斯坦尼斯瓦夫·乌拉姆Stanisław Ulam

乌拉姆在当时的伦贝格一个富裕的波兰犹太家庭中长大。第一次世界大战后，该城更名为Lwów，现在称为利沃夫，位于乌克兰。他的父母是Józef 乌拉姆（1879-1941）和Hania Auerbach（1887-1938），后者被称为Anna。Jozef Ulam是一名律师，出生于Lwów。（尽管当时它实际上被称为伦贝格，但为简便起见，在本传记中我们始终称其为Lwów。）Józef的父亲，即Stan的祖父，是马克斯·亚伯拉罕 Berl 乌拉姆，他曾是一名建筑师和建筑承包商。Stan的母亲Anna出生于Stryj，这是伦贝格以南约65公里的一个城镇，现位于乌克兰。她的父亲Michael Auerbach是一位实业家，从事钢铁生意，并参与加利西亚和匈牙利的工厂。Jozef和Anna Ulam有三个孩子：斯坦尼斯瓦夫·乌拉姆，生于1909年，即本传记的主角；Stefania Teofila 乌拉姆，生于1912年；以及Adam Bruno Ulam，生于1922年4月8日。我们将在下文叙述Stan的妹妹和弟弟的一些细节，但首先我们继续乌拉姆的传记。

第一次世界大战于1914年7月开始，到那年9月，俄军进攻加利西亚并很快占领了Lwów。乌拉姆一家逃往维也纳，住在圣斯蒂芬大教堂附近的一家旅馆。Józef 乌拉姆成为奥地利军队的一名军官，与大多数波兰人不同，这家人是同盟国的支持者。Józef的军队角色使这家人频繁旅行，Stan无法上学，因此他们为他聘请了一位家庭教师。他们唯一停留较长时间的地方是Ostrava，他在那里上了学。他在学校学习了乘法表，他觉得这段经历“有点痛苦”。在Lwów时，这家人讲波兰语，但Stan在奥地利期间学会了德语。1918年第一次世界大战结束后，这家人返回Lwów，住在Ulica Kosciuszko 16号。

遗憾的是，当1918年11月乌克兰士兵进攻Lwów时，他们再次发现自己身处战区。乌拉姆的家位于城市相对安全的区域，所有亲戚都来了，所以房子里挤满了30多人。地下室在炮击期间提供了安全，但这并没有持续多久，几周后波兰军队到达后就结束了。波兰作为一个独立国家已不存在100多年，但在1919年，它重生了，Lwów成为波兰的一个重要城市。

十岁时，乌拉姆进入Lwów的文理中学，大约此时，他先是对天文学感兴趣，然后对物理学感兴趣。当他大约12岁时，一位叔叔给了乌拉姆一台望远镜，后来乌拉姆试图理解阿尔伯特·爱因斯坦的狭义相对论。然而，这需要数学知识，因此，在14岁时，他开始从书籍中学习数学，远远超出了他在学校学习的数学水平。他读的第一本数学书是莱昂哈德·欧拉的Algebra，这是他在父亲的书房里找到的。他在采访[99]中说：-

到我十五岁时，我正在读数论；有一本由瓦茨瓦夫·谢尔宾斯基写的引人入胜的书——当然是波兰语的。然后我读了集合论。那时我想，如果可能，或者实际可行，成为一名数学家，我就想成为其中一员。当然，从实际角度来看，决定在大学学习数学——只学数学——是非常困难的，因为职业的紧迫性：职位非常少。靠数学谋生是非常非常困难的。

乌拉姆说（[30]或[31]）：-

……我十六岁时，完全自学了微积分，从Kowalevski的一本书中，他是一位德国人，不要与柯瓦列夫斯卡娅混淆……然后我还读了瓦茨瓦夫·谢尔宾斯基的一本关于集合论的书，我想我理解了。我们在高中有一位好教授，Zygmunt Zawirski，他是大学的逻辑学讲师。那时我和他谈论了这些，当我进入理工学院时也是如此。

1926年，他还在中学时，就连续几天去听了胡戈·施泰因豪斯、Stanislaw Ruziewicz和斯特凡·巴拿赫等一流数学家的讲座，这是他最早听的讲座。由于对天文学、物理学和数学都感兴趣，但又明白获得大学数学职位很困难，乌拉姆申请了利沃夫理工学院学习电气工程。然而该课程名额已满，于是他转而选择在新成立的普通学系学习。1927年，他在大学的第一年，选修了卡齐米日·库拉托夫斯基刚被任命到利沃夫后开设的集合论二年级课程。乌拉姆说（[30]或[31]）：-

[卡齐米日·库拉托夫斯基]开了一门集合论基础课程，我问了一些问题，然后课后和他交谈，他对一个显然对数学感兴趣并且有一些想法的年轻学生产生了兴趣。我很幸运地解决了他提出的一个未解决的问题。

