J.É. 蒙蒂克拉Jean-Étienne Montucla

Étienne J.É. 蒙蒂克拉的父亲是一位在里昂生活和工作的商人。他的儿子Étienne就是在那个城镇出生、长大并开始接受教育的。

艾蒂安在里昂的耶稣会学院接受教育，但在1741年，当他在那里学习时，他的父亲去世了，他成了孤儿。在这个阶段，他的祖母接管了他的抚养。艾蒂安在耶稣会学院对广泛的研究感兴趣。里德尔在[4]中写道：-

他的注意力主要转向古代经典；但由于对哲学研究有天然的爱好，并且记忆力强，他能够准确掌握几种现代语言；其中包括意大利语、德语、荷兰语和英语。在后来成为拉朗德导师的贝罗神父指导下，他在数学和物理研究方面取得了相当大的进步。

1745年，J.É. 蒙蒂克拉 的祖母去世，此时他前往图卢兹，开始学习法律。在完成图卢兹的学业后，他决定前往巴黎，那里将是接受进一步法律训练最合适的地方。在那里，他与狄德罗、拉朗德 和 让·勒朗·达朗贝尔 成为朋友，他们是在 Charles Antoine Jombert 组织的科学晚会上结识的。他还结识了当时许多顶尖数学家的其他朋友，并开始将他众多的兴趣结合起来，研究数学史。结识 Jombert 还有其他好处，因为他是一位书商和出版商。来自 Jombert、让·勒朗·达朗贝尔 和狄德罗的建议，使 J.É. 蒙蒂克拉 走上了出版数学史著作的道路。

他的第一部作品是Histoire des recherches sur la quadrature du cercle Ⓣ（化圆为方研究史），由Jombert于1754年在巴黎出版，这部作品受到的高度评价可以从以下事实看出：仅凭这部作品，J.É. 蒙蒂克拉就被选为柏林科学院的通讯成员。尽管自J.É. 蒙蒂克拉时代以来，squaring the circle问题的历史发生了巨大变化，但这本书仍然是同类中的经典。此时他已经在创作他的杰作Histoire des mathématiques Ⓣ（数学史），并在1754年宣布将在未来出版。他正在承担一项非常重大的任务，一项以前从未真正以这种形式承担过的任务，四年后才出版。J.É. 蒙蒂克拉需要收入来追求他的研究兴趣，大约在这个时候他在Gazette de Paris工作。

1756年，J.É. 蒙蒂克拉出版了一部作品，展示了他科学兴趣的广度。与医生约瑟夫·莫里索-德朗德合作出版了Recueil de pièces concernant l'inoculation de la petite vérole et propres à en prouver la sécurité et l'utilité Ⓣ（关于天花接种的文件集，特别是为了证明其安全性和实用性），该书提供了关于天花疫苗接种的资料来源集。然后在1758年，他出版了两卷本著作，再次由乔姆伯特作为他的出版商，Histoire des mathématiques。第一卷涵盖了从古代到1700年的数学史，而第二卷完全致力于17世纪的数学。沃格尔[6]将J.É. 蒙蒂克拉的论著描述为：-

……首次尝试数学思想和问题的历史。[早期作品大多是]姓名、标题和日期的列表……

J.É. 蒙蒂克拉原本打算撰写第三卷，涵盖18世纪上半叶，但这一时期涌现的大量著作，以及将近期成果置于历史背景中的困难，使他放弃了这一目标。这两卷理所当然地为J.É. 蒙蒂克拉在巴黎赢得了很高的声誉，他开始为法国政府工作。

1761年，他前往格勒诺布尔，被任命为多菲内的总督。多菲内是法国东南部的一个地区，最初是独立的。在14世纪，它被卖给了法国的查理五世，后者随后将多菲内割让给他的继承人，后来的国王继续这种做法。1453年，查理七世的儿子创建了多菲内议会，他利用在那里的职位与父亲发生争执，父亲随后将多菲内并入法国。1628年，法国政府任命了一位总督到多菲内，以防止它可能有的任何独立想法。总督是一位重要的皇家官员，控制着该地区，1761年J.É. 蒙蒂克拉被任命的就是这个职位。他驻扎在多菲内的主要城镇格勒诺布尔。在那里，他遇到了Marie Françoise Romand，他们于1763年结婚。

