| 中文摘要 |
數學史上，從沒有出現如尤拉（Leonhard Euler，1707～1783）一樣創作力如此旺盛的天才。他用畢生76年的創作歲月為我們留下73冊偉大科學鉅著『尤拉全集』（oper omnia），其中包括886本書及近千篇的學術論文。他的研究範圍幾乎含蓋所有科學領域，數學方面包括分析、代數、數論、幾何。物理方面則包括力學、光學、聲學、彈道。此外還涉及天文、航海、地理、建築、社會福利、保險等等。他的作品不論是在質或在量上都屬上乘之作，更令人佩服的是他許多作品都是在1771年兩眼全盲後所完成。有人形容他是數學的巴哈（The Bach of Mathematics），也有人稱他為數學界的莎士比亞（The Shakespeare of Mathematics）。他不只是一為科學創作高手，他更是一位謙和敦厚，平易近人的好老師。數學家拉普拉斯（Laplace，1749～1827）形容他是「全能的大師」。本文是作者繼「Eureka！Eureka！阿基米德的數學」、「偉哉牛頓」後之「向數學大師致敬」系列之作。希望透過簡明清晰的筆觸，為學子們介紹這位大師的成就與風範。文分三段，第一段是尤拉的生平簡介，在第二段探討尤拉的數學成就，第三段介紹這位大師之風範及其教育精神。In the history of mathematics, there was not a mathematics talent as creative and prolific as Leonhard Euler (1707~1783). He spent his entire life of 76 years on writing 886 books and nearly 1,000 research papers, which were all collected in the great work left to us, Leonhardi Euleri Opera Omnia (Complete Works of Leonhard Euler) published in 73 volumes. In fact, the scope of his research almost covered all the science fields. For mathematics, his works were about analysis, algebra, category, and geometry; and for physics, his works were about mechanics, optics, acoustics, and ballistics. Besides, he involved in the studies of astronomy, navigation, geography, architecture, social welfare, insurance, and so on. No matter qualitatively or quantitatively, his works were valuable and contributive. The most admirable thing about him was that many of his works were completed after his both eyes became totally blind as from 1771. Some people considered Euler to be 'The Bach of Mathematics,' and some people called him 'The Shakespeare of Mathematics.' Nevertheless, he was not merely a talent in scientific creation, but also a humble, honest, sincere, amiable and good teacher who was easy to approach. Another mathematician, Laplace (1749~1827) described him as a 'master of us all.' This is another paper of the researcher following the essays of 'Eureka, Eureka! Archimedes' Mathematics' and 'Marvelous, Newton!' in the serial study, 'Salute to Masters of Mathematics.' It is hoped that through the clear and explicit explanation in this paper, the great master of mathematics, Leonhard Euler can be introduced to students. The paper is divided into three sections: the first section introduces the entire life and events of Euler; the second section investigates the mathematical achievements of Euler; and the third section presents the manner and education spirit of the great master |
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