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“真相”的真相--方舟子的抄袭
“真相”的真相洪荞
2006年9月方舟子在《经济观察》发表了一篇题为“数学史上一个大恩怨的真相”的科普文章。后来文章改名“被冤枉的数学家”被收录在《爱因斯坦信上帝吗？——方舟子解读科学史著名谜团》一书。通过下面的比较我们可以看到这篇文章又是抄袭之作。
这次被抄袭的是 University of St Andrews 的两位数学教授。文章来自两位教授的数学史网站。在网站上两位教授说：我们非常欢迎各位使用我们准备的材料，但使用时要提到我们是原。我们也非常欢迎各位把我们准备的材料翻译成其它文字，但翻译时要提到我们是原[1]。
“真相”一文讲的是三次方程求解的争论史。上述网站对四位相关人物每人都有一份精彩有趣的介绍[2，3，4，5]。“真相”所讲的故事主要来自[2]，个别句子来自其它三篇或wiki[6]。在这次抄袭中，其前半部分方的做法基本是维持原文结构，但砍掉一些句子。到了后半部分，就是一路照抄（这使得我的对比工作变得异常简单）。
除了可以被肯定是抄袭的句子外，“真相”一文还有一些段落间的连接句或可有可无的评论句。这样的句子真假难辨，因此全部罗列如下，由读者自己判断。换句话说，“真相”一文的原创句子不会超出下面几句（文章的整体构思是从[2]照搬过来的）。
第一段：头尾是连接句，中间是网文《数学和数学家的故事》的复诉。
第二段：“这个流行版本从总体到细节都是错误的”， “而且也留下了有关这一争执的著作。后人对此事的看法在很大程度上就是受塔塔利亚一面之词的影响”
第三段：“塔塔利亚与卡当之间并未进行过数学比赛，和塔塔利亚比赛的另有其人。在当时的意大利，两个数学家进行解题比赛成了风气”
第四段：“当时经常出现的比赛题目是三次方程，因为三次方程的解法还未被发现”，“塔塔利亚欣喜若狂”
第五段：无
第六段：“卡当把武林秘笈拿到手，并没有就对塔塔利亚翻脸，但塔塔利亚却像许多泄密者一样”
第七段：“卡当与塔塔利亚不同，热衷于通过著书立说发布新发现来赢得名利”。
第八段：无
第九段：“万一输了脸可就丢大了”
第十段：“费拉里可谓占尽了天时地利人和”
第十一段：“看来那个时候并没有禁止拖欠教师工资的规定”
第十二段：无
第十三段：这段应该是原创
最后让我们以“真相”的结尾来结尾： 不过事实的真相毕竟难以掩盖，尤其是在信息发达的今天，更是如此。
[1] [www-history.mcs.st-and.ac.uk]
[2] [www-history.mcs.st-and.ac.uk]
[3] [www-history.mcs.st-and.ac.uk]
[4] [www-history.mcs.st-and.ac.uk]
[5] [www-history.mcs.st-and.ac.uk]
[6] [en.wikipedia.org]
数学史上一个大恩怨的真相
•方舟子•
数学史上著名的一个大恩怨许多人在中学学解方程时都听老师讲过。故事说，文艺复兴时期意大利数学家塔塔利亚发现了三次方程的解法，秘而不宣。一位叫卡当的骗子把解法骗到了手，公布出来，并宣称是他自己发现的。塔塔利亚一气之下向卡当挑战比赛解方程，大获全胜，因为塔塔利亚教他时留了一招。不过至今这些公式还被称作卡当公式，而塔塔利亚连名字都没有留下来，塔塔利亚只是一个外号，意大利语意思是“结巴”。网上广为流传的一篇《数学和数学家的故事》长文就是这么介绍的。
这个流行版本从总体到细节都是错误的。塔塔利亚不仅留下了名字（真名尼科洛•方塔纳），Niccolo Fontana, known as Tartaglia [2] 而且也留下了有关这一争执的著作。后人对此事的看法在很大程度上就是受塔塔利亚一面之词的影响。
塔塔利亚与卡当之间并未进行过数学比赛，和塔塔利亚比赛的另有其人。在当时的意大利，两个数学家进行解题比赛成了风气，方式是两人各拿出赌金，给对方出若干道题，30天后提交答案，解出更多道题的人获胜，胜者赢得全部赌金。Each contestant had to put up a certain amount of money and to propose a number of problems for his rival to solve. Whoever solved more problems within 30 days would get all the money. [6] 塔塔利亚很热衷于参加这种比赛，并多次获胜。Tartaglia gradually acquired a reputation as a promising mathematician by participating successfully in a large number of debates. [2]
当时经常出现的比赛题目是三次方程，因为三次方程的解法还未被发现。意大利博洛尼亚数学家费罗发现了三次方程的一种特殊形式“三次加一次”的解法，临死前传给了学生费奥。费奥的数学水平其实很差，得到费罗的秘传后便吹嘘自己能够解所有的三次方程。塔塔利亚也自称能够解三次方程，于是两人在1535年进行了比赛。塔塔利亚给费奥出了30道其他形式的三次方程，把费奥给难住了。费奥则给塔塔利亚出了30道清一色的“三次加一次”方程题，认定塔塔利亚也都解不出来。塔塔利亚在接受费奥挑战的时候，的确还不知道如何解这类方程题。据说是在最后一天的早晨，塔塔利亚在苦思冥想了一夜之后，突然来了灵感，发现了解法，用了不到两个小时就全部解答了。塔塔利亚欣喜若狂，宽宏大量地放弃了费奥交的赌金。