约瑟夫·洪尼格-朗斯基Józef Maria Hoene-Wroński

Jozéf Hoëné 约瑟夫·洪尼格-朗斯基 出生在波兹南西南约60公里的沃尔什滕镇，出生后取名 洪尼格-朗斯基 Hoëné。他的父母来自定居在波兰西部的捷克家庭，母亲是 Elzbieta Pernicka，父亲是 Antoni Hoehne，曾任波兹南市政建筑师。洪尼格-朗斯基 Hoëné 在波兹南和华沙接受教育，但1794年他卷入了科希丘什科起义。

尽管为独立而战，俄罗斯和普鲁士还是在1793年瓜分了波兰。塔德乌什·科希丘什科将军是美国独立战争的英雄，他于1794年返回波兰，集结了一支波兰军队再次为独立而战。Hoëné 洪尼格-朗斯基（我们使用这个名字，尽管他直到1810年左右刚结婚后才采用 洪尼格-朗斯基）作为炮兵少尉加入了科希丘什科。在赢得拉茨瓦维采战役并占领华沙和维尔诺之后，科希丘什科的军队在华沙被围困后被俄罗斯和普鲁士军队击败。科希丘什科受伤并被俄罗斯军队俘虏，俄军对华沙居民进行了屠杀。Hoëné 洪尼格-朗斯基 也被俘，被迫在俄罗斯军队中服役，直到1797年获释，当时已晋升为中校。

此时，Hoëné 洪尼格-朗斯基的父亲已经去世，留给他一笔钱，使他能够在接下来的几年里在德国多所大学学习哲学。他在法国马赛加入了波兰军团，并于1800年成为法国公民。他开始在马赛从事科学工作，于1803年加入那里的天文台，并开始研究宇宙及其起源的理论。然后在1810年，他搬到了巴黎，并在同一年与Victoire Henriette Sarrazin de Mountferrier结婚，她的兄弟是数学家Alexandre Mountferrier。正是在这个时候，他采用了姓氏洪尼格-朗斯基，但他并没有一直使用它，而是交替使用洪尼格-朗斯基和Hoehne。然而，在撰写论文时，他使用Hoëné 洪尼格-朗斯基这个名字，不使用任何名字。Bushaw在[7]中写道，Hoëné 洪尼格-朗斯基：-

……才华横溢、博学、勤勉、多才多艺且雄心勃勃。他的众多计划从水厂、航海仪器和铁路车轮的设计，延伸到数学、天文学及其他科学，直至形而上学的最高深领域……洪尼格-朗斯基的性格也很棘手，并且被指责傲慢、招摇撞骗、偏执以及其他性格瑕疵，这些指责并非全无道理。

他关于数学基础的第一篇论文于1810年在那里发表，但在西尔维斯特·佛朗索瓦·拉克鲁瓦和约瑟夫·拉格朗日给予不佳评价之后，洪尼格-朗斯基中断了与巴黎研究院的关系。然而，他抵达巴黎后确实得到了金融家Pierre Arson的强力资助，这持续了许多年。最终他们因已安排的财务安排而闹翻，这场纠纷在1819年通过高调的法庭诉讼变得非常公开。他在此期间完成的一项工作导致1812年发表了Résolution générale des équations de tous degrés Ⓣ（所有次数方程的一般解），声称证明每个方程都有代数解。这与保罗·鲁菲尼已发表的结果相矛盾，但当然保罗·鲁菲尼未能说服许多人相信其真实性。洪尼格-朗斯基在此处的工作虽然当然是错误的，但仍然有重要应用，并包含有趣的新思想。

洪尼格-朗斯基 在1819年至1822年间在伦敦度过。他来到英国试图从经度委员会获得奖励，但他的仪器在入境时被海关扣留。他发现自己陷入严重的经济困难，但在仪器归还给他后，他能够向经度委员会发表演讲。他的演讲 On the Longitude 只包含泛泛之谈，没有给人留下深刻印象。正如 洪尼格-朗斯基 的冒险似乎总是发生的那样，它退化成一场与科学几乎无关的争论。然后他试图让 皇家学会 对他的流体动力学工作感兴趣。这再次迅速退化成一场与科学无关的争论。