卡齐米日·库拉托夫斯基在[47]中写道：-

……在我第一次讲座之后，乌拉姆——对他来说这也是第一次讲座——立刻带着一个问题来找我，这个问题既显示了他的进步也显示了他的才智。从那一刻起，我开始对他感兴趣，并试图把他引入数学。不久他就成了我的合作者，同时也是一位独立的数学家和我的密友。

乌拉姆觉得卡齐米日·库拉托夫斯基的讲座鼓舞人心[98]：-

这门课程有大约十五名学生参加，与我高中的经历相比，这些讲座是逻辑、清晰、系统呈现和准备的典范。

乌拉姆 在理工学院才读到二年级时，就写了他的头两篇论文。这两篇论文给出了 卡齐米日·库拉托夫斯基 在其讲座中提出的问题的解答：Remark on the generalised Bernstein's theorem（1929）和 Concerning functions of sets（1929）。令人惊讶的是，乌拉姆 选择用英文写这两篇各3页的论文，且都发表在 Fundamenta Mathematicae 上。

还在读研究生时，他就被邀请在多个会议上演讲，特别是1931年在维尔诺和1932年在苏黎世的国际数学家大会上，他在那里作了Zum Maßbegriffe in ProdukträumenⓉ（论乘积空间中的测度概念）的演讲。他以说明这是与Zbigniew Łomnicki的合作工作开始这次演讲，并以承诺很快将发表这项关于测度论在概率计算中的应用结束。事实上，Łomnicki和乌拉姆的合作论文Sur la théorie de la mesure dans les espaces combinatoires et son application au calcul des probabilitésⓉ（论组合空间中的测度理论及其在概率计算中的应用）于1934年发表。让我们在此记录一个令人悲伤的事实：Zbigniew Łomnicki于1941年7月被德国人杀害。

乌拉姆于1933年在利沃夫的理工学院获得博士学位，卡齐米日·库拉托夫斯基是他的导师。他研究了一个源于昂利·勒贝格在1902年提出的问题，即在[0,1]上寻找具有某些性质的测度。斯特凡·巴拿赫在1929年解决了一个相关的测度问题，但假设了广义连续统假设。乌拉姆在1930年通过在不使用广义连续统假设的情况下证明它，加强了斯特凡·巴拿赫的结果。他在[93]中声称他在一个晚上六小时内写完了他的学位论文。

关于乌拉姆与其老师卡齐米日·库拉托夫斯基互动的更多信息，请参见乌拉姆在THIS LINK上为卡齐米日·库拉托夫斯基写的讣告。

获得博士学位后，乌拉姆访问了各个城市，会见顶尖数学家。在维也纳，他会见了卡尔·门格尔，在苏黎世，他会见了海因茨·霍普夫和马塞尔·格罗斯曼，在巴黎，他会见了埃利·嘉当，在英国剑桥，他会见了戈弗雷·哈罗德·哈代、阿布拉姆·萨莫伊洛维奇·贝西科维奇、亚瑟·爱丁顿、利奥波德·英费尔德、J J Thomson和苏布拉马尼扬·钱德拉塞卡。

1935年，乌拉姆收到冯·诺伊曼的邀请，前往普林斯顿的高级爱德华·斯图迪访问几个月。他计划在那里待三个月，于是乘坐阿基塔尼亚号从法国瑟堡启航前往纽约，于1936年1月7日抵达。关于乌拉姆与冯·诺伊曼之间友谊的更多细节，参见乌拉姆与吉安-卡洛·罗塔在THIS LINK关于冯·诺伊曼的讨论。

在高等研究院，斯图迪乌拉姆遇到了乔治·戴维·伯克霍夫，后者邀请他去哈佛大学。乌拉姆说（[30]或[31]）：-

……我回到波兰，但第二年秋天我作为所谓的学会会士——哈佛的一个新机构——的成员回到剑桥。……我立即开始教学：先是基础课程，然后是相当高级的课程。1940年我成为哈佛的讲师，但在1935-39年期间，我每年都在波兰和美国之间往返。夏天我探望家人、朋友和数学家。在波兰，数学生活非常紧张，数学家们经常在苏格兰咖啡馆和罗马咖啡馆这样的地方见面。我们在那里坐几个小时做数学。夏天我又这样做。然后在39年，实际上我在第二次世界大战开始前大约一个月离开了波兰。

你可以在 THIS LINK 上看到更多关于苏格兰咖啡馆的信息。

看看乌拉姆进入美国时填写的表格很有意思。在1936年至1939年间的五份入境表格上，乌拉姆的身高分别写为5英尺11英寸、6英尺、6英尺、5英尺8英寸和5英尺11英寸。他的眼睛颜色分别写为棕色、灰色、绿色、绿色和绿色。在这五次从波兰到美国的最后一次旅行中，他由十七岁的弟弟Adam Ulam陪同。他们的父亲确信波兰即将遭到德国攻击，说服亚当与弟弟一起离开，在美国继续学业。他们于1939年8月11日从但泽（现格但斯克）乘坐Piłsudski号（不是乌拉姆在[93]中所说的Batory号，许多人照抄了这个错误；Piłsudski号和Batory号是姊妹船。例如参见[100]）启航。他们于1939年8月21日抵达纽约，仅仅一个多星期后，当他们住在纽约哥伦布圆环的一家旅馆时，维托尔德·胡列维茨打电话告诉他们德国正在轰炸华沙。在继续乌拉姆的传记之前，让我们稍微谈谈乌拉姆在利沃夫的家人。