The first person known to have solved cubic equations algebraically was del Ferro but he told nobody of his achievement. On his deathbed, however, del Ferro passed on the secret to his (rather poor) student Fior. ... and Fior had only been shown by del Ferro how to solve one type, namely 'unknowns and cubes equal to numbers'... Fior began to boast that he was able to solve cubics and a challenge between him and Tartaglia was arranged in 1535. ... Tartaglia submitted a variety of different questions, exposing Fior as an, at best, mediocre mathematician. Fior, on the other hand, offered Tartaglia thirty opportunities to solve the 'unknowns and cubes' problem since he believed that he would be unable to solve this type, as in fact had been the case when the contest was set up. However, in the early hours of 13 February 1535, inspiration came to Tartaglia and he discovered the method to solve 'squares and cubes equal to numbers'. Tartaglia was then able to solve all thirty of Fior's problems in less than two hours.Tartaglia did not take his prize for winning from Fior, however, the honour of winning was enough.[2]
当时担任米兰官方数学教师的卡当听说了此事，通过他人转告塔塔利亚，希望能够知道解法，遭到塔塔利亚的拒绝。于是卡当直接给塔塔利亚写信，暗示可以向米兰总督推荐塔塔利亚。At this point Cardan enters the story. As public lecturer of mathematics at the Piatti Foundation in Milan, ... he contacted Tartaglia, through an intermediary, ... asked to be shown the method, promising to keep it secret. Tartaglia, however, refused. An incensed Cardan now wrote to Tartaglia directly, ... hinting that he had been discussing Tartaglia's brilliance with the governor of Milan, Alfonso d'Avalos, the Marchese del Vasto, who was one of Cardan's powerful patrons. [2]
在威尼斯当穷教师的塔塔利亚一见有高升的机会，态度大变，于1539年 3月动身前往米兰，受到卡当的热情招待。在卡当苦苦哀求，并向上帝发誓绝不泄密后，塔塔利亚终于向卡当传授了用诗歌暗语写成的解法。On receipt of this letter, Tartaglia radically revised his attitude, ... So, in March 1539, Tartaglia left Venice and travelled to Milan. ... Cardan attended to his guest's every need and soon the conversation turned to the problem of cubic equations. Tartaglia, after much persuasion, agreed to tell Cardan his method, if Cardan would swear never to reveal it, ... and Tartaglia divulged his formula in the form of a poem.[2] 卡当把“武林秘笈”拿到手，并没有就对塔塔利亚翻脸，但塔塔利亚却像许多泄密者一样，马上就后悔了，无心再在米兰求发展，匆忙赶回威尼斯。在那一年卡当出版了两本数学著作，塔塔利亚都细细研读，一方面很高兴卡当没有在著作中公布三次方程解法，一方面又觉得自己受了卡当的欺骗，在给卡当的信中把这两本书嘲笑了一番，断绝了与卡当的交情。Anxious now to leave Cardan's house, he obtained from his host, a letter of introduction to the Marchese and left to seek him out. Instead though, he turned back for Venice, wondering if his decision to part with his formula had been a mistake ... Cardan published two mathematical books later that year and, as soon as he could get copies, Tartaglia checked to make sure his formula was not included. Though he felt a little happier to find that the formula was not included in the texts, when Cardan wrote to him in a friendly manner Tartaglia rebuffed his offer of continued friendship and mercilessly ridiculed his books on the merest trivialities.[2]
