On the Hypothesis that Forms the Basis of Geometry - On the Hypothesis that Forms the Basis of Science

…He made contributions to theoretical physics, such as electromagnetism and heat conduction, but he also established the foundations of analytical functions of complex variables, especially algebraic functions, and made important contributions to integral theory and trigonometric series theory. He also invented a new method of considering the Zeta function as a function of complex variables to deal with the problem of the distribution of prime numbers, an old mystery in number theory. In this way, he made original contributions to many fields of pure mathematics, but his inaugural lecture at the University of Göttingen in 1854, On the Hypothesis Underlying Geometry, is particularly important. Prior to that, in his Theory of Surfaces (1827), Gauss discussed the properties of sufficiently smooth surfaces that are invariant under isometric transformations (transformations that do not change length), and in particular showed that the total curvature of each point on a surface has this property. …

*Some of the terminology explanations that refer to "On the Hypotheses Underlying Geometry" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

…彼は電磁気学や熱伝導論など理論物理学への寄与もあるが，複素変数の解析関数論，ことに代数関数論の基礎を定め，積分論や三角級数論にも重要な貢献をし，数論上古くからのなぞとされた素数分布の問題を扱うのに，ゼータ関数を複素変数の関数として考えるという新しい方法を創始した。このように純粋数学の多くの分野にそれぞれ独創的な貢献をしたが，1854年ゲッティンゲン大学の就任講演《幾何学の基礎をなす仮説について》はとくに重要である。　その前にガウスは彼の《曲面論》(1827)で十分滑らかな曲面の等長変換(長さを変えない変換)によって変わらない性質を論じ，とくに曲面上の各点の全曲率がその性質をもつことを示した。…

※「《幾何学の基礎をなす仮説について》」について言及している用語解説の一部を掲載しています。

出典｜株式会社平凡社世界大百科事典 第２版について | 情報