乌拉姆 的母亲安娜生病了，频繁前往维也纳咨询医生。她于1938年3月18日在维也纳去世。乌拉姆 的妹妹斯特凡尼娅结婚后成为斯特凡尼娅·克鲁格。她于1940年生了一个孩子，并继续住在利沃夫，该地起初被俄罗斯人占领。1941年6月，德国人进攻俄罗斯，并于6月30日占领利沃夫。米凯莱·亚米奥尔科夫斯基讲述了斯特凡尼娅的死 [7]：-

……与斯特凡尼娅 乌拉姆 和她的小孩一起，我们躲藏在一座慷慨的基督徒妇女的房子里，她无偿地接待了我们。藏身处有三个成年人：我的母亲卢西亚、她的父亲和斯特凡尼娅，还有两个孩子，我自己（11岁）和斯特凡尼娅的小孩。……我们的邻居背叛了我们。我们被盖世太保逮捕，带到利沃夫的“亚诺夫斯基集中营”……我们慷慨的基督徒恩人被枪杀，我们这群人被带到一个叫做“地堡”的小拘留中心，等待第二天黎明被枪决。但前一天晚上，指挥官来审问我们。在审讯中，很明显他愿意接受贿赂，并且作为补偿，他会把我们送到集中营而不是枪毙我们。因此，我母亲带他去了利沃夫的一个藏匿处，她在那里藏了珠宝和贵重地毯，在取回这些之后，他决定这些贵重物品不足以拯救所有人的生命。他只愿意救两个人免于被杀，并给我母亲几个小时来做出这个巨大的选择：谁将被从必然的死亡中救出，而被带到集中营。……黎明时，我母亲和我被带到集中营，而斯特凡尼娅、她的婴儿和我的祖父被杀害。

乌拉姆 的父亲也在1941年德国人占领利沃夫时被杀害。

战争意味着乌拉姆兄弟无法从波兰获得资金，因此两人都不得不靠斯坦乌拉姆所领取的微薄薪水维持生活。他在哈佛的奖学金于1939年到期，但乔治·戴维·伯克霍夫任命他为哈佛1939-40学年的讲师。Adam Ulam于1939年9月在布朗大学开始了他的大学历史学习。

乌拉姆于1939年秋天在马萨诸塞州剑桥的一次聚会上遇到了弗朗索瓦丝·阿龙。弗朗索瓦丝（1918-2011）于1918年3月8日出生在巴黎，正值第一次世界大战接近尾声。她于1938年8月前往美国，在加利福尼亚的米尔斯学院学习，然后获得了马萨诸塞州曼荷莲学院的奖学金。弗朗索瓦丝为乌拉姆兄弟做饭，帮助他们。

1940年，乌拉姆被任命为威斯康星大学的助理教授。1941年8月19日，他在麦迪逊与Françoise Aron结婚；他们选择了由法官Roy H Proctor在其办公室主持的廉价简短的婚礼仪式。Stan和Françoise育有一个孩子Claire Anne Ulam（1944-2020），1944年7月15日出生于新墨西哥州圣菲。1943年，乌拉姆成为美国公民。那一年，冯·诺伊曼要求他承担一些非常重要的战争工作。他们同意会面（[30]或[31]）：-

……在芝加哥的某个火车站，为了多了解一些情况。我去了那里，他不能告诉我他要去哪里。有两个家伙，像是保镖，看起来像大猩猩，和他在一起。他和我讨论了一些数学，一些有趣的物理，以及这项工作的重要性。那就是洛斯阿拉莫斯的最初阶段。几个月后，我带着妻子来了……第一次到达一个非常奇怪的地方。

此时，新墨西哥州洛斯阿拉莫斯国家实验室正在进行的主要工作涉及裂变炸弹。这个项目于1945年7月16日在新墨西哥沙漠中引爆原子弹而成功完成。然而，乌拉姆在Edward Teller的小组工作，该小组着眼于裂变炸弹之外，研究聚变炸弹——氢弹的可能性。

吉安-卡洛·罗塔 [74]描述了乌拉姆的性格在1946年如何改变：-

1946年的一天早晨，在洛杉矶，新被任命为南加州大学教授的乌拉姆醒来发现自己无法说话。几个小时后，在诊断出脑炎后，他接受了一次危险的手术。……然而，随着时间的推移，那些认识他的人开始明显看出他性格上的一些变化。……他的想法，他不时地冒出来，比我以前或以后见过的任何东西都更迷人。然而，他似乎刻意避免深入细节。……他逐渐依赖他未受损的想象力来获得想法，并依赖他人的[辛勤工作]来获得技术支持。……

