奧古斯塔斯·德摩根

奧古斯塔斯·德摩根
Augustus De Morgan
奧古斯塔斯·德摩根; Augustus De Morgan
	奧古斯塔斯·德摩根像
出生	1806年6月27日; 不列顛帝國馬德拉斯省馬杜賴 (今屬印度)
逝世	1871年3月18日（64歲）; 英國倫敦
居住地	印度、英格蘭
國籍	英國
母校	劍橋大學三一學院
知名於	德摩根定律; 德摩根代數（英語：De Morgan algebra）; 關係代數; 泛代數
信仰	英國國教會 (Non-conformist)
	科學生涯
研究領域	數學，邏輯學
機構	倫敦大學學院; University College School
學術指導者	John Philips Higman; 喬治·皮科克 ; 威廉·休厄爾
著名學生	愛德瓦·勞斯（英語：Edward Routh）; 詹姆斯·西爾維斯特; Frederick Guthrie; 威廉·傑文斯; 愛達·勒芙蕾絲; Francis Guthrie; Stephen Joseph Perry
受影響自	喬治·布爾
施影響於	托馬斯·寇文·門登哈爾（英語：Thomas Corwin Mendenhall）; 艾薩克·托德夯特（英語：Isaac Todhunter）
備註
	他是陶匠兼任瓦片圖案設計師威廉 (William De Morgan) 的父親。

奧古斯塔斯·德摩根（Augustus De Morgan，1806年6月27日—1871年3月18日，英語發音[ɔːˈgʌstəs də ˈmɔːgən]），英國數學家及邏輯學家。他明確陳述了德摩根定律，將數學歸納法的概念嚴格化。他生前多以報刊評論員的身份而知名。^[1]

生平

童年

他生於印度馬德拉斯省。其父在東印度公司工作，母親是詹姆斯·多德森（英語：James Dodson）（曾編製反對數表）的後代。

其姓氏中的「de」可作介詞用，相當於英文的「of」；而「Morgan」本意為「早晨」。

在他7個月大時，全家遷回英國。10歲時，父親去世，她母親帶他搬到英國西部。其數學才華一直未被發現，直至十四歲時，一位家庭的朋友意外發現他精心繪製的尺規作圖。

他有一目失明。於是他求學時期沒有參與任何體育活動，因此被同學取笑。

他的母親是英國教會的活躍分子，寄望兒子成為牧師。而他的中學老師，畢業於牛津大學奧里爾學院的帕森斯，是個擅長古典文學多於數學的人。可是他都不受這些長輩的影響。

大學教育

1823年，16歲的他進入劍橋大學三一學院，與喬治·皮庫克和威廉·修艾爾成為終身的好朋友。他受皮庫克影響，引起了對代數和邏輯的興趣。

他主要的娛樂是笛。

倫敦大學

退休至逝世

數學成就

思想

18世紀時仍有數學家懷疑負數的合法性，德摩根是其中的代表。德摩根自己在解代數方程時也會算出負數，但他認為當算出的答案為負數時，必需作特殊的說明，以迴避負數本身的數學實在性。^[2]德摩根使用負數和虛數，但他仍懷疑它們的數學意義。^[3]他認為如果一個問題的最終答案算出來是負數，那說明原問題的提法不對。當算出最終答案為負數後，把原問題反過來提就可以保證答案為正數，困難就解決了。因此，他不認為負數一無是處，計算結果出現負數可以告訴解題者其問題的陳述方式搞反了。^[1]

紀念

月球上的德摩根環形山

參考資料

^ ^1.0 ^1.1 Ralph A. Raimi. Augustus De Morgan and the Absurdity of Negative Numbers. University of Rochester. 1996年（英語）. In his own time he was better known as a newspaper columnist...","'For example, 8-3 is easily understood; 3 can be taken from 8 and the remainder is 5; but 3-8 is an impossibility; it requires you to take from 3 more than there is in 3, which is absurd. If such an expression as 3-8 should be the answer to a problem, it would denote either that there was some absurdity inherent in the problem itself, or in the manner of putting it into an equation. Nevertheless, as such answers will occur, the student must be aware what sort of mistakes give rise to them, and in what manner they affect the process of investigation...'","... that his general idea, as we shall see, is that playing with absurdities like 3-8 AS IF they made sense can be made to lead to correct final conclusions.","'The principle is, that a negative solution indicates that the nature of the answer is the very reverse of that which it was supposed to be in the solution; for example, if the solution supposes a line measured in feet in one direction, a negative answer, such as -c, indicates that c feet must be measured in the opposite direction; if the answer was thought to be a number of days after a certain epoch, the solution shows that it is c days before that epoch; if we supposed that A was to receive a certain number of pounds, it denotes that he is to pay c pounds, and so on.' 缺少或|url=為空 (幫助);
^ Negative Numbers. University of North Dakota. [2016年1月12日]. （原始內容存檔於2016年2月11日）（英語）. Augustus de Morgan (1806-1871), an English mathematician, thought numbers less than zero were unimaginable.
^ Daniel D. Merrill. Augustus De Morgan and the Logic of Relations. : 185–186 [2016-01-12]. （原始內容存檔於2019-05-19）.

[rochester-1] 1.0 ^1.1 Ralph A. Raimi. Augustus De Morgan and the Absurdity of Negative Numbers. University of Rochester. 1996年（英語）. In his own time he was better known as a newspaper columnist...","'For example, 8-3 is easily understood; 3 can be taken from 8 and the remainder is 5; but 3-8 is an impossibility; it requires you to take from 3 more than there is in 3, which is absurd. If such an expression as 3-8 should be the answer to a problem, it would denote either that there was some absurdity inherent in the problem itself, or in the manner of putting it into an equation. Nevertheless, as such answers will occur, the student must be aware what sort of mistakes give rise to them, and in what manner they affect the process of investigation...'","... that his general idea, as we shall see, is that playing with absurdities like 3-8 AS IF they made sense can be made to lead to correct final conclusions.","'The principle is, that a negative solution indicates that the nature of the answer is the very reverse of that which it was supposed to be in the solution; for example, if the solution supposes a line measured in feet in one direction, a negative answer, such as -c, indicates that c feet must be measured in the opposite direction; if the answer was thought to be a number of days after a certain epoch, the solution shows that it is c days before that epoch; if we supposed that A was to receive a certain number of pounds, it denotes that he is to pay c pounds, and so on.' 缺少或|url=為空 (幫助);

[2] Negative Numbers. University of North Dakota. [2016年1月12日]. （原始內容存檔於2016年2月11日）（英語）. Augustus de Morgan (1806-1871), an English mathematician, thought numbers less than zero were unimaginable.

[DD.M-3] Daniel D. Merrill. Augustus De Morgan and the Logic of Relations. : 185–186 [2016-01-12]. （原始內容存檔於2019-05-19）.

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