结婚一年后，法国政府将J.É. 蒙蒂克拉派往南美洲东北海岸的卡宴。让·里歇尔几乎正好在100年前被法国政府派往那里，J.É. 蒙蒂克拉也作为天文学家去了那里。1643年，法国商人在现今卡宴市（法属圭亚那的一个港口）的遗址上建立了一个城镇，称该定居点为La Ravardière。印第安人后来摧毁了该镇，但法国人于1664年重新占领，并在1667年的一项条约中获得了法属圭亚那，四年后他们派让·里歇尔去了那里。在1700年代，法国人努力建设他们的南美领土。J.É. 蒙蒂克拉于1764年被任命为皇家天文学家和法国远征法属圭亚那的秘书，并被派往La Ravardière。在那里度过一年多后，他于1765年返回法国。我们顺便注意到，La Ravardière在1777年更名为卡宴。

回到法国后，J.É. 蒙蒂克拉又获得了一项重要的政府任命，担任皇家建筑首席文书，从1766年到1789年任职。他还在1775年被任命为数学著作的皇家审查官。几年后，他出版了他因此闻名的另一部文本，即1778年雅克·奥扎南的Récréations mathématiques et physiquesⓉ（数学与物理娱乐）的新版本。里德尔在[4]中写道，J.É. 蒙蒂克拉：-

……如此大幅度地扩充并改进了雅克·奥扎南的《娱乐》，以至于可以说他把这部著作变成了自己的作品。……他如此小心地隐瞒了自己与这部著作的关系，以至于在该书完成后，一本样书被送到他那里，以审查官的身份进行审查和批准。除了从雅克·奥扎南的著作中删去许多荒谬、幼稚和过时的内容外，他还以关于几乎每一个实用科学分支的论述丰富了自己的版本……

他的版本在普及几何剖分问题方面颇具影响力，这类问题涉及将几何图形切割成可以重新排列成其他几何图形的碎片。查尔斯·赫顿于1803年将J.É. 蒙蒂克拉版本的雅克·奥扎南的Récréations mathématiques et physiquesⓉ（数学与物理娱乐）翻译成英文，里德尔的版本于1844年出版，名为Recreations in science and natural philosophy。

1788年，约瑟夫·傅里叶将一篇代数论文寄给J.É. 蒙蒂克拉征求意见。然而，约瑟夫·傅里叶没有收到意见，并在一年后的一封信中写道：-

我开始相信J.É. 蒙蒂克拉先生的话，他告诉我们他已经与博学的分析闹翻了：我平静地等待他与它和解。

这可能意味着J.É. 蒙蒂克拉此时已停止做数学，但约瑟夫·傅里叶的评论没有得到正确理解。

毫不奇怪，当1789年法国大革命开始时，J.É. 蒙蒂克拉的皇家职位消失了。此时他已相当富有，因为多年担任高级职务，但大革命使他失去了大部分财富，正如Riddle所写：-

……在他年老时将他抛入世间，除了正直以及朋友的爱与尊重之外，一切都被剥夺。

此时他退休并住在凡尔赛，在那里他研究数学史文本。然而，尽管他此时已七十岁，1795年他还是获得了进一步的公职。他被赋予评估外交部条约的任务，但报酬太少，他在经济上亏损了。他还在国家彩票办公室担任职务。

J.É. 蒙蒂克拉的朋友们说服他修订他著名的Histoire des mathématiquesⓉ（数学史）的新版本。1799年8月，J.É. 蒙蒂克拉通过巴黎的Agasse出版了最初于1758年出版的两卷本的新版本。J.É. 蒙蒂克拉对这两卷进行了大量修订和扩充。他本打算将历史覆盖范围延伸到18世纪末，到他去世时，关于这一主题的第三卷部分已经印刷，此时距1799年新版本出版已过去四个月。拉朗德在其他一些科学家的帮助下，完成了第三卷和第四卷，以实现J.É. 蒙蒂克拉的意图。第三卷涵盖18世纪纯数学、光学和力学，共832页，而第四卷涵盖18世纪天文学、数学地理学和航海学，共688页。Vogel在[1]中写道：-

