洛多维科·费拉里Lodovico Ferrari

洛多维科·费拉里的祖父Bartholomew Ferrari被迫离开家乡米兰，定居于博洛尼亚。对生活在意大利北部的人来说，这是一个特别艰难的时期，因为不仅有权势的家族控制着城镇并试图以武力扩张其影响，而且法国人、神圣罗马帝国皇帝和教皇都试图用军队夺取领土。Bartholomew Ferrari有两个儿子，Vincent Ferrari和Alexander Ferrari，后者是本传记传主费拉里的父亲。费拉里最初在父亲家中长大，父亲被杀后便去与叔父文森特同住。Vincent Ferrari有一个名叫卢克的儿子，是个难相处的年轻人，他决定离家出走寻找工作。卢克去了米兰，在那里发现吉罗拉莫·卡尔达诺正在找一名仆人。工作不太合卢克的心意，在为吉罗拉莫·卡尔达诺工作了一段时间后，他觉得还是回家更好，便没有告诉吉罗拉莫·卡尔达诺就离开了他的家。吉罗拉莫·卡尔达诺联系了Vincent Ferrari，要求他把儿子送回来继续在他家当仆人。然而，文森特看到了机会，既能让自己的儿子留在家里，又能卸下抚养表弟费拉里的责任，于是他没有把卢克送回米兰的吉罗拉莫·卡尔达诺那里，而是送去了费拉里。

费拉里于11月30日来到吉罗拉莫·卡尔达诺家，这个十四岁的男孩准备接替表兄卢克的位置，成为一名仆人。吉罗拉莫·卡尔达诺发现这孩子能读会写后，便免除了他的杂役，任命这个少年为他的秘书。吉罗拉莫·卡尔达诺很快就清楚，他的秘书是一个天赋异禀的年轻人，于是决定教他数学。费拉里通过帮助主人处理手稿来报答他，并在十八岁时开始教书。1541年，吉罗拉莫·卡尔达诺慷慨地辞去米兰皮亚蒂基金会的职位为他让路，费拉里在一场辩论中轻松击败了他唯一的职位竞争者Zuanne da Coi，并在二十岁时成为几何学公开讲师。

吉罗拉莫·卡尔达诺和费拉里在尼科洛·塔尔塔利亚不情愿地留给他们的基础上取得了显著进展。他们研究Zuanne da Coi提出的问题，最终能够推广在这些特殊情形中发现的解法。费拉里在1540年用一个相当漂亮的论证发现了四次方程的解法，但它依赖于三次方程的解法，所以在三次方程的解法发表之前无法发表。然而，若不违背吉罗拉莫·卡尔达诺所立的神圣誓言，就无法将此公之于众。由于对发表他们开创性工作感到绝望，吉罗拉莫·卡尔达诺和费拉里前往博洛尼亚拜访他们的数学同行Annibale della Nave，后者在Scipione del 希皮奥内·德尔·费罗去世后被任命到那里。吉罗拉莫·卡尔达诺和费拉里使della Nave确信他们能解决那个无处不在的科萨与立方问题，而della Nave则向他们展示了已故del 希皮奥内·德尔·费罗的论文作为回报，证明尼科洛·塔尔塔利亚并非第一个发现三次方程解法的人。

吉罗拉莫·卡尔达诺在Ars MagnaⓉ（The great art）（1545）中发表了三次数方程的解法以及费拉里关于四次方程的解法，确信自己可以违背誓言，因为尼科洛·塔尔塔利亚并非第一个解出三次方程的人。尼科洛·塔尔塔利亚怒不可遏，费拉里写信给尼科洛·塔尔塔利亚，无情地斥责他并向他发起公开辩论的挑战。尼科洛·塔尔塔利亚极不愿意与费拉里争论，后者仍是一个相对不知名的年轻人，即使战胜他也得不到多少实际好处。

尼科洛·塔尔塔利亚回信给费拉里，试图把吉罗拉莫·卡尔达诺拉入辩论。费拉里和尼科洛·塔尔塔利亚互相通信约一年，毫无结果，交换着最具攻击性的个人侮辱，但在解决争端方面几乎毫无进展。事情似乎就要不了了之，这时在1548年，尼科洛·塔尔塔利亚突然收到了一份令人瞩目的邀请，请他到家乡布雷西亚担任讲席。为了证明自己是这份工作的合适人选，尼科洛·塔尔塔利亚被要求前往米兰，与费拉里了结这场较量。

1548年8月10日，全意大利都想观看的这场较量在米兰Frati Zoccolanti花园的教堂中举行，因为两位对手之间的通信已采取了公开信的形式。大批人群聚集而来，米兰的名流倾巢而出，米兰总督Don Ferrante di Gonzaga担任最高仲裁者。费拉里尽管在此类事务上缺乏经验，却对成功充满信心，并带来了一大群朋友和支持者。尼科洛·塔尔塔利亚除了他的兄弟外孤身一人，但他是一位经验极其丰富的辩论者，也对自己的胜算颇有信心。

到第一天结束时，事情显然没有朝着尼科洛·塔尔塔利亚有利的方向发展。他不愿意给费拉里时间回应他的批评，而当费拉里回应时，是费拉里打出了更致命的打击。费拉里显然比他的对手更透彻地理解三次和四次方程，后者决定当晚就离开米兰，从而使这场较量悬而未决，于是胜利归于费拉里。凭借这场挑战，费拉里的名声一飞冲天，聘约如潮水般涌来，其中包括皇帝本人的请求，他想为儿子找一位家庭教师。

