路德维希·赛德尔Philipp Ludwig von Seidel

路德维希·赛德尔的母亲是Julie 埃拉斯穆斯·赖因霍尔德。他的父亲Justus Christian Felix Seidel为德国邮政局工作，他的工作使他频繁搬家。这意味着赛德尔在成长过程中就读了几所不同的学校。这些学校中的第一所是在Nördlingen，下一所是在Nuremberg，然后最终他在Hof完成了学校教育。

赛德尔于1839年秋天完成了他的学业，他没有立即进入大学，而是在开始大学生涯之前接受了数学方面的私人辅导。他由L C Schnürlein辅导，后者是Hof的文理中学的数学教师。这对赛德尔来说是宝贵的辅导，特别是因为Schnürlein是一位优秀的数学家，曾在卡尔·弗里德里希·高斯门下学习。

赛德尔于1840年进入柏林大学，在约翰·彼得·古斯塔夫·勒热纳·狄利克雷和约翰·弗朗茨·恩克门下学习。当时德国学生的习惯是在不同的大学度过时间，按照通常的习惯，赛德尔于1842年搬到Königsberg，在那里他在弗里德里希·威廉·贝塞尔、卡尔·古斯塔夫·雅各布·雅可比和恩斯特·弗朗茨·诺伊曼门下学习。1843年秋天，卡尔·古斯塔夫·雅各布·雅可比因健康原因离开Königsberg，与卡尔·威廉·博尔夏特、约翰·彼得·古斯塔夫·勒热纳·狄利克雷、路德维希·施莱夫利和雅各布·施泰纳一起前往意大利。弗里德里希·威廉·贝塞尔似乎确实预期卡尔·古斯塔夫·雅各布·雅可比会离开Königsberg很长一段时间，因为他建议赛德尔去慕尼黑攻读博士学位。他于1846年在慕尼黑获得博士学位，论文为Über die beste Form der Spiegel in Teleskopen Ⓣ（关于望远镜中镜子的最佳形式。）。六个月后，他提交了他的教授资格论文（Habilitation）学位论文Untersuchungen über die Konvergenz und Divergenz der Kettenbrüche，并有资格成为慕尼黑的讲师。值得注意的是，这两篇论文仅相隔六个月提交，却涉及两个完全不同的主题——第一篇是关于天文学，而第二篇是关于数学分析。

像这两篇论文一样，赛德尔在他的整个职业生涯中致力于屈光学和数学分析。他在透镜方面的工作，并在数学上识别了描述透镜像差的五个系数，现在称为'赛德尔和'。这些赛德尔和对应于球面像差、彗差、像散、约瑟夫·佩兹瓦尔曲率和畸变。他还引入了非一致收敛的概念，并将probability应用于天文学。

赛德尔在慕尼黑进展迅速。他于1847年被任命为慕尼黑大学的编外教授，1855年成为正式教授。他获得了许多荣誉，例如被任命为皇家枢密顾问。他因其工作获得了许多奖章，并于1851年当选为巴伐利亚科学院院士。其他科学院也授予他荣誉，例如他当选为哥廷根科学院和柏林科学院的院士。

正如我们上面提到的，赛德尔天文学工作中一个有趣的方面涉及概率论的使用。然而，他并没有将这一数学学科的使用局限于天文学，因为他还将这一领域的技能应用于研究某些疾病的频率，并探讨了与气候有关的某些问题。他讲授概率论，也讲授最小二乘法。

视力问题迫使赛德尔提前退休。由于他从未结婚，生病时没有直系亲属帮助他，但他有一个未婚的妹妹露西赛德尔，一直照顾他到1889年。到那时，他肯定无法照顾自己，却没有家人能帮忙。在他生命的最后七年里，一位牧师的遗孀照顾着他。

Philipp von Seidel's mother was Julie Reinhold. His father, Justus Christian Felix Seidel, worked for the German post office and his job entailed him moving frequently. This meant that Philipp attended several different schools during his upbringing. The first of these schools was in Nördlingen, the next was in Nuremberg, then finally he completed his school education in Hof.

Although Seidel completed his school studies in the autumn of 1839 he did not enter university immediately but received private coaching in mathematics before beginning his university career. He was coached by L C Schnürlein who was a mathematics teacher at the Gymnasium in Hof. This was valuable coaching for Seidel, particularly since Schnürlein was a good mathematician who had studied under Gauss.

Seidel entered the University of Berlin in 1840 and studied under Dirichlet and Encke. The custom among German students at this time was to spend time at different universities and, following the usual custom, Seidel moved to Königsberg in 1842 where he studied under Bessel, Jacobi and Franz Neumann. In the autumn of 1843 Jacobi left Königsberg on the grounds of ill health and set off for Italy with Borchardt, Dirichlet, Schläfli and Steiner. Bessel certainly seems to have expected Jacobi to be away from Königsberg for a long while since he advised Seidel to go to Munich to study for his doctorate. He obtained his doctorate from Munich in 1846 for a thesis Über die beste Form der Spiegel in Teleskopen Ⓣ. Six months later he submitted his habilitation dissertation Untersuchungen über die Konvergenz und Divergenz der Kettenbrüche and qualified to become a lecturer at Munich. It is worth noting that these two theses, submitted only six months apart, were on two completely different topics - the first was on astronomy while the second was on mathematical analysis.

Like these two theses, Seidel worked on dioptics and mathematical analysis throughout his career. His work on lenses, and identified mathematically five coefficients describing the aberration of a lens, now called 'Seidel sums'. These Seidel sums correspond to spherical aberration, coma, astigmatism, Petzval curvature and distortion. He also introduced the concept of nonuniform convergence and applied probability to astronomy.

Seidel progressed rapidly at Munich. He was appointed as an extraordinary professor in Munich in 1847 and then an ordinary professor in 1855. He received many honours such as appointment as a Royal Privy Councillor. He received many medals for his work and, in 1851, was elected to the Bavarian Academy of Sciences. Other academies also honoured him, for example he was elected to the academies of Göttingen and of Berlin.

An interesting aspect of Seidel's astronomical work involved, as we mentioned above, the use of probability theory. However, he did not restrict his use of this mathematical discipline to astronomy, for he also applied his skills in this area to study the frequency of certain diseases and also looked at certain questions relating to the climate. He lectured on probability theory, and also on the method of least squares.

Problems with his eyesight forced Seidel into early retirement. Since he had never married he had no immediate family to help him when he became ill, but he had an unmarried sister Lucie Seidel who looked after him until 1889. By this time he certainly could not care for himself, yet had no family who could help out. In his last seven years he was looked after by the widow of a clergyman.