J.É. 蒙蒂克拉的主要著作，第一部经典数学史，全面且相对于当代学术状况而言准确地描述了该学科在各个国家的发展。该记述还包括力学、天文学、光学和音乐……

Sarton [5] 写道：-

它仍然是一本非常有价值的书，不过只适合谨慎的“鉴赏家”；新手最好别碰它。

1968年Histoire des mathématiques四卷本重印版的导言对J.É. 蒙蒂克拉的贡献作了如下评价：-

J.É. 蒙蒂克拉在数学史方面给了我们双重教训。在这些教训中，第一重是他为我们所撰写的内容。第二重是他无意中写下的内容，即通过他的个性，“se trouve être l'image des idées, des manières de voir de son époque et du milieu scientifique qu'il fréquentait et connaissait très bien”Ⓣ（……成为他那个时代以及他所熟悉并经常往来的科学界的思想和思维方式的映像。）。

Étienne Montucla's father was a merchant who lived and worked in Lyon. It was in that town that his son Étienne was born, was brought up, and began his education.

Étienne was educated in the Jesuit College in Lyon but, in 1741, while he was studying there his father died and he was left an orphan. At this stage his grandmother took over his upbringing. Étienne was interested in a wide range of studies at the Jesuit College. Riddle writes in [4]:-

His attention was chiefly directed to the ancient classics; but having a natural taste for philosophical studies, and a powerful memory, he was enabled to acquire an accurate knowledge of several modern languages; among which Italian, German, Dutch, and English are mentioned. Under Le Père Bêraud, who was subsequently the tutor of Lalande, he made considerable proficiency in the study of mathematics and physics.

In 1745 Montucla's grandmother died and at this point he went to Toulouse where he began to study law. After completing his studies at Toulouse, he decided to go to Paris which would be the most suitable place to gain further legal training. There he became friends with Diderot, Lalande and d'Alembert whom he met at the scientific soirées organised by Charles Antoine Jombert. He made many other friends among the top mathematicians of his day, and he began to combine his many interests and study the history of mathematics. Making the acquaintance of Jombert had other advantages, for he was a bookseller and publisher. The advice from Jombert, d'Alembert and Diderot set Montucla on the road of publishing on the history of mathematics.

His first work was Histoire des recherches sur la quadrature du cercle Ⓣ which was published by Jombert in Paris in 1754, and the high regard in which this work was held can be judged by the fact that on the strength of this work alone Montucla was elected a corresponding member of the Berlin Academy. Although the history of the problem of squaring the circle has changed greatly since Montucla's day this book is still a classic of its kind. Already at this time he was working on his masterpiece, Histoire des mathématiques Ⓣ, and in 1754 he announced that it would be published at a future date. He was undertaking a very major task, one which had never really been undertaken in this form before, and four years would pass before publication. Montucla needed an income to allow him to pursue his research interests and around this time he worked at the Gazette de Paris.

In 1756 Montucla published a work which shows the breadth of his scientific interests. A collaboration with the physician Joseph Morisot-Deslandes led to the publication of Recueil de pièces concernant l'inoculation de la petite vérole et propres à en prouver la sécurité et l'utilité Ⓣ, which provided a collection of sources on smallpox vaccination. Then in 1758 he published his two volume work, again with Jombert as his publisher, Histoire des mathématiques. The first volume covered the history of mathematics from ancient times to 1700, while the second volume was entirely devoted to 17th century mathematics. Vogel [6] describes Montucla's treatise as:-

... the first attempt of a history of mathematical ideas and problems. [Earlier works being mostly] lists of names, titles and dates ...

Montucla had been intending to produce a third volume covering the first half of the 18th century but the volume of work which had appeared during this time, and the difficulties of putting recent work into its historical context, led him to give up this aim. These two volumes rightly led to Montucla gaining a high reputation in Paris and he began to work for the French government.

In 1761 he went to Grenoble where he was appointed to the position of intendant to Dauphiné. Dauphiné was a region of south-eastern France which had originally been independent. In the 14th century it had been sold to Charles V of France who then ceded Dauphiné to his heir, a practice which later Kings continued. A Parlement of Dauphiné was created in 1453 by the son of Charles VII who used his position there to cause an argument with his father, who then responded by annexing Dauphiné to France. In 1628 the French government appointed an intendant to Dauphiné to prevent any notions of independence it might have. The intendant was an important royal official with control over the area, and it was to that position that Montucla was appointed in 1761. He was based in Grenoble, the principal town of Dauphiné. There he met Marie Françoise Romand and they married in 1763.