不过，费拉里更中意一个经济回报更丰厚的职位，于是接受了米兰总督Ferrando Gonzaga的税务评估官任命。在转入教会服务后，他年纪轻轻便作为巨富退休。他搬回家乡博洛尼亚，与守寡的姐姐Maddalena同住，并于1565年被聘为博洛尼亚大学数学教授，但遗憾的是，费拉里于当年晚些时候去世。据称他死于白砒霜中毒，下毒者是他自己的姐姐。当然，根据吉罗拉莫·卡尔达诺的说法，Maddalena在弟弟的葬礼上拒绝哀悼，并在继承了费拉里的财产后，两周后就再婚了。她将所有财产转交给新丈夫后，他立刻抛弃了她，她最终在贫困中死去。

Lodovico Ferrari's grandfather, Bartholomew Ferrari, was forced to leave his home town of Milan and settled in Bologna. This was a particularly difficult time for those living in the north of Italy for not only did powerful families control towns and try to extend their influence by force, but also the French, the Holy Roman Emperor, and the Pope, all tried to take territory with their armies. Bartholomew Ferrari had two sons, Vincent Ferrari and Alexander Ferrari, the latter being the father of Lodovico who is the subject of this biography. Initially brought up in his father's house, Lodovico went to live with his uncle Vincent after his father was killed. Vincent Ferrari had a son named Luke, a difficult young man, who decided to run away from home and seek employment. Luke went to Milan and there discovered that Cardan was looking for a servant. Work did not suit Luke much and after working for Cardan for a while he decided that things were better back home and, without telling Cardan, just left his house. Cardan contacted Vincent Ferrari requesting that he send his son back to continue his employment as a servant in his house. Vincent, however, saw his chance to keep his own son at home and offload the responsibility of supporting his cousin Lodovico, so instead of sending Luke back to Cardan in Milan, he sent Lodovico.

Lodovico arrived at Cardan's house on 30 November, a fourteen year old boy ready to take over his cousin Luke's position and become a servant. Cardan, upon the discovery that the lad could read and write, exempted him from menial tasks and appointed the youngster as his secretary. It was soon clear to Cardan that his secretary was an exceptionally gifted young man and he decided to teach him mathematics. Ferrari repaid his master by helping him with his manuscripts and, when he was eighteen years old, he began to teach. When Cardan generously resigned his post at the Piatti Foundation in Milan to make way for him in 1541, Ferrari easily defeated Zuanne da Coi, his only rival for the post, in a debate and, at the age of twenty, became a public lecturer in geometry.

Cardan and Ferrari made remarkable progress on the foundations that Tartaglia had unwillingly given them. They worked on problems set by Zuanne da Coi and eventually were able to extend solutions discovered in these special cases. Ferrari discovered the solution of the quartic equation in 1540 with a quite beautiful argument but it relied on the solution of cubic equations so could not be published before the solution of the cubic had been published. However, there was no way to make this public without the breaking the sacred oath made by Cardan. Despairing of ever publishing their ground breaking work, Cardan and Ferrari travelled to Bologna to call upon their mathematical colleague, Annibale della Nave, who had been appointed there on the death of Scipione del Ferro. Cardan and Ferrari satisfied della Nave that they could solve the ubiquitous cosa and cube problem, and della Nave showed them in return the papers of the late del Ferro, proving that Tartaglia was not the first to discover the solution of the cubic.

Cardan published both the solution to the cubic and Ferrari's solution to the quartic in Ars Magna Ⓣ (1545) convinced that he could break his oath since Tartaglia was not the first to solve the cubic. Tartaglia was furious and Ferrari wrote to Tartaglia, berating him mercilessly and challenging him to a public debate. Tartaglia was extremely reluctant to dispute with Ferrari, still a relatively unknown youngster, against whom even a victory would do little material good.

Tartaglia wrote back to Ferrari, trying to bring Cardan into the debate. Ferrari and Tartaglia wrote fruitlessly to each other for about a year, trading the most offensive personal insults but achieving little in the way of resolving the dispute. Things seemed to fizzle out when suddenly, in 1548, Tartaglia received an impressive offer of a lecturing position in his home town, Brescia. To establish he was the man for the job, Tartaglia was asked to journey to Milan and conclude the contest with Ferrari.

On 10 August 1548, the contest which all Italy wanted to see, for the correspondence between the two antagonists had taken the form of open letters, took place in the Church in the Garden of the Frati Zoccolanti in Milan. A huge crowd had gathered, and the Milanese celebrities came out in force, with Don Ferrante di Gonzaga, governor of Milan, the supreme arbiter. Ferrari was confident of success, despite his inexperience in such matters, and brought a large crowd of friends and supporters. Alone but for his brother, Tartaglia was a vastly experienced disputant and also fancied his chances.

By the end of the first day, it was clear that things were not going Tartaglia's way. He was unwilling to give Ferrari time to respond to his criticisms and when he did, it was Ferrari who got in the more telling blows. Ferrari clearly understood the cubic and quartic equations more thoroughly than his opponent who decided that he would leave Milan that very night and thus leave the contest unresolved, so victory went to Ferrari. On the strength of this challenge, Ferrari's fame soared and he was inundated with offers of employment, including a request from the emperor himself, who wanted a tutor for his son.

Ferrari fancied a more financially rewarding position though, and took up an appointment as tax assessor to the governor of Milan, Ferrando Gonzaga. After transferring to the service of the church, he retired as a young and very rich man. He moved back to his home town of Bologna where he lived with his widowed sister Maddalena, and was called to a professorship of mathematics at the University of Bologna in 1565 but, sadly, Ferrari died later that year. It is claimed that he died of white arsenic poisoning, administered by his own sister. Certainly, according to Cardan, Maddalena refused to grieve at her brother's funeral and, having inherited Ferrari's fortune, she remarried two weeks later. Having transferred all her possessions to her new husband, he promptly left her and she died in poverty.