他的主要工作涉及将哲学应用于数学，哲学优先于严格的数学证明。他写了关于数学哲学的著作。他的书 Introduction to a course in mathematics 于1821年在伦敦出版。他批评 约瑟夫·拉格朗日 对无穷级数的使用，并引入了自己关于函数级数展开的想法。由此产生了他的“通用 Hoëné-洪尼格-朗斯基 级数”或“la série universelle 洪尼格-朗斯基”。这包括将函数展开为任意函数的级数。此外，他还给出了他的“最高定律”或“La loi suprême”，这是一个给出计算系数的一般规则的定律。这个级数中的系数是 行列式，现在称为朗斯基行列式（由 托马斯·穆尔 在1882年命名）。

1827年，他出版了他的Canons de logarithmes Ⓣ（对数表）。Bushaw写道：-

在[表的历史中]可能没有比洪尼格-朗斯基的“对数法则”更引人注目的聪明例子了。对于一个使得能够将七位常用对数表以可读字体放在一张小于17厘米乘22厘米大小的单页上的方案来说，这似乎不算太强的说法。……

小册子Canons de logarithmes [6]：-

……包括使用六张单页常用对数表的说明、示例和理论。此外，它还包含“五次方程一般解”的摘要。在Prospectus中，洪尼格-朗斯基论证传统表格昂贵、笨重、翻页太多且令人畏惧。因此他设计了他极其紧凑的“法则”（该术语可追溯到约翰·纳皮尔），没有这些缺点。

这并不是洪尼格-朗斯基在计算和计算辅助工具方面唯一的工作[6]：-

洪尼格-朗斯基显然是一位不知疲倦的计算者。这种兴趣的一种表现形式是设计计算辅助工具，不仅为科学家，也为非科学家——学童、士兵、商人和其他人。其中一些装置应被称为前电子计算器，事实上洪尼格-朗斯基将他的一项发明称为“通用计算器”。他留下了几个这类未完成的项目……

他在19世纪30年代所做的其他事情中，包括设计履带式车辆以与铁路竞争。然而它们从未被制造出来。多年来，洪尼格-朗斯基的所有工作都被视为垃圾。这很大程度上是由于他的个性导致了[1]：-

……对自己研究重要性的夸大其词，对最轻微批评的激烈反应，以及反复求助于非科学媒体作为盟友来对抗所谓的阴谋。

然而，近年来对这项工作的更仔细审视表明，尽管有些是错误的，而且他确实对自己和自己的思想有着令人难以置信的高度评价，但论文中也隐藏着一些具有巨大深度和才华的数学见解。

虽然实际上不是他的遗言，然而，在他最后病情的晚期阶段，他说：-

万能的上帝啊，我想说的话还有那么多！

Jozéf Hoëné Wronski was named Josef Hoëné after his birth in the town of Wolsztyn about 60 km south west of Poznań. His parents, from Czech families that had settled in western Poland, were Elzbieta Pernicka and Antoni Hoehne who was the municipal architect of Poznań. Josef Hoëné was educated in Poznań and Warsaw but in 1794 he became involved in the Kosciuszko Uprising.

Despite battles for independence, Russia and Prussia partitioned Poland in 1793. General Tadeusz Kosciuszko, a hero of the American War of Independence, returned to Poland in 1794 and gathered an army of Poles to again fight for independence. Hoëné Wronski (we use this name although he did not adopt Wronski until around 1810 just after he married) joined Kosciuszko as second lieutenant in the artillery. After winning the battle of Raclawice and capturing Warsaw and Wilno, Kosciuszko's army was defeated by Russian and Prussian forces after a siege of Warsaw. Kosciuszko was wounded and taken prisoner by the Russian army which carried out a massacre of the population in the Warsaw. Hoëné Wronski was also taken prisoner, and made to serve in the Russian army which he did until 1797 when he was released having reached the rank of lieutenant colonel.

