弗洛里安·卡乔里Florian Cajori

弗洛里安·卡乔里的父亲Georg Cajori是一名工程师。他在瑞士修建道路和桥梁，鉴于该国多山，这需要高超的技能和专业知识。卡乔里的母亲是凯瑟琳·卡梅尼施。卡乔里在瑞士上学，先是在齐利斯，该地位于图西斯以南约七公里处，然后在库尔，即瑞士东部格劳宾登州的首府。

卡乔里于1875年十六岁时移居美国。他于1876年进入威斯康星州怀特沃特的州立师范学校，两年后毕业。卡乔里毕业后没有立即进入大学，而是在一所乡村学校任教，之后才开始在威斯康星大学学习数学。1883年在威斯康星获得学士学位后，他于1884年1月进入约翰斯威廉·霍普金斯大学。在约翰斯霍普金斯大学学习了大约十八个月后，卡乔里于1885年6月离开，次年由威斯康星大学授予硕士学位。

离开约翰斯霍普金斯大学后，卡乔里于1885年被任命为新奥尔良杜兰大学的助理教授，甚至在他获得硕士学位之前。他于1887年成为杜兰大学的应用数学教授。他从1889年到1898年在科罗拉多斯普林斯的科罗拉多学院担任物理学讲席，在此期间，于1890年与伊丽莎白·G·爱德华兹结婚；他们有一个儿子。同样在此期间，于1894年，他获得了杜兰大学的博士学位。

卡乔里从1898年到1918年在科罗拉多学院担任数学讲席，在科罗拉多斯普林斯的最后十五年里担任工程系主任。他于1918年被任命到加利福尼亚大学乔治·伯克利分校专门设立的数学史讲席。这是美国设立的第一个数学史讲席，在这所顶尖大学专门设立一个讲席，充分说明了卡乔里的崇高声誉。

当他接近七十岁时，他的健康开始衰退。他于1930年2月接受了一次大手术，从未完全康复，六个月后在他伯克利的家中去世。

现在我们必须考察一下卡乔里对数学史所作贡献的一小部分，以理解他在这一学科中享有的崇高国际声誉——这使他在世时获得了许多荣誉，但今天科学史家对他的评价却略低一些。在考察他关于数学史的主要著作之前，让我们首先注意到，他确实写过一些并非历史著作的教科书，如An introduction to the modern theory of equations（1904）和Elementary algebra: First year course（1915）。除了数学史之外，他没有对数学的任何其他领域进行过研究。

卡乔里写了许多历史著作，我们将对其中几部作一些评论。一部早期的著作是The teaching and history of mathematics in the United States（1890），它介绍了二十二所美国机构。这部有趣的著作显示了这些机构中研究生学习和研究的主要趋势。该书在[7]中得到了详细考察。

也许最初使卡乔里成名的著作是A History of Mathematics（1894，第2版1919）。我们[EFR和JJOC]有一本此书，它至今仍是一本值得参考的好书。它确实是第一本试图以通俗易读的方式呈现数学史的著作，而且确实在其目标上非常成功。

A History of Mathematical Notations，2卷（1928-29）无疑是卡乔里最伟大的著作。Zund在[8]中写道，它：-

……简直是里程碑式的，在其细节和严谨的学术上至今未被超越……

卡乔里的去世Sir Isaac Newton's "Mathematical principles" of Natural Philosophy and His System of the World于1934年出版。卡乔里非常清楚地表明了他制作这个艾萨克·牛顿的Principia版本的目的，即通过替换现有艾萨克·牛顿拉丁文文本英译本中使用的古旧语言，使文本对现代读者可读。然而[8]：-

他“改进”的语言基于对1729年莫特译本的现代化——没有参考艾萨克·牛顿的拉丁文版本——并且包含大量错误和偏离原意的内容。同样，他对技术语言的现代化也不完整，且不完全一致。因此，就艾萨克·牛顿的原始思想而言，他的艾萨克·牛顿呈现既不忠实服务于现代读者，也不忠实服务于科学史家。

卡乔里写了大约十二本书和大量关于数学史的论文和报告。他的其他贡献包括A History of Elementary Mathematics with Hints on Methods of Teaching（1896年）、A History of the Logarithmic Slide Rule and Allied Instruments（1909年）、William Oughtred, a Great Seventeenth- Century Teacher of Mathematics（1916年）和Early Mathematical Sciences in North and South America（1928年）。

尽管我们已经指出，卡乔里的著作有时缺乏人们期望这样一位杰出科学家所具有的学术性，但我们不应给这位重要人物留下过于负面的印象。他几乎单枪匹马地在美国将数学史创建为一门学科，尤其是凭借他关于数学符号史的著作，他至今仍是当今被引用最多的数学史家之一。

最后，我们应该看看卡乔里获得的荣誉。他于1917-18年当选为美国数学协会主席，1923年任美国科学促进会副主席。他还以同样身份任职于科学史学会（1924-25）和国际科学史委员会（1929-30）。他获得了理学博士学位和三个荣誉法学博士学位的殊荣。

Florian Cajori's father, Georg Cajori, was an engineer. He built roads and bridges in Switzerland which, given the mountainous country, required great skill and expertise. Florian's mother was Catherine Camenisch. Florian attended schools in Switzerland, first in Zillis, which lies about seven kilometres south of Thusis, and then in Chur, the capital of Graubünden canton in eastern Switzerland.