一个严重的技能缺陷与一个非凡的创造性想象力相结合，就是Stan 乌拉姆的戏剧性。在我遇见他后不久，我就明白了，就我们的谈话而言，他的戏剧性将是一个禁忌话题。……但他知道我知道，我也知道他知道我知道。

乌拉姆在洛斯阿拉莫斯时，发展了“蒙特卡洛方法”，该方法利用随机数的统计抽样方法来寻找数学问题的解。他解释了这一想法是如何产生的[27]：-

我第一次思考和尝试实践蒙特卡洛方法，是由1946年我生病康复期间玩纸牌时想到的一个问题所启发的。问题是，用52张牌摆出的坎菲尔德纸牌游戏成功通关的概率是多少？

蒙特卡洛方法现在广泛用于数学软件的计算机实现中。乌拉姆1949年描述蒙特卡洛方法的论文[57]，与尼古拉斯·梅特罗波利斯合写，摘要如下：-

我们在此介绍处理数学物理中一类问题的方法的动机和一般描述。该方法本质上是研究微分方程，或更一般地，研究出现在自然科学各个分支中的积分微分方程的一种统计方法。

乌拉姆回到洛斯阿拉莫斯继续从事氢弹工作。这项工作在[15]中有所描述：-

乌拉姆与物理学家爱德华·泰勒合作，解决了聚变弹工作中遇到的一个主要问题，他提出压缩对爆炸至关重要，裂变弹的冲击波可以产生所需的压缩。他进一步提出，精心设计可以将机械冲击波聚焦，从而促进聚变燃料的快速燃烧。泰勒建议使用辐射内爆而非机械冲击来压缩热核燃料。这种后来被称为泰勒-乌拉姆构型的双级辐射内爆设计，导致了现代热核武器的诞生。

乌拉姆的这一非凡洞见，或许本应使他而非Teller被称为“氢弹之父”。Françoise 乌拉姆在丈夫解决该问题后作了如下描述[26]：-

中午我发现他在家，死死盯着窗外，脸上带着一种非常奇怪的表情。我永远忘不了他那茫然的眼神，仿佛视而不见地凝视着花园，他用细弱的声音说，我至今仍能听见，“我找到办法让它成功了。”

然而，乌拉姆的洞见是在经过许多小时的计算之后才出现的，这些计算最初由他和J C Everett完成，后来得到一组受雇操作电子计算器的女性计算员的协助。乌拉姆写道[68]：-

每天早晨，我都会尝试对某些系数的值提供若干猜测，这些系数涉及运动组件的纯几何性质，关系到穿过其中并进而引发更多反应的中子和其他粒子的命运。……我们每天开始工作四到六小时，用计算尺、铅笔和纸，频繁地进行定量猜测。

乌拉姆还与J C Everett一起提出了用于航天器核推进的“Orion”计划。

1963年，在一场无聊的讲座中，乌拉姆在他的方格记事本上涂鸦。他将正整数排列成方形螺旋图案，并注意到当他标记素数时，它们似乎集中在对角线上。
你可以在THIS LINK了解更多相关信息

他留在洛斯阿拉莫斯直到1965年，被任命为科罗拉多大学数学讲席。去世时，他是科罗拉多大学的生物数学教授。

当被要求总结他的工作时，他给出了这样谦逊的回答（[30]或[31]）：-

最初我研究集合论，其中一些问题至今仍被深入研究。这太技术性了，难以描述：可测基数、集合论中的测度、抽象测度。后来在拓扑学中我有了一些结果。……然后我在遍历理论中做了一点工作。Oxtoby和我解决了一个老问题，其他一些问题后来在其他领域得到解决。总的来说，我会说运气起了一定作用，至少在我的情况是这样。此外，我在集合论、群论、拓扑学、数学物理以及其他方法中都有幸拥有极其出色的合作者，这不是什么了不起的智力成就，但非常有用，诸如此类的一些事情。

乌拉姆的著作包括A collection of mathematical problems（1960年）、（与马克·卡茨合著）Mathematics and logic: Retrospect and prospects（1968年）、Sets numbers and universes （1974年）、Adventures of a Mathematician（1976年）、Science, computers, and people from the tree of mathematics（1986年）和Analogies between analogies（1990年）。关于这些书籍第一版及后续版本的信息，包括评论和序言的摘录，见THIS LINK。

吉安-卡洛·罗塔这样描述他[74]：-

乌拉姆的头脑是一个储存了数千个故事、传说、笑话、警句、评论、谜题、绕口令、脚注、结论、口号、公式、图表、引语、打油诗、摘要、妙语、墓志铭和标题的宝库。在正常交谈过程中，他只需从头脑中抽出五十来个相关条目，然后按线性顺序呈现出来。二级记忆使他不会在同一听众面前过于频繁地重复自己。

