The last member of the English school whom I need mention here is Thomas Simpson, who was born in Leicestershire on August 20, 1710, and died on May 14, 1761. His father was a weaver and he owed his education to his own efforts. His mathematical interests were first aroused by the solar eclipse which took place in 1724, and with the aid of a fortune-telling pedlar he mastered Cocker's Arithmetic and the elements of algebra. He then gave up his weaving and became an usher at a school, and by constant and laborious efforts improved his mathematical education, so that by 1735 he was able to solve several questions which had been recently proposed and which involved the infinitesimal calculus. He next moved to London, and in 1743 was appointed professor of mathematics at Woolwich, a post which he continued to occupy till his death.
The works published by Simpson prove him to have been a man of extraordinary natural genius and extreme industry. The most important of them are his Fluxions , 1737 and 1750, with numerous applications to physics and astronomy; his Laws of Chance and his Essays , 1740; his theory of Annuities and Reversions (a branch of mathematics that is due to James Dodson, died in 1757, who was a master at Christ's Hospital, London), with tables of the value of lives, 1742; his Dissertations , 1743, in which the figure of the earth, the force of attraction at the surface of a nearly spherical body, the theory of the tides, and the law of astronomical refraction are discussed; his Algebra , 1745; his Geometry , 1747; his Trigonometry , 1748, in which he introduced the current abbreviations for the trigonometrical functions; his Select Exercises , 1752, containing the solutions of numerous problems and a theory of gunnery; and lastly, his Miscellaneous Tracts , 1754.
The work last mentioned consists of eight memoirs, and these contain his best known investigations. The first three papers are on various problems in astronomy; the fourth is on the theory of mean observations; the fifth and sixth on problems in fluxions and algebra; the seventh contains a general solution of the isoperimetrical problem; the eighth contains a discussion of the third and ninth sections of the Principia , and their application to the lunar orbit. In this last memoir Simpson obtained a differential equation for the motion of the apse of the lunar orbit similar to that arrived at by Clairaut, but instead of solving it by successive approximations, he deduced a general solution by indeterminate coefficients. The result agrees with that given by Clairaut. Simpson solved this problem in 1747, two years later than the publication of Clairaut's memoir, but the solution was discovered independently of Clairaut's researches, of which Simpson first heard in 1748.
背景介紹與作者介紹
湯瑪斯·辛普森是一位傑出的數學家，出生於 18 世紀初的英格蘭萊斯特郡。 儘管他出身卑微——他的父親是一名織工——但辛普森對學習和數學的熱情，卻因 1724 年目睹日食而點燃。 這一事件激發了他的好奇心，促使他獨立學習算術和代數，甚至在算命小販的幫助下。 他的奉獻精神非常強烈，以至於他放棄了織布，成為一名教師，並繼續嚴格地自學。 最終，他成為伍爾維奇的數學教授，直到 1761 年去世。
辛普森的故事鼓舞人心，因為它表明自我激勵和努力工作如何克服障礙，例如有限的正規教育和社會地位。 他對數學的貢獻，特別是在微積分、概率和天文學方面，具有開創性和影響力。
辛普森作品的詳細分析和意義
辛普森的出版作品涵蓋了廣泛的數學領域。 他關於流數（微積分的早期術語）的著作展示了其在物理學和天文學中的實際應用，有助於彌合理論數學與現實世界現象之間的差距。 他對機會法則的研究為概率論奠定了重要的基礎，這在從統計學到經濟學的各個領域都至關重要。
他的一項顯著成就，是他對年金和歸復的研究，其中涉及計算預期壽命的價值——這個概念在今天的保險和金融領域仍然很重要。 他的論文探討了複雜的主題，如地球的形狀、潮汐力以及天文學中光的彎曲，展示了他廣泛的科學興趣。
辛普森還為代數、幾何和三角學做出了貢獻，引入了至今仍在使用的三角函數的縮寫。 他的解決問題的技巧延伸到炮術，他運用數學來提高火砲的準確性，展示了他的研究的實際影響。
他的最後一部回憶錄包括對天文學和微積分問題的深入討論，例如月球軌道的運動，他使用創新方法獨立解決了這些問題。 這突出了他的獨創性和對數學原理的深刻理解。
給學生的教訓和啟發
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自學的力量： 辛普森的一生告訴學生，好奇心和毅力可以帶來巨大的成就，即使沒有獲得優越的教育機會。 這鼓勵年輕的學習者在學習中主動，並且永遠不要因為他們的背景而氣餒。
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跨學科學習： 辛普森的作品表明數學如何與物理學、天文學、金融學甚至軍事科學聯繫起來。 學生可以學習跨不同領域應用知識來解決複雜問題的重要性。
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解決問題的技巧： 他致力於解決困難的數學問題，激勵學生培養批判性思維和毅力。 這些技能不僅在學術上，而且在日常生活的挑戰中都很有價值。
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創新和獨創性： 辛普森獨立發現解決方案，表明創造力和獨創性在科學進步中的重要性。 應該鼓勵學生探索他們的想法，並超越標準方法。
在生活和學習中的實際應用
- 在學校： 學生可以借鑒辛普森的例子，在他們認為困難的科目中保持動力，理解掌握來自於持續的努力和練習。
- 在社交場合： 這個故事鼓勵謙遜和尊重他人的才能和背景，因為偉大可以來自意想不到的地方。
- 在未來的職業生涯中： 學習將不同的學科聯繫起來並實際應用知識，為學生準備了不同的職業道路，尤其是在 STEM 領域。
- 在個人成長中： 辛普森的一生體現了終身學習和韌性，這些品質有助於個人適應並在快速變化的世界中取得成功。
從辛普森的故事中培養積極的特質
為了體現湯瑪斯·辛普森的精神，學生可以：
- 設定個人的學習目標，並穩步朝著這些目標努力。
- 將挑戰視為成長的機會，而不是障礙。
- 通過書籍、實驗和好奇心驅動的項目，在課堂之外尋求知識。
- 與同伴合作，分享想法並一起解決問題。
- 反思他們的進步，並慶祝小的成功以建立信心。
通過研究辛普森的旅程和貢獻，學生不僅可以獲得關於數學和科學的知識，還可以培養一種重視努力工作、創造力和毅力的心態——這些品質將在他們的一生中為他們提供良好的服務。
