奧古斯塔斯·德摩根

奥古斯塔斯·德摩根
Augustus De Morgan
奥古斯塔斯·德摩根; Augustus De Morgan
	奥古斯塔斯·德摩根像
出生	1806年6月27日; 不列颠帝国馬德拉斯省马杜赖 (今属印度)
逝世	1871年3月18日（64歲）; 英国伦敦
居住地	印度、英格兰
国籍	英国
母校	剑桥大学三一学院
知名于	德摩根定律; 德摩根代数（英语：De Morgan algebra）; 关系代数; 泛代数
信仰	英國國教會 (Non-conformist)
	科学生涯
研究领域	数学，逻辑学
机构	伦敦大学学院; University College School
学术指导者	John Philips Higman; 乔治·皮科克 ; 威廉·休厄尔
著名學生	爱德瓦·劳斯（英语：Edward Routh）; 詹姆斯·西尔维斯特; Frederick Guthrie; 威廉·杰文斯; 爱达·勒芙蕾丝; Francis Guthrie; Stephen Joseph Perry
受影响自	乔治·布尔
施影响于	托马斯·寇文·门登哈尔（英语：Thomas Corwin Mendenhall）; 艾萨克·托德夯特（英语：Isaac Todhunter）
备注
	他是陶匠兼任瓦片图案设计师威廉 (William De Morgan) 的父亲。

奥古斯塔斯·德摩根（Augustus De Morgan，1806年6月27日—1871年3月18日，英语发音[ɔːˈgʌstəs də ˈmɔːgən]），英国数学家及逻辑学家。他明确陈述了德摩根定律，将数学归纳法的概念严格化。他生前多以报刊评论员的身份而知名。^[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（英语：James Dodson）（曾編製反對數表）的後代。

其姓氏中的“de”可作介词用，相当于英文的“of”；而“Morgan”本意为“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世纪时仍有数学家怀疑负数的合法性，德摩根是其中的代表。德摩根自己在解代数方程时也会算出负数，但他认为当算出的答案为负数时，必需作特殊的说明，以回避负数本身的数学实在性。^[2]德摩根使用负数和虚数，但他仍怀疑它们的数学意义。^[3]他认为如果一个问题的最终答案算出来是负数，那说明原问题的提法不对。当算出最终答案为负数后，把原问题反过来提就可以保证答案为正数，困难就解决了。因此，他不认为负数一无是处，计算结果出现负数可以告诉解题者其问题的陈述方式搞反了。^[1]

紀念

月球上的德摩根环形山

参考资料

^ ^1.0 ^1.1 Ralph A. Raimi. Augustus De Morgan and the Absurdity of Negative Numbers. University of Rochester. 1996年（英语）. 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=为空 (帮助);
^ Negative Numbers. University of North Dakota. [2016年1月12日]. （原始内容存档于2016年2月11日）（英语）. 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]. （原始内容存档于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（英语）. 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=为空 (帮助);

[2] Negative Numbers. University of North Dakota. [2016年1月12日]. （原始内容存档于2016年2月11日）（英语）. 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]. （原始内容存档于2019-05-19）.

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