他的妻子Françoise 乌拉姆在[97]中描述了乌拉姆的工作方法：-

乌拉姆……几乎完全是一个健谈的人，一个口头表达的人。不思考的时候……他最喜欢的就是与朋友和同事交谈、讨论、争论、对话。依靠他非凡的记忆力，他把一切都记在脑子里。……

对他来说，提笔在纸上写字这个物理动作一直很痛苦。他的头脑和眼睛是障碍。头脑，因为它的运转比手指快得多……；眼睛，因为一只高度近视，另一只高度远视。……出于童年的恐惧，后来出于年轻的虚荣，他拒绝戴眼镜，直到最近才改变。因此，乌拉姆一直很难让自己为发表而写任何东西，无论是手写还是用打字机。机器和其他机械物件总是让他反感。……那么他究竟是如何写出文本的呢？主要是通过口述……

让我们以Claire Ulam童年时关于她父亲[88]的评论作为结束：-

有一天，小Claire Ulam看着一些孩子和他们的父亲玩球，一个朋友问她父亲是否也曾这样和她玩。回答是斩钉截铁的“不！不！我父亲所做的就是思考，思考，思考！除了思考什么也不做！”

Stan Ulam grew up in a well-off Polish-Jewish family in Lemberg as it was then called. After World War I it changed its name to Lwów and it is now called Lviv and is in Ukraine. His parents were Józef Ulam (1879-1941) and Hania Auerbach (1887-1938) known as Anna. Jozef Ulam was a lawyer who had been born in Lwów. (Although it was actually called Lemberg at that time let us for simplicity call it Lwów throughout this biography.) Józef's father, Stan's Józef grandfather, was Abraham Berl Ulam who had been an architect and a building contractor. Stan's mother Anna had been born in Stryj, a town about 65 km south of Lemberg which is now in Ukraine. Her father, Michael Auerbach, was an industrialist who dealt in steel and was involved with factories in both Galicia and Hungary. Jozef and Anna Ulam had three children, Stanisław Ulam, born 1909 the subject of this biography, Stefania Teofila Ulam, born 1912, and Adam Bruno Ulam, born 8 April 1922. We shall relate below some details about Stan's sister and brother but first we continue with Stan Ulam's biography.

World War I began in July 1914 and by September of that year Russian troops attacked Galicia and soon occupied Lwów. The Ulam family fled to Vienna and lived in a hotel close to St Stephen's Cathedral. Józef Ulam became an officer in the Austrian army and, in contrast to most Poles, the family were supporters of the Central Powers. Józef's army role involved the family in much travelling and Stan could not attend school so they employed a tutor for him. The only place where they stayed for some time was Ostrava where he did attend school. He was taught multiplication tables at the school, an experience he found "mildly painful." The family had been Polish speaking when in Lwów but Stan learnt German during his years in Austria. After World War I ended in 1918, the family returned to Lwów where they lived at 16 Ulica Kosciuszko.

Sadly, once again they found themselves in a war zone when Ukrainian soldiers attacked Lwów in November 1918. The Ulam's home was in a relatively safe part of the city and all their relatives arrived so the house was filled with over 30 people. The basement provided safety during shelling but it did not last long ending after a couple of weeks when the Polish army arrived. Poland had not existed as an independent country for over 100 years but, in 1919, it was reborn with Lwów a major Polish city.

At the age of ten, Ulam entered the gymnasium in Lwów and, about this time, he became interested first in astronomy and then in physics. An uncle gave Ulam a telescope when he was about 12 years old and later Ulam tried to understand Einstein's special theory of relativity. This, however, required an understanding of mathematics and so, at age 14, he began to study mathematics from books, going well beyond the school level mathematics he was learning. The first mathematics book he read was Euler's Algebra which he found in his father's library. He said in the interview [99]:-

By the time I was fifteen I was reading number theory; there was a fascinating book by Sierpinski - in Polish, of course. And then I read about set theory. At that time I thought that if it's possible at all, or practical, to become a mathematician, I would want to be one. Of course, from the practical point of view, it was very difficult to decide on studying mathematics - only mathematics - at the university because of the exigencies of a career: there were very few positions. To make a living in mathematics was very, very difficult.

Ulam said ([30] or [31]):-

... I was sixteen when I really learned calculus all by myself from a book by Kowalevski, a German not to be confused with Sonia Kovalevskaya .... Then I read also about set theory in a book by Sierpinski, and I think I understood that. We had a good professor in high school, Zygmunt Zawirski, who was a lecturer in logic at the university. I talked to him about it then and when I entered the Polytechnic Institute.