Cajori emigrated to the United States in 1875 when he was sixteen years old. He entered the State Normal School in Whitewater, Wisconsin in 1876 and graduated two years later. Cajori did not enter university immediately after graduating, but he taught in a country school before beginning his studies of mathematics at the University of Wisconsin. After being awarded a B.S. from Wisconsin in 1883, he entered Johns Hopkins University in January 1884. Having studied for about eighteen months at Johns Hopkins, Cajori left in June 1885 and was awarded his Master's degree by the University of Wisconsin the following year.

After leaving Johns Hopkins University, Cajori was appointed as assistant professor at Tulane University in New Orleans in 1885 even before receiving his Master's degree. He became professor of applied mathematics at Tulane in 1887. He held the chair of physics at Colorado College in Colorado Springs from 1889 to 1898 and during this time, in 1890, he married Elizabeth G Edwards; they had one son. Also during this time, in 1894, he was awarded his doctorate from Tulane University.

Cajori held the chair of mathematics at Colorado College from 1898 until 1918, being Dean of the Department of Engineering for the last fifteen years of his time at Colorado Springs. He was appointed to a specially created chair in the history of mathematics at the University of California at Berkeley in 1918. This was the first chair in the history of mathematics to be founded in the United States and it says much of Cajori's high reputation that a special chair was created at this leading university.

As he approached the age of seventy his health began to fail. He underwent a major operation in February 1930, never made a full recovery and died at his home in Berkeley six months later.

We must now examine a little of the contribution which Cajori made to the history of mathematics to understand his high international reputation in the subject which gained him many honours in his lifetime but the somewhat less regard in which he is held by historians of science today. Before looking at his main work on the history of mathematics, let us first note that he did write some textbooks which were not historical texts such as An introduction to the modern theory of equations (1904) and Elementary algebra: First year course (1915). He did not carry out research into any area of mathematics other than its history.

Cajori wrote many historical books and we shall make some comments on a few of them. An early book was The teaching and history of mathematics in the United States (1890) which profiles twenty-two American institutions. This interesting work shows a major trend towards graduate study and research in these institutions. The book is examined in detail in [7].

Perhaps the book which first brought Cajori fame was A History of Mathematics (1894, 2nd ed. 1919). We [EFR and JJOC] have a copy of this book and it is still a good book to consult. It was literally the first book to attempt to present the history of mathematics in a popular and readable fashion and indeed it was highly successful in its aims.

A History of Mathematical Notations, 2 volumes (1928-29) is undoubtedly Cajori's greatest work. Zund writes in [8] that it:-

... is simply monumental and remains unsurpassed in its detail and meticulous scholarship ...

After Cajori's death Sir Isaac Newton's "Mathematical principles" of Natural Philosophy and His System of the World was published in 1934. Cajori makes very clear his aim in producing this edition of Newton's Principia which was to make the text readable to modern readers by replacing the archaic language used in the existing English translations of Newton's Latin text. However [8]:-

His "improved" language was based on a modernisation of the 1729 Motte translation - without reference to Newton's Latin edition - and contains numerous errors and deviations from the original meaning. Likewise, his modernisation of the technical language was incomplete and not entirely consistent. Hence, his presentation of Newton neither faithfully serves the modern reader nor the historian of science with regard to Newton's original thoughts.

Cajori wrote about twelve books and a large number of papers and reports on the history of mathematics. Among his other contributions are A History of Elementary Mathematics with Hints on Methods of Teaching (1896), A History of the Logarithmic Slide Rule and Allied Instruments (1909), William Oughtred, a Great Seventeenth- Century Teacher of Mathematics (1916), and Early Mathematical Sciences in North and South America (1928).

Although we have made indicated that at times Cajori's work lacked the scholarship which one would expect of such an eminent scientist, we must not give too negative an impression of this important figure. He almost single-handedly created the history of mathematics as an academic subject in the United States and, particularly with his book on the history of mathematical notation, he is still one of the most quoted historians of mathematics today.

Finally we should look at honours Cajori received. He was elected president of the Mathematical Association of America in 1917-18, vice-president of the American Association for the Advancement of Science in 1923. He also served in that capacity for the History of Science Society (1924-25) and the Comité International d'Histoire des Sciences (1929-30). He had the distinction of being awarded a D.Sc. and three honorary LL.D. degrees.