卡当在获得塔塔利亚的解法后，在其基础上很快就发现所有的三次方程的解法。次年，卡当18岁的秘书费拉里在三次方程解法的基础上又发现了四次方程的解法。Based on Tartaglia's formula, Cardan and Ferrari, his assistant, made remarkable progress finding proofs of all cases of the cubic and, even more impressively, solving the quartic equation. [2] Cardan ... appointed the youngster as his secretary ... Ferrari repaid his master by helping him with his manuscripts and, when he was eighteen years old, he began to teach. ... Cardan and Ferrari made remarkable progress on the foundations that Tartaglia had unwillingly given them. They ... 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 ... relied on the solution of cubic equations.[3] 卡当与塔塔利亚不同，热衷于通过著书立说发布新发现来赢得名利。但是他和费拉里发现的解法都是建立在塔塔利亚的解法基础上的，根据卡当立下的誓言，塔塔利亚不公布其解法，他们的解法就不得公布。However, there was no way to make this public without the breaking the sacred oath made by Cardan.[3] 而塔塔利亚显然是想把其解法当成赢得比赛的秘密武器，丝毫也没有想公布出来的迹象。Tartaglia made no move to publish his formula ... Tartaglia probably wished to keep his formula in reserve for any upcoming debates.[2] 这让卡当很苦恼。 Despairing of ever publishing their ground breaking work, Cardan and Ferrari travelled to Bologna ...[3]
1543年，卡当和费拉里前往博洛尼亚，见到在那里接替费罗当数学教授的费罗的女婿，后者向他们出示了费罗的手稿，证明费罗在塔塔利亚之前就已经发现了解法。这使卡当如释重负，觉得没有必要再遵守誓言，于是在1545年出版的著作《大术》中公布了三次方程和四次方程的解法。为了避免被指控剽窃，卡当在书中特别提到了费罗和塔塔利亚的贡献。 Cardan and Ferrari travelled to Bologna in 1543 and learnt from della Nave that it had been del Ferro, not Tartaglia, who had been the first to solve the cubic equation. Cardan felt that although he had sworn not to reveal Tartaglia's method surely nothing prevented him from publishing del Ferro's formula. In 1545 Cardan published Artis magnae sive de regulis algebraicis liber unus, or Ars magna as it is more commonly known, which contained solutions to both the cubic and quartic equations and all of the additional work he had completed on Tartaglia's formula. Del Ferro and Tartaglia are credited with their discoveries, as is Ferrari, and the story written down in the text.[2] Cardan and Ferrari satisfied della Nave ... 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.[3] del Ferro ... kept a notebook in which he recorded his most important discoveries. This notebook passed to del Ferro's son-in-law Hannibal Nave ... Hannibal Nave took over del Ferro's lecturing duties at the University of Bologna [4]
但是这并没有减轻塔塔利亚对他的憎恨。塔塔利亚在第二年出版了一本书，在书中揭露卡当背信弃义，淋漓尽致地对卡当进行人身攻击。卡当此时由于《大术》一书已名满天下，不想和塔塔利亚计较，但费拉里决定要为主人讨回公道，在公开信中对塔塔利亚反唇相讥，向塔塔利亚提出比赛挑战。塔塔利亚对此很不情愿，因为和无名小辈比赛即使赢了也没有什么好处，万一输了脸可就丢大了。塔塔利亚在给费拉里的回信中，要求由卡当来应战。但是卡当仍不予理会。塔塔利亚和费拉里来来回回打了一年的笔墨官司，仍然没有解决争端。到1548年事情出现转机，塔塔利亚的家乡布雷西亚向塔塔利亚提供了一份酬不薄的教职，条件是塔塔利亚必须去和费拉里比赛解决争端。
