Nikolay Ivanovich Lobachevskiy (English spelling)

Russian mathematician. The founder of hyperbolic non-Euclidean geometry (also known as "Bolyai-Lobachevsky geometry"), he dedicated his life to the study of non-Euclidean geometry and to university administration. He was born in Nizhniy Novgorod (now Gorky) as the second son of a low-ranking civil servant. His father died when Nikolai was seven years old, and he was raised by his mother along with his older and younger brothers. Although the family was poor, his mother put everything into the education of her three children, and sent them to the Kazan gymnasium. At the time, this school attracted the most talented students, and particularly strict exams were required for children of ordinary classes other than the nobility. Nicholas was admitted to Kazan University in 1802, but he already showed a natural talent for mathematics during the entrance exam. By the time he entered Kazan University at the age of 14, he had already studied many mathematical texts and treatises, including Newton's Principia. After entering the university, he initially aimed to study medicine, but then developed an unusual interest in mathematics and astronomy, and began to show his talent in those fields. At the age of 18, he incurred the wrath of the school authorities by getting into a dispute, but he received his master's degree that same year, and in 1814 he became an assistant in the physics and mathematics department, and in 1816 he became an associate professor. In 1820 he headed the mathematics and physics department, in 1822 he was a member of the construction committee (since 1825 he was its chairman), in 1826 he became a full professor, and in 1827 he was confirmed as the rector of Kazan University, a position he held continuously until 1846. During this time, in February 1826, he presented a research paper including the principles of non-Euclidean geometry at the Physics and Mathematics Committee, and published "On the Principles of Geometry" in the Kazan Bulletin in 1829-1830. This was the first paper on non-Euclidean geometry to be published in print. He subsequently published "Imaginary Geometry" and "Geometry with the Complete Parallel Axiom", among others, and over the course of about 10 years built the foundations of a new geometry, namely non-Euclidean geometry. "Imaginary Geometry" was published in France in 1837, and a pamphlet entitled "Geometrical Studies on the Theory of Parallel Lines" was published in German in Berlin in 1840. It was through this work that Gauss learned of Lobachevsky's work. His final research was published in General Geometry in 1855, but he was dismissed from his position as rector in the same year, and died of illness the following year in 1856 at the age of 63.

[Isamu Mogi]

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

ロシアの数学者。双曲的非ユークリッド幾何学（「ボヤイ‐ロバチェフスキーの幾何学」ともいわれる）の創始者で、一生を非ユークリッド幾何学の研究と大学の行政とに捧(ささ)げた。下級官吏の次男として、ニジニー・ノブゴロド（現、ゴーリキー）に生まれる。父はニコライが7歳のときに死亡、兄と弟とともに母の手で育てられた。一家は貧困のなかにあったが、母は3人の子供の教育にすべてをかけ、子供たちをカザンのギムナジウムに入学させた。当時、ここはもっとも能力のある生徒が集められ、貴族階級以外の一般の階級の子弟には、とくに厳しい試験が課せられていた。ニコライが入学を許されたのは1802年であるが、入学試験のときすでに数学に天賦の才能があることを示し、14歳でカザン大学に進学したころには、すでにニュートンの『プリンキピア』をはじめ、多くの数学の専門書や論文を勉強してしまっていた。入学後、一時、医学を志したが、やがて数学と天文学に異常な興味をもち、その方面での才能を発揮し始めた。18歳のとき、学校当局との間にいざこざを起こして不興を買ったりしたが、その年修士の学位をとり、1814年には物理・数学科助手、1816年には員外教授となった。1820年に数学・物理学部長、1822年に建設委員会委員（1825年から委員長）、1826年に正教授となり、1827年カザン大学学長として承認され、1846年まで連続して学長の任にあった。その間、1826年2月には、物理・数学部会において非ユークリッド幾何学の原理を含む研究報告を行い、1829～1830年の『カザン通報』に「幾何学の原理について」を発表した。これが印刷の形で発表された非ユークリッド幾何学の最初の論文である。その後さらに「想像の幾何学」「完全な平行線公理をもった幾何学」などを発表し、10年ほどかかって新しい幾何学、すなわち非ユークリッド幾何学の基礎をつくりあげた。『想像の幾何学』が1837年フランスで公表され、『平行線の理論に関する幾何学的研究』という小冊子が1840年ベルリンにおいてドイツ語で出版された。ガウスがロバチェフスキーの業績を知ったのもこの著作によってである。最後の研究は1855年『汎幾何学(はんきかがく)』に公表されたが、同年学長を解任され、翌1856年病のため63歳で世を去った。

［茂木　勇］

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