Riemann, Georg Friedrich Bernhard

Japanese: リーマン（英語表記）Riemann， Georg Friedrich Bernhard

Born: September 17, 1826 in Breserentz
Died: July 20, 1866. Celaska German mathematician. One of the most creative mathematicians of the 19th century. Although he published only a small number of papers, each of them had a profound impact on the development of analysis and geometry. He entered the University of Göttingen (1846). In 1847, he attended the courses of mechanics by K. Jacobi and number theory by P. Dirichlet at the University of Berlin. He returned to Göttingen (49) and became assistant to W. Weber in physics (50). In 1851, he published his doctoral thesis, "Foundations of the General Theory of Complex Functions," which contained an important idea that was later formulated by H. Weyl as the "Riemann surface." He also prepared "On the Representation of Functions by Trigonometric Series" for the lecturer qualification examination (published posthumously), in which he formulated the concept of the Riemann integral (→definite integral). In 1854, he proposed the concept of space called "Riemannian geometry." In 1957 he became an assistant professor at the University of Göttingen, and in 1959 he succeeded Dirichlet as a professor, and married Elise Koch (62). However, he soon contracted tuberculosis, and despite a period of recuperation he passed away before the age of 40. His number theory paper, "On the Number of Primes Less Than a Certain Number," which he wrote in 1959, was only a nine-page paper, but it investigated the distribution of prime numbers using the "Riemann Zeta function," and is considered an important achievement in analytical number theory.

Lehman
Riemann, Hugo

Born: July 18, 1849, Grossmerla
Died: July 10, 1919. Leipzig. German musicologist. Studied philosophy and music, and received his doctorate from the University of Göttingen in 1873. In 1878 he wrote Studien zur Geschichte der Notenschrift (A Study on the History of Musical Notation) and qualified to teach at the University of Leipzig. He became a professor at the same university in 1901. He pioneered various theories including functional theory, and was also known for his achievements in music history research, such as a new evaluation of the Mannheim School. Some of his claims are being reconsidered today, but his contributions as an establisher of modern musicology are significant. His main works were Musik-lexikon (1882) and Outlines of the History of Music (1901-13).

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

[生]1826.9.17. ブレーゼレンツ
[没]1866.7.20. セラスカ
ドイツの数学者。 19世紀の最も創造的な数学者の一人。発表した論文の数は少いが，そのひとつひとつが解析学や幾何学の発展に深刻な影響を与えた。ゲッティンゲン大学入学 (1846) 。 1847年にはベルリン大学で K.ヤコービの力学や P.ディリクレの整数論を聴講。ゲッティンゲンに戻り (49) ，物理学の W.ウェーバーの助手になる (50) 。 51年学位論文『複素関数の一般理論の基礎』を出す。このなかにのちに H.ワイルによって「リーマン面」として定式化される重要なアイデアが含まれていた。さらに講師資格試験に向けて『三角級数による関数の表現について』を準備し (死後発表された) ，そのなかにリーマン積分 (→定積分 ) の概念が定式化されている。 54年，「リーマン幾何学」と呼ばれる空間概念を提案。 57年ゲッティンゲン大学助教授，59年ディリクレの跡を継いで教授となり，エリーゼ・コッホと結婚 (62) 。しかし，まもなく結核にかかり，転地療養のかいもなく 40歳に満たない生涯を閉じる。彼が 59年に書いた整数論の『ある数以下の素数の個数について』は，わずか9ページの論文であるが，「リーマンのゼータ関数」を用いて素数の分布を調べたもので，解析的整数論における重要な業績とされている。

リーマン
Riemann， Hugo

[生]1849.7.18. グロースメールラ
[没]1919.7.10. ライプチヒ
ドイツの音楽学者。哲学および音楽を学び，1873年ゲッティンゲン大学で博士号を取得。 78年『記譜法の歴史に関する一研究』 Studien zur Geschichte der Notenschriftを書きライプチヒ大学で教授資格を得た。 1901年より同大学教授。機能理論をはじめとする諸理論を開拓し，音楽史研究でもマンハイム楽派の新しい評価などの業績を残した。その主張は今日再検討されている部分もあるが，近代音楽学の確立者としての貢献は大きい。主著『リーマン音楽辞典』 Musik-lexikon (1882) ，『音楽史提要』 (1901～13) 。

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