepted and appreciated. Lobachevsky was a rector and a professor of mathematics at Kazan University for nineteen years, devised a method for finding roots of a polynomial and published a plethora of material on algebra, numerical analysis, astronomy and probability. His most important discovery was the idea of non-Euclidian geometry, the thought of which was met with scorn and derision during his lifetime, but one that would go on to be a cornerstone for our modern understanding of …show more content…
His father was a clerk with a land surveying office, and his mother stayed at home with their three children. However, things took a turn for the worse as Lobachevsky’s father died, presumably of pneumonia, and the family moved in Kazan in 1802. [2] Lobachevsky started to attend a recently opened Gymnasium and in 1807 moved up to a university on a government scholarship. Although originally earning his degree in physics, Lobachevsky was soon influenced by several of the german mathematicians that lectured at the university, in particular Martin Bartel. Bartel was a formidable mathematician in his own right and maintained correspondence with Carl Gauss. In fact many have postulated that Gauss may have pushed Lobachevsky’s research towards exploring the possibility of non-Euclidean geometry, although this seems rather far fetched as the two had never actually corresponded. [3] Lobachevsky became enthralled by mathematics, becoming a professor in the field, and ultimately a rector of the college. He enjoyed a relative fame in the mathematical community, publishing not only in Russia, but also Germany and France and eventually being awarded a medal by Nicolas the second. In 1832 Lobachevsky married Varvara Moiseeva, a woman half his age who went on to bear seven children. Unfortunately living above his means and providing for such a large family wore down Lobachevsky’s fortune as well as his health, and …show more content…
At the time most mathematicians were trying desperately to prove Euclid 's fifth postulate as derived from other axioms. We now know that in fact this can not be done as it must be taken as an axiom to define a Euclidean space. This postulate, reformulated in modern terms, reads as “given a line and a point not on it, one can draw through the point one and only one coplanar line not intersecting the given line.” [8] Meanwhile a different idea occurred to Lobachevsky. Instead of trying to prove the fifth postulate he imagined a system where the fifth postulate was different. Instead of specifying only one line being parallel to the original passing through some point, Lobachevsky imagined a space where infinitely many lines could pass through such a point and be parallel to the first line. Today we call this hyperbolic geometry and can imagine it as a saddle shaped space. [4] This convex space has some fascinating properties, such as all “triangles” having their angles add up to less than 180 degrees. Following some exploration Lobachevsky concluded that his newly devised geometry was in fact consistent with all other postulates in Euclid’s elements. He thus concluded that Euclidean geometry is a specific case and there are other, more general geometries. Although published in 1826 these ideas did not become widely accepted until long after Lobachevsky’s death, around 1868, when