By this time Hoëné Wronski's father had died and left him money which allowed him to spend the next years in Germany studying philosophy at a number of different universities. He enlisted in the Polish Legion at Marseilles, in France, and become a French citizen in 1800. He began to undertake scientific work in Marseilles, joining the observatory there in 1803, and started to work out a theory of the universe and its origins. Then in 1810 he moved to Paris and, in the same year, he married Victoire Henriette Sarrazin de Mountferrier, whose brother was the mathematician Alexandre Mountferrier. It was at this time that he adopted the surname Wronski but he did not use it consistently, rather alternately used Wronski and Hoehne. When writing papers, however, he used the name Hoëné Wronski without the use of any first name. Bushaw writes in [7] that Hoëné Wronski:-

... was brilliant, erudite, industrious, versatile, and ambitious. His many projects ranged from the design of water works, navigational instruments, and railway car wheels, through mathematics, astronomy, and other sciences to the farthest reaches of metaphysics ... Wronski also had a difficult personality, and has been accused, not without plausibility, of arrogance, charlatanry, paranoia, and other blemishes of character.

His first memoir on the foundations of mathematics was published there in 1810 but, after it received less than good reviews from Lacroix and Lagrange, Wronski broke off relations with the Institute in Paris. He did, however, have strong financial support from a financier Pierre Arson after he arrived in Paris and this continued for many years. Eventually they fell out over the financial arrangement which had been put in place and this dispute became very public with high profile court actions in 1819. A piece of work which he had undertaken during this period resulted in a publication Résolution générale des équations de tous degrés Ⓣ in 1812 claiming to show that every equation had an algebraic solution. This contradicted Ruffini's results which were already published but of course Ruffini had failed to convince many of the truth. Wronski's work here, although of course wrong, nevertheless still has important applications and contains interesting novel ideas.

Wronski spent the years 1819 to 1822 in London. He came to England to try to obtain an award from the Board of Longitude but his instruments were detained by the Customs as he entered the country. He found himself in severe financial difficulties but, after his instruments had been returned to him, he was able to address the Board of Longitude. His address On the Longitude only contained generalities and did not impress. As always seemed to happen with Wronski's ventures, it degenerated into an argument which had little to do with the science. He then tried to get the Royal Society to show an interest in his work on hydrodynamics. This again quickly degenerated into an argument which had nothing to do with the science.

His main work involved applying philosophy to mathematics, the philosophy taking precedence over rigorous mathematical proofs. He wrote on the philosophy of mathematics. His book Introduction to a course in mathematics was published in London in 1821. He criticised Lagrange's use of infinite series and introduced his own ideas for series expansions of a function. Out of this came his "universal Hoëné-Wronski series" or "la série universelle de Wronski". This consisted of the development of a function as a series in terms of arbitrary functions. Also he gave his "highest law" or "La loi suprême" which was a law giving a general rule to calculate the coefficients. The coefficients in this series are determinants now known as Wronskians (so named by Muir in 1882).

In 1827 he published his Canons de logarithmes Ⓣ. Bushaw writes:-

There may be no more striking example of cleverness [in the history of tables] than Wronski's 'canons of logarithms'. This does not seem too strong a claim to make for a scheme that made it possible to put a seven-place table of common logarithms, in readable type, on a single page less that 17 cm by 22 cm in size. ...

The booklet Canons de logarithmes [6]:-

... includes instructions, examples, and theory for the use of six one-page tables of common logarithms. For good measure, it contains a summary of the "general solution of the fifth degree equation". In the Prospectus, Wronski argued that conventional tables are expensive, are bulky, have too many pages to turn, and frighten people. He had therefore devised his extremely compact "canons" (the term goes back to Napier) with none of those disadvantages.

This was not Wronski's only work in calculating and aids for calculating [6]:-

Wronski was apparently a tireless reckoner. One form this interest took was designing computational aids not only for scientists but also for non-scientists - school children, soldiers, business people, and others. Some of these devices should be called pre-electronic calculators, and in fact Wronski called one of his inventions the 'calculateur universel'. He left unfinished several projects of this kind ...

Among other things he did in the 1830s was design caterpillar vehicles to compete with the railways. However they were never manufactured. For many years all Wronski's work was dismissed as rubbish. This was largely due to his personality leading to [1]:-

... grandiose exaggeration of the importance of his own research, violent reaction to the slightest criticism, and repeated recourse to non-scientific media as allies against a supposed conspiracy.

However a closer examination of the work in more recent times shows that, although some is wrong and he does have an incredibly high opinion of himself and his ideas, there is also some mathematical insights of great depth and brilliance hidden within the papers.

Although not actually his last words, nevertheless, during last stages of his final illness he said:-

God Almighty, there's still so much more I wanted to say!