In 1926, when still at the gymnasium, he attended his first lectures by leading mathematicians going to lectures by Hugo Steinhaus, Stanislaw Ruziewicz and Stefan Banach on successive days. With interests in astronomy, physics and mathematics, but understanding the difficulty of obtaining a university mathematics position, Ulam applied to the Polytechnic Institute in Lwów to study electrical engineering. The course, however, was full so instead he opted to study in the newly founded Department of General Studies. In 1927, his first year at the university, he took a second year course on set theory given by Kazimierz Kuratowski who had just been appointed to Lwów. Ulam said ([30] or [31]):-

[Kuratowski] gave an elementary course on set theory, and I asked some questions, then I talked to him after classes, and he became interested in a young student who evidently was interested in mathematics and had some ideas. I was lucky to solve an unsolved problem that he proposed.

Kuratowski writes in [47] that:-

... immediately after my first lecture Stanislaw Ulam - for whom it was also the first lecture - approached me with a question which gave evidence both of his advancement and intelligence. From that moment I became interested in him and tried to introduce him to mathematics. In a short time he became my collaborator, as well as an independent mathematician and my close friend.

Ulam found Kuratowski's lectures inspiring [98]:-

The course was attended by some fifteen students and the lectures were, in contrast to my high school experiences, monuments of logic, clarity, systematic presentation, and preparation.

Amazingly, Ulam was only in his second year at the Polytechnic Institute when he wrote his first two papers. These gave the solutions to the problems that Kuratowski had posed in his lectures: Remark on the generalised Bernstein's theorem (1929) and Concerning functions of sets (1929). It is surprising that Ulam chose to write these two 3-page papers, which were both published in Fundamenta Mathematicae, in English.

While still a postgraduate student he was invited to lecture at a number of conferences, in particular at Wilno in 1931 and at the International Congress of Mathematicians in Zurich in 1932 where he gave the lecture Zum Maßbegriffe in Produkträumen Ⓣ. He begins this lecture by saying that it is joint work with Zbigniew Łomnicki and ends with a promise that applications of this work on measure theory to the calculus of probabilities will soon be published. Indeed the joint paper Sur la théorie de la mesure dans les espaces combinatoires et son application au calcul des probabilités Ⓣ by Łomnicki and Ulam was published in 1934. Let us record here the sad fact that Zbigniew Łomnicki was murdered by the Germans in July 1941.

Ulam obtained his Ph.D. from the Polytechnic Institute in Lwów in 1933 having written a thesis with Kuratowski as his advisor. He investigated a problem which originated with Lebesgue in 1902 to find a measure on [0,1] with certain properties. Banach in 1929 had solved a related measure problem, but assuming the Generalised Continuum Hypothesis. Ulam, in 1930, strengthened Banach's result by proving it without using the Generalised Continuum Hypothesis. He claims in [93] that he wrote his thesis in six hours during a single night.

For more information about Ulam's interaction with his teacher Kuratowski, see Ulam's obituary of Kuratowski at THIS LINK.

After the award of his doctorate, Ulam made visits to various cities to meet the leading mathematicians. In Vienna he met Karl Menger, in Zurich he met Heinz Hopf and Marcel Grossmann, in Paris he met Elie Cartan and in Cambridge, England, he met G H Hardy, Abram Besicovitch, Arthur Eddington, Leopold Infeld, J J Thomson and Subrahmanyan Chandrasekhar.

In 1935 Ulam received an invitation from von Neumann to visit the Institute for Advanced Study in Princeton for a few months. Planning to spend three months there he sailed on the Aquitania from Cherbourg, France to New York arriving on 7 January 1936. For more details of the friendship between Ulam and von Neumann, see the discussion between Ulam and Rota about von Neumann at THIS LINK.

At the Institute for Advanced Study Ulam met G D Birkhoff who invited him to Harvard University. Ulam said ([30] or [31]):-

... I went back to Poland, but the next fall I returned to Cambridge as a member of the so-called Society of Fellows, a new Harvard institution. ... I started teaching right away: first, elementary courses and then quite advanced courses. I became a lecturer at Harvard in 1940, but every year during that time 1935-39 I commuted between Poland and the United States. In the summers I visited my family and friends and mathematicians. In Poland mathematical life was very intense, the mathematicians saw each other often in cafes such as the Scottish Cafe and the Roma Cafe. We sat there for hours and did mathematics. During the summers I did this again. And then in '39, I actually left Poland about a month before World War II started.

You can see more about the Scottish Café at THIS LINK.

It is interesting to look at the forms completed on Ulam's entry to the United States. On the five entry forms, between 1936 and 1939, Ulam's height is given as 5 ft 11 in, 6 ft, 6 ft, 5 ft 8 in and 5 ft 11 in. The colour of his eyes is given as Brown, Gray, Green, Green, and Green. On the last of these five trips from Poland to the United States, he was accompanied by his brother Adam Ulam who was seventeen years old. Their father, convinced that Poland was about to be attacked by Germany, persuaded Adam to leave with his brother and continue his education in the United States. They sailed from Danzig, now Gdańsk, on 11 August 1939 on the Piłsudski (not the Batory as Ulam states in [93] and many have copied; the Piłsudski and the Batory were sister ships. See, for example, [100]). They arrived in New York on 21 August 1939 and, just over a week later, they were staying in a hotel on Columbus Circle in New York when Witold Hurewicz phoned to tell them that Germany was bombing Warsaw. Before continuing with Ulam's biography, let us say a little about Ulam's family in Lwów.