Tartaglia was furious when he discovered that Cardan had disregarded his oath and his intense dislike of Cardan turned into a pathological hatred. The following year Tartaglia published a book, New Problems and Inventions which clearly stated his side of the story and his belief that Cardan had acted in extreme bad faith. For good measure, he added a few malicious personal insults directed against Cardan. Ars Magna had clearly established Cardan as the world's leading mathematician and he was not much damaged by Tartaglia's venomous attacks. Ferrari, however, wrote to Tartaglia, berating him mercilessly and challenged him to a public debate. Tartaglia was extremely reluctant to dispute with Ferrari, still a relatively unknown mathematician, against whom even a victory would do little material good ... So Tartaglia replied to Ferrari, trying to bring Cardan into the debate. Cardan, however, had no intention of debating with Tartaglia. 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. Suddenly in 1548, Tartaglia received an impressive offer of a lectureship in his home town, Brescia. To clearly establish his credentials for the post, Tartaglia was asked to journey to Milan and take part in the contest with Ferrari. [2]
1548年8月10日，比赛在米兰总督的主持下在米兰的教堂举行，吸引了大量的看客。费拉里带了众多支持者助阵，而塔塔利亚只带了一位同胞兄弟，费拉里可谓占尽了天时地利人和，而且在开场白中就已经表现出他对三次和四次方程的理解要比塔塔利亚透彻。身经百战的塔塔利亚一见大势不妙，在当天晚上悄悄地离开了米兰。 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 ... 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. .... 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. [3]
结果塔塔利亚不仅名誉扫地，而且经济也陷入困境。布雷西亚虽然让他教了一年书，却不支付他的薪水。看来那个时候并没有禁止拖欠教师工资的规定，塔塔利亚打了几场官司也没能把欠薪讨回来，灰溜溜又回到威尼斯继续当他的穷教师。1557年，57岁的塔塔利亚带着对卡当的满腔仇恨，在贫困中死去。Tartaglia suffered as a result of the contest. After giving his lectures for a year in Brescia, he was informed that his stipend was not going to be honoured. Even after numerous lawsuits, Tartaglia could not get any payment and returned, seriously out of pocket, to his previous job in Venice, nursing a huge resentment of Cardan. Tartaglia ... Died: 13 Dec 1557 in Venice, Republic of Venice (now Italy) [2]
费拉里在比赛后名声大震，甚至连皇帝都来请他给太子当老师。但费拉里选择了给米兰总督当估税员发财。1565年，年仅43岁的费拉里已成了富翁，提前退休回博洛尼亚，不幸当年就去世了，据说是被他的妹妹毒死的，为了继承他的财产。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 ... 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.[2] 只有卡当得以长寿，活到了75岁，不过他本来可以活得更长——迷信占星术的卡当预测自己将死于1575年9月21日，为了实现自己的预言，他在那一天自杀。 Cardan is reported to have correctly predicted the exact date of his own death but it has been claimed that he achieved this by committing suicide. [5]
科学研究毕竟是人从事的事业，人性的弱点也会在其中表现出来。做为一项最为看重首创权的工作，因争名夺利结下的种种个人恩怨也就难以避免，有时也难以让人看清其中的是非曲折。虽然根据现代科研的规范和历史资料来看，卡当在这个事件中的所作所为并无过错，他并没有试图去剽窃他人成果，为了公布学术成果与众人分享所作的努力还很值得赞赏，反倒是塔塔利亚死守学术成果的偏执和对卡当的憎恨都有点变态。奇怪的是，在后人的传说中，卡当却成了欺世盗名的骗子，人们对弱者的同情有时会超过了对真相的探求。不过事实的真相毕竟难以掩盖，尤其是在信息发达的今天，更是如此。
2006.9.17.