A year after his marriage the French government sent Montucla to Cayenne on the north-eastern coast of South America. Jean Richer had been sent there by the French government almost exactly 100 years earlier and Montucla also went there as an astronomer. In 1643 French merchants founded a town on the site of the present day city of Cayenne, a port of French Guiana, calling the settlement La Ravardière. The Indians later destroyed the town but the French reoccupied it in 1664 and were awarded French Guiana in a treaty of 1667, four years before they sent Jean Richer there. In the 1700s the French worked hard at building up their South American territory. Montucla was appointed royal astronomer and secretary to a French expedition to French Guiana in 1764 and was sent to La Ravardière. After spending over a year he returned to France in 1765. We note in passing that La Ravardière was renamed Cayenne in 1777.

After his return to France, Montucla received another major government appointment, as Head Clerk of Royal Buildings, holding the post from 1766 to 1789. He was also appointed as Royal Censor of mathematical works in 1775. A few years later he published another text for which he is famed, namely a new edition of Ozanam's Récréations mathématiques et physiques Ⓣ in 1778. Riddle writes in [4] that Montucla:-

... so greatly enlarged and improved the "Recreations" of Ozanam, that he may be said to have made the work his own. ... so carefully had he concealed his connection with the work, that, on its completion, a copy of it was sent to him, in his capacity of censor, for examination and approval. Besides expunging from the work of Ozanam much that was absurd, puerile, and obsolete, he enriched his edition with dissertations upon almost every branch of practical science ...

His edition was influential in popularising geometric dissection problems which involve the cutting of geometric figures into pieces that can be arranged to form other geometric figures. Charles Hutton translated Montucla's edition of Ozanam's Récréations mathématiques et physiques Ⓣ into English in 1803 and Riddle's edition was published in 1844, called Recreations in science and natural philosophy.

In 1788 Fourier sent an algebra paper to Montucla for his opinion. Fourier, however, did not receive an opinion and wrote in a letter a year later:-

I begin to take M Montucla at his word when he tells us he has fallen out with learned analysis: I wait calmly for him to be reconciled with it.

This may mean that Montucla had stopped doing mathematics at this time but Fourier's comment is not properly understood.

Not surprisingly Montucla's royal posts vanished when the French Revolution began in 1789. By this time he was quite well off, having held high office for many years, but the Revolution saw him lose most of his wealth, as Riddle writes:-

... throwing him on the world in his old age, stripped of everything but his integrity, and the love and respect of his friends.

At this time he retired and went to live at Versailles where he worked on history of mathematics texts. He was, however, given further public appointments in 1795 even although he was seventy years old by this time. He was given the task of evaluating the treaties in the Ministry of Foreign Affairs, but was paid so little he lost financially. He also held a position in the office of the National Lottery.

Montucla's friends persuaded him to work on a new edition of his famous Histoire des mathématiques Ⓣ. In August 1799 Montucla published new editions through Agasse in Paris of the two volumes originally published in 1758. Montucla extensively revised and enlarged the two volumes. He had intended to extend his cover of history to the end of the 18th century and part of the third volume on this topic was printed by the time he died, four months after the publication of the new editions of 1799. Lalande, with the help of some other scientists, completed volumes three and four to give the coverage that Montucla had intended. Volume three covered 18th century pure mathematics, optics and mechanics in 832 pages, while the fourth volume covered 18th century astronomy, mathematical geography and navigation in 688 pages. Vogel writes in [1]:-

Montucla's major work, the first classical history of mathematics, was a comprehensive and, relative to the state of contemporary scholarship, accurate description of the development of the subject in various countries. the account also included mechanics, astronomy, optics, and music ...

Sarton [5] wrote:-

It is still a very valuable book, though only for the wary 'connoisseur'; novices will do well to leave it alone.

The introduction to a reprint of the four volumes of Histoire des mathématiques in 1968 gives this assessment of Montucla's contribution:-

Montucla has given us a double lesson in the history of mathematics. Of these lessons, the first is what he has composed for us. The second is what he has written without intending to, that which, through his personality, "se trouve être l'image des idées, des manières de voir de son époque et du milieu scientifique qu'il fréquentait et connaissait très bien" Ⓣ.