Ulam's mother, Anna, became ill and made frequent trips to Vienna to consult doctors. She died in Vienna on 18 March 1938. Ulam's sister, Stefania, married and became Stefania Kruger. She had a child in 1940 and continued living in Lwów which at first was taken by the Russians. In June 1941 the Germans attacked Russia and occupied Lwów by 30 June. Michele Jamiolkowski told how Stefania died [7]:-

... together with Stefania Ulam, and her little child, we lived in hiding in the house of a generous Christian woman who gave us hospitality without any compensation. There were three adults in the hideout: my mother Lusia, her father and Stefania, together with two children, myself (11 years old) and Stefania's little child. ... our neighbours betrayed us. We were arrested by the Gestapo and brought to the "Janowski Lager" in Lwów ... Our generous Christian benefactress was shot and our group brought to a small detention centre called the "bunker," waiting to be shot the following morning at dawn. But the evening before, the commanding officer came to interrogate us. During the inquisition it appeared quite plain that he was open to bribery and that, against compensation, he would carry us to a camp instead of shooting us. Accordingly, my mother took him to a hideaway in Lwów, where she had hidden jewellery and valuable carpets, after recovering which, he decided that the valuables were not of an adequate amount to save everybody's lives. He would only save two individuals from being killed and gave my mother a few hours to make the tremendous choice on whom would be saved from certain death and be taken, instead, to a concentration camp. ... at dawn my mother and myself were brought to the camp, while Stefania, her baby and my grandfather were killed.

Ulam's father was also killed when the Germans occupied Lwów in 1941.

The war meant that the Ulam brothers could not get funds from Poland so both had to survive on the small salary that Stan Ulam was receiving. His fellowship at Harvard ran out in 1939 but Birkhoff appointed him as a lecturer in Harvard for the year 1939-40. Adam Ulam began his university studies of history at Brown University in September 1939.

Stan Ulam met Françoise Aron at a party in Cambridge, Massachusetts, in the autumn of 1939. Françoise (1918-2011) had been born in Paris on 8 March 1918, near the end of World War I. She had gone to the United States in August 1938 to study at Mills College in California, then was awarded a scholarship to Mount Holyoke college in Massachusetts. Françoise helped the Ulam brothers by cooking meals for them.

In 1940 Ulam was appointed as an assistant professor at the University of Wisconsin. He married Françoise Aron on 19 August 1941 in Madison; they chose the cheap short wedding service conducted by Judge Roy H Proctor in his office. Stan and Françoise had one child Claire Anne Ulam (1944-2020) born 15 July 1944 in Santa Fe, New Mexico. In 1943 Ulam became an American citizen. In that year von Neumann asked him to undertake some very important war work. They agreed to meet ([30] or [31]):-

... in Chicago in some railroad station to learn a little bit more about it. I went there, and he could not tell me where he was going. There were two guys, sort of guards, looking like gorillas, with him. He discussed with me some mathematics, some interesting physics, and the importance of this work. And that was Los Alamos at the very start. A few months later I came with my wife ... arriving for the first time in a very strange place.

The main work going on at the Los Alamos National Laboratory in New Mexico at this time involved the fission bomb. This project was successfully accomplished on 16 July 1945 with the detonation of the atomic bomb in the New Mexican desert. Ulam, however, worked in Edward Teller's group which was looking beyond the fission bomb, and studying the possibility of a fusion bomb - the hydrogen bomb.

Rota [74] describes how Ulam's personality changed in 1946:-

One morning in 1946, in Los Angeles, Stanisław Ulam, a newly appointed professor at the University of Southern California, awoke to find himself unable to speak. A few hours later, he underwent a dangerous surgical operation after the diagnosis of encephalitis. ... In time, however, some changes in his personality became obvious to those who knew him. ... his ideas, which he spouted out at odd intervals, were fascinating beyond anything I have witnessed before or since. However, he seemed to studiously avoid going into details. ... he came to lean on his unimpaired imagination for his ideas, and on the [hard work] of others for technical support. ...

A crippling technical weakness coupled with an extraordinarily creative imagination is the drama of Stan Ulam. Soon after I met him, I was made to understand that, as far as our conversations went, his drama would be one of the Forbidden Topics. ... But he knew I knew, and I knew he knew I knew.

While Ulam was at Los Alamos, he developed the 'Monte-Carlo method' which searched for solutions to mathematical problems using a statistical sampling method with random numbers. He explained when the idea came to him [27]:-

The first thoughts and attempts I made to practice the Monte Carlo method were suggested by a question which occurred to me in 1946 as I was convalescing from an illness and playing solitaires. The question was what are the chances that a Canfield solitaire laid out with 52 cards will come out successfully?