（《经济观察》2006.9.23）
2006年9月方舟子在《经济观察》发表了一篇题为“数学史上一个大恩怨的真相”的科普文章。后来文章改名“被冤枉的数学家”被收录在《爱因斯坦信上帝吗？——方舟子解读科学史著名谜团》一书。通过下面的比较我们可以看到这篇文章又是抄袭之作。
这次被抄袭的是 University of St Andrews 的两位数学教授。文章来自两位教授的数学史网站。在网站上两位教授说：我们非常欢迎各位使用我们准备的材料，但使用时要提到我们是原。我们也非常欢迎各位把我们准备的材料翻译成其它文字，但翻译时要提到我们是原[1]。
“真相”一文讲的是三次方程求解的争论史。上述网站对四位相关人物每人都有一份精彩有趣的介绍[2，3，4，5]。“真相”所讲的故事主要来自[2]，个别句子来自其它三篇或wiki[6]。在这次抄袭中，其前半部分方的做法基本是维持原文结构，但砍掉一些句子。到了后半部分，就是一路照抄（这使得我的对比工作变得异常简单）。
除了可以被肯定是抄袭的句子外，“真相”一文还有一些段落间的连接句或可有可无的评论句。这样的句子真假难辨，因此全部罗列如下，由读者自己判断。换句话说，“真相”一文的原创句子不会超出下面几句（文章的整体构思是从[2]照搬过来的）。
第一段：头尾是连接句，中间是网文《数学和数学家的故事》的复诉。
第二段：“这个流行版本从总体到细节都是错误的”， “而且也留下了有关这一争执的著作。后人对此事的看法在很大程度上就是受塔塔利亚一面之词的影响”
第三段：“塔塔利亚与卡当之间并未进行过数学比赛，和塔塔利亚比赛的另有其人。在当时的意大利，两个数学家进行解题比赛成了风气”
第四段：“当时经常出现的比赛题目是三次方程，因为三次方程的解法还未被发现”，“塔塔利亚欣喜若狂”
第五段：无
第六段：“卡当把武林秘笈拿到手，并没有就对塔塔利亚翻脸，但塔塔利亚却像许多泄密者一样”
第七段：“卡当与塔塔利亚不同，热衷于通过著书立说发布新发现来赢得名利”。
第八段：无
第九段：“万一输了脸可就丢大了”
第十段：“费拉里可谓占尽了天时地利人和”
第十一段：“看来那个时候并没有禁止拖欠教师工资的规定”
第十二段：无
第十三段：这段应该是原创
最后让我们以“真相”的结尾来结尾： 不过事实的真相毕竟难以掩盖，尤其是在信息发达的今天，更是如此。
[1] [www-history.mcs.st-and.ac.uk]
[2] [www-history.mcs.st-and.ac.uk]
[3] [www-history.mcs.st-and.ac.uk]
[4] [www-history.mcs.st-and.ac.uk]
[5] [www-history.mcs.st-and.ac.uk]
[6] [en.wikipedia.org]
数学史上一个大恩怨的真相
•方舟子•
数学史上著名的一个大恩怨许多人在中学学解方程时都听老师讲过。故事说，文艺复兴时期意大利数学家塔塔利亚发现了三次方程的解法，秘而不宣。一位叫卡当的骗子把解法骗到了手，公布出来，并宣称是他自己发现的。塔塔利亚一气之下向卡当挑战比赛解方程，大获全胜，因为塔塔利亚教他时留了一招。不过至今这些公式还被称作卡当公式，而塔塔利亚连名字都没有留下来，塔塔利亚只是一个外号，意大利语意思是“结巴”。网上广为流传的一篇《数学和数学家的故事》长文就是这么介绍的。
这个流行版本从总体到细节都是错误的。塔塔利亚不仅留下了名字（真名尼科洛•方塔纳），Niccolo Fontana, known as Tartaglia [2] 而且也留下了有关这一争执的著作。后人对此事的看法在很大程度上就是受塔塔利亚一面之词的影响。
塔塔利亚与卡当之间并未进行过数学比赛，和塔塔利亚比赛的另有其人。在当时的意大利，两个数学家进行解题比赛成了风气，方式是两人各拿出赌金，给对方出若干道题，30天后提交答案，解出更多道题的人获胜，胜者赢得全部赌金。Each contestant had to put up a certain amount of money and to propose a number of problems for his rival to solve. Whoever solved more problems within 30 days would get all the money. [6] 塔塔利亚很热衷于参加这种比赛，并多次获胜。Tartaglia gradually acquired a reputation as a promising mathematician by participating successfully in a large number of debates. [2]
当时经常出现的比赛题目是三次方程，因为三次方程的解法还未被发现。意大利博洛尼亚数学家费罗发现了三次方程的一种特殊形式“三次加一次”的解法，临死前传给了学生费奥。费奥的数学水平其实很差，得到费罗的秘传后便吹嘘自己能够解所有的三次方程。塔塔利亚也自称能够解三次方程，于是两人在1535年进行了比赛。塔塔利亚给费奥出了30道其他形式的三次方程，把费奥给难住了。费奥则给塔塔利亚出了30道清一色的“三次加一次”方程题，认定塔塔利亚也都解不出来。塔塔利亚在接受费奥挑战的时候，的确还不知道如何解这类方程题。据说是在最后一天的早晨，塔塔利亚在苦思冥想了一夜之后，突然来了灵感，发现了解法，用了不到两个小时就全部解答了。塔塔利亚欣喜若狂，宽宏大量地放弃了费奥交的赌金。The first person known to have solved cubic equations algebraically was del Ferro but he told nobody of his achievement. On his deathbed, however, del Ferro passed on the secret to his (rather poor) student Fior. ... and Fior had only been shown by del Ferro how to solve one type, namely 'unknowns and cubes equal to numbers'... Fior began to boast that he was able to solve cubics and a challenge between him and Tartaglia was arranged in 1535. ... Tartaglia submitted a variety of different questions, exposing Fior as an, at best, mediocre mathematician. Fior, on the other hand, offered Tartaglia thirty opportunities to solve the 'unknowns and cubes' problem since he believed that he would be unable to solve this type, as in fact had been the case when the contest was set up. However, in the early hours of 13 February 1535, inspiration came to Tartaglia and he discovered the method to solve 'squares and cubes equal to numbers'. Tartaglia was then able to solve all thirty of Fior's problems in less than two hours.Tartaglia did not take his prize for winning from Fior, however, the honour of winning was enough.[2]
当时担任米兰官方数学教师的卡当听说了此事，通过他人转告塔塔利亚，希望能够知道解法，遭到塔塔利亚的拒绝。于是卡当直接给塔塔利亚写信，暗示可以向米兰总督推荐塔塔利亚。At this point Cardan enters the story. As public lecturer of mathematics at the Piatti Foundation in Milan, ... he contacted Tartaglia, through an intermediary, ... asked to be shown the method, promising to keep it secret. Tartaglia, however, refused. An incensed Cardan now wrote to Tartaglia directly, ... hinting that he had been discussing Tartaglia's brilliance with the governor of Milan, Alfonso d'Avalos, the Marchese del Vasto, who was one of Cardan's powerful patrons. [2]
在威尼斯当穷教师的塔塔利亚一见有高升的机会，态度大变，于1539年 3月动身前往米兰，受到卡当的热情招待。在卡当苦苦哀求，并向上帝发誓绝不泄密后，塔塔利亚终于向卡当传授了用诗歌暗语写成的解法。On receipt of this letter, Tartaglia radically revised his attitude, ... So, in March 1539, Tartaglia left Venice and travelled to Milan. ... Cardan attended to his guest's every need and soon the conversation turned to the problem of cubic equations. Tartaglia, after much persuasion, agreed to tell Cardan his method, if Cardan would swear never to reveal it, ... and Tartaglia divulged his formula in the form of a poem.[2] 卡当把“武林秘笈”拿到手，并没有就对塔塔利亚翻脸，但塔塔利亚却像许多泄密者一样，马上就后悔了，无心再在米兰求发展，匆忙赶回威尼斯。在那一年卡当出版了两本数学著作，塔塔利亚都细细研读，一方面很高兴卡当没有在著作中公布三次方程解法，一方面又觉得自己受了卡当的欺骗，在给卡当的信中把这两本书嘲笑了一番，断绝了与卡当的交情。Anxious now to leave Cardan's house, he obtained from his host, a letter of introduction to the Marchese and left to seek him out. Instead though, he turned back for Venice, wondering if his decision to part with his formula had been a mistake ... Cardan published two mathematical books later that year and, as soon as he could get copies, Tartaglia checked to make sure his formula was not included. Though he felt a little happier to find that the formula was not included in the texts, when Cardan wrote to him in a friendly manner Tartaglia rebuffed his offer of continued friendship and mercilessly ridiculed his books on the merest trivialities.[2]