The Monte-Carlo method is now widely used in computer implementations of mathematical software. Ulam's 1949 paper [57] describing the Monte-Carlo method, written jointly with Nicholas Metropolis, has the following Abstract:-

We shall present here the motivation and a general description of a method dealing with a class of problems in mathematical physics. The method is, essentially, a statistical approach to the study of differential equations, or more generally, of integro-differential equations that occur in various branches of the natural sciences.

After World War II, Ulam returned to Los Alamos to continue working on the hydrogen bomb. This work is described in [15]:-

Working with physicist Edward Teller, Ulam solved one major problem encountered in work on the fusion bomb by suggesting that compression was essential to explosion and that shock waves from a fission bomb could produce the compression needed. He further suggested that careful design could focus mechanical shock waves in such a way that they would promote rapid burning of the fusion fuel. Teller suggested that radiation implosion, rather than mechanical shock, be used to compress the thermonuclear fuel. This two-stage radiation implosion design, which became known as the Teller-Ulam configuration, led to the creation of modern thermonuclear weapons.

This remarkable insight by Ulam should, perhaps, have seen him known as the 'father of the hydrogen bomb', rather than Teller. Françoise Ulam gives the following description of her husband after he solved the problem [26]:-

I found him at home at noon staring intensely out of a window with a very strange expression on his face. I can never forget his faraway look as peering unseeing in the garden, he said in a thin voice, I can still hear it, "I found a way to make it work."

Ulam's insight only came, however, after many hours of calculations done first by himself and J C Everett, then assisted by a group of women computers employed to operate electronic calculators. Ulam wrote [68]:-

Each morning I would attempt to supply several guesses as to the value of certain coefficients referring to purely geometrical properties of the moving assembly involving the fate of the neutrons and other particles going through it and causing, in turn, more reactions. ... We started each day for four to six hours with slide rule, pencil and paper, making frequent quantitative guesses.

Ulam, with J C Everett, also proposed the 'Orion' plan for nuclear propulsion of space vehicles.

In 1963, during a boring lecture, Ulam was doodling on his squared notepad. He arranged the positive integers in a square spiral pattern and noticed that when he marked the prime ones they seemed to concentrate themselves in diagonal lines.
You can see more about this at THIS LINK

He remained at Los Alamos until 1965 when he was appointed to the chair of mathematics at the University of Colorado. At the time of his death he was professor of biomathematics at the University of Colorado.

When asked to sum up his work, he gave this modest reply ([30] or [31]):-

Originally I worked in set theory and some of these problems are still being worked on intensively. It is too technical to describe: measurable cardinals, measure in set theory, abstract measure. Then in topology I had a few results. ... Then I worked a little in ergodic theory. Oxtoby and I solved an old problem and some other problems were solved in other fields later. In general I would say luck plays a part, at least in my case. Also I had luck with tremendously good collaborators in set theory, in group theory, in topology, in mathematical physics, and in other method, which is not a tremendously intellectual achievement but is very useful, a few things like that.

Ulam's writing include A collection of mathematical problems (1960), (with Mark Kac) Mathematics and logic: Retrospect and prospects (1968), Sets numbers and universes (1974), Adventures of a Mathematician (1976), Science, computers, and people from the tree of mathematics (1986), and Analogies between analogies (1990). For information about the first and later editions of these books, including extracts from reviews and prefaces, see THIS LINK.

He was described by Rota in the following way [74]:-

Ulam's mind is a repository of thousands of stories, tales, jokes, epigrams, remarks, puzzles, tongue-twisters, footnotes, conclusions, slogans, formulas, diagrams, quotations, limericks, summaries, quips, epitaphs, and headlines. In the course of a normal conversation he simply pulls out of his mind the fifty-odd relevant items, and presents them in linear succession. A second-order memory prevents him from repeating himself too often before the same public.

His wife, Françoise Ulam, writing in [97] described Ulam's working methods:-

Ulam ... is almost exclusively a talking man, a verbal person. When not thinking ... what he enjoys most is to talk, to discuss, to argue, to converse, with friends and colleagues. Relying on his phenomenal memory, he carries everything in his head. ...

The physical act of taking pen to paper has always been painful for him. His mind and his eyes are the obstacles. His mind, because it works much faster than his fingers...; his eyes because one is very myopic the other very presbyopic. ... From childhood fears, then from youthful vanity he spurned wearing glasses, until very recently. Thus Ulam has always had a very hard time bringing himself to write anything for publication, either in long hand or with a typewriter. Machines and other mechanical objects have always turned him off. ... How then does he ever produce a written text? Mainly by talking ...

Let us end with Claire Ulam's childhood comment about her father [88]:-

One day when little Claire Ulam was watching some children playing ball with their father, a friend asked whether her father ever played like that with her. The answer was an emphatic "No! No! All my father does is think, think, think! Nothing but think!"