卡当在获得塔塔利亚的解法后，在其基础上很快就发现所有的三次方程的解法。次年，卡当18岁的秘书费拉里在三次方程解法的基础上又发现了四次方程的解法。Based on Tartaglia's formula, Cardan and Ferrari, his assistant, made remarkable progress finding proofs of all cases of the cubic and, even more impressively, solving the quartic equation. [2] Cardan ... appointed the youngster as his secretary ... Ferrari repaid his master by helping him with his manuscripts and, when he was eighteen years old, he began to teach. ... Cardan and Ferrari made remarkable progress on the foundations that Tartaglia had unwillingly given them. They ... 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 ... relied on the solution of cubic equations.[3] 卡当与塔塔利亚不同，热衷于通过著书立说发布新发现来赢得名利。但是他和费拉里发现的解法都是建立在塔塔利亚的解法基础上的，根据卡当立下的誓言，塔塔利亚不公布其解法，他们的解法就不得公布。However, there was no way to make this public without the breaking the sacred oath made by Cardan.[3] 而塔塔利亚显然是想把其解法当成赢得比赛的秘密武器，丝毫也没有想公布出来的迹象。Tartaglia made no move to publish his formula ... Tartaglia probably wished to keep his formula in reserve for any upcoming debates.[2] 这让卡当很苦恼。 Despairing of ever publishing their ground breaking work, Cardan and Ferrari travelled to Bologna ...[3]
1543年，卡当和费拉里前往博洛尼亚，见到在那里接替费罗当数学教授的费罗的女婿，后者向他们出示了费罗的手稿，证明费罗在塔塔利亚之前就已经发现了解法。这使卡当如释重负，觉得没有必要再遵守誓言，于是在1545年出版的著作《大术》中公布了三次方程和四次方程的解法。为了避免被指控剽窃，卡当在书中特别提到了费罗和塔塔利亚的贡献。 Cardan and Ferrari travelled to Bologna in 1543 and learnt from della Nave that it had been del Ferro, not Tartaglia, who had been the first to solve the cubic equation. Cardan felt that although he had sworn not to reveal Tartaglia's method surely nothing prevented him from publishing del Ferro's formula. In 1545 Cardan published Artis magnae sive de regulis algebraicis liber unus, or Ars magna as it is more commonly known, which contained solutions to both the cubic and quartic equations and all of the additional work he had completed on Tartaglia's formula. Del Ferro and Tartaglia are credited with their discoveries, as is Ferrari, and the story written down in the text.[2] Cardan and Ferrari satisfied della Nave ... 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.[3] del Ferro ... kept a notebook in which he recorded his most important discoveries. This notebook passed to del Ferro's son-in-law Hannibal Nave ... Hannibal Nave took over del Ferro's lecturing duties at the University of Bologna [4]
但是这并没有减轻塔塔利亚对他的憎恨。塔塔利亚在第二年出版了一本书，在书中揭露卡当背信弃义，淋漓尽致地对卡当进行人身攻击。卡当此时由于《大术》一书已名满天下，不想和塔塔利亚计较，但费拉里决定要为主人讨回公道，在公开信中对塔塔利亚反唇相讥，向塔塔利亚提出比赛挑战。塔塔利亚对此很不情愿，因为和无名小辈比赛即使赢了也没有什么好处，万一输了脸可就丢大了。塔塔利亚在给费拉里的回信中，要求由卡当来应战。但是卡当仍不予理会。塔塔利亚和费拉里来来回回打了一年的笔墨官司，仍然没有解决争端。到1548年事情出现转机，塔塔利亚的家乡布雷西亚向塔塔利亚提供了一份酬不薄的教职，条件是塔塔利亚必须去和费拉里比赛解决争端。
Tartaglia was furious when he discovered that Cardan had disregarded his oath and his intense dislike of Cardan turned into a pathological hatred. The following year Tartaglia published a book, New Problems and Inventions which clearly stated his side of the story and his belief that Cardan had acted in extreme bad faith. For good measure, he added a few malicious personal insults directed against Cardan. Ars Magna had clearly established Cardan as the world's leading mathematician and he was not much damaged by Tartaglia's venomous attacks. Ferrari, however, wrote to Tartaglia, berating him mercilessly and challenged him to a public debate. Tartaglia was extremely reluctant to dispute with Ferrari, still a relatively unknown mathematician, against whom even a victory would do little material good ... So Tartaglia replied to Ferrari, trying to bring Cardan into the debate. Cardan, however, had no intention of debating with Tartaglia. 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. Suddenly in 1548, Tartaglia received an impressive offer of a lectureship in his home town, Brescia. To clearly establish his credentials for the post, Tartaglia was asked to journey to Milan and take part in the contest with Ferrari. [2]
1548年8月10日，比赛在米兰总督的主持下在米兰的教堂举行，吸引了大量的看客。费拉里带了众多支持者助阵，而塔塔利亚只带了一位同胞兄弟，费拉里可谓占尽了天时地利人和，而且在开场白中就已经表现出他对三次和四次方程的理解要比塔塔利亚透彻。身经百战的塔塔利亚一见大势不妙，在当天晚上悄悄地离开了米兰。 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 ... 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. .... 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. [3]
结果塔塔利亚不仅名誉扫地，而且经济也陷入困境。布雷西亚虽然让他教了一年书，却不支付他的薪水。看来那个时候并没有禁止拖欠教师工资的规定，塔塔利亚打了几场官司也没能把欠薪讨回来，灰溜溜又回到威尼斯继续当他的穷教师。1557年，57岁的塔塔利亚带着对卡当的满腔仇恨，在贫困中死去。Tartaglia suffered as a result of the contest. After giving his lectures for a year in Brescia, he was informed that his stipend was not going to be honoured. Even after numerous lawsuits, Tartaglia could not get any payment and returned, seriously out of pocket, to his previous job in Venice, nursing a huge resentment of Cardan. Tartaglia ... Died: 13 Dec 1557 in Venice, Republic of Venice (now Italy) [2]
费拉里在比赛后名声大震，甚至连皇帝都来请他给太子当老师。但费拉里选择了给米兰总督当估税员发财。1565年，年仅43岁的费拉里已成了富翁，提前退休回博洛尼亚，不幸当年就去世了，据说是被他的妹妹毒死的，为了继承他的财产。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 ... 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.[2] 只有卡当得以长寿，活到了75岁，不过他本来可以活得更长——迷信占星术的卡当预测自己将死于1575年9月21日，为了实现自己的预言，他在那一天自杀。 Cardan is reported to have correctly predicted the exact date of his own death but it has been claimed that he achieved this by committing suicide. [5]
科学研究毕竟是人从事的事业，人性的弱点也会在其中表现出来。做为一项最为看重首创权的工作，因争名夺利结下的种种个人恩怨也就难以避免，有时也难以让人看清其中的是非曲折。虽然根据现代科研的规范和历史资料来看，卡当在这个事件中的所作所为并无过错，他并没有试图去剽窃他人成果，为了公布学术成果与众人分享所作的努力还很值得赞赏，反倒是塔塔利亚死守学术成果的偏执和对卡当的憎恨都有点变态。奇怪的是，在后人的传说中，卡当却成了欺世盗名的骗子，人们对弱者的同情有时会超过了对真相的探求。不过事实的真相毕竟难以掩盖，尤其是在信息发达的今天，更是如此。
2006.9.17.
（《经济观察》2006.9.23）
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