桑德斯·麦克兰恩Saunders Mac Lane

桑德斯·麦克兰恩来自一个苏格兰家庭，该家庭在1746年卡洛登战役后逃离苏格兰。他的祖父William Ward McLane于1846年出生在宾夕法尼亚州的Lewisville，成为一名长老会牧师，但在宣讲进化论后被迫离开教会。他成为公理会的牧师，其第二次婚姻的长子Donald Bradford McLane于1882年1月19日出生在Steubenville。Donald于1908年与George Aretas 麦克兰恩的长女Winifred 麦克兰恩结婚。Winifred毕业于曼荷莲学院，婚前在高中教授英语、拉丁语和数学。婚后，Donald成为康涅狄格州Taftville的公理会牧师，他的长子Leslie 麦克兰恩 MacLane，即本传记的主人公，出生在靠近Taftville的Norwich。当他仅一个月大时，他的父母决定不喜欢Leslie这个名字，从那时起他就被称为麦克兰恩 MacLane。从MacLane改为麦克兰恩是在他结婚多年后才发生的。麦克兰恩有两个兄弟，Gerald R MacLane，后来成为莱斯大学和普渡大学的数学教授，以及弗洛伦斯·南丁格尔·大卫 Tyler MacLane，1922年1月20日出生在纽约州尤蒂卡，后来成为学校教师和商人。麦克兰恩的早年是在几个不同的小镇度过的，但他确实住过一个大城市，大约七岁时在波士顿待了几年。

麦克兰恩的高中教育始于纽约州尤蒂卡，但在1924年他14岁时中断，因为那时他的父亲去世了。父亲去世后，麦克兰恩搬到马萨诸塞州的Leominster，与他的祖父同住，如上所述，祖父也是公理会牧师。麦克兰恩于1926年高中毕业，并于同年进入耶鲁大学。是他的同父异母叔叔John Fisher MacLane（生于1878年）拜访了他，并解释说他和他的几个亲戚都去了耶鲁大学。他提出为麦克兰恩提供足够的资金以支付他在耶鲁的费用，但他期望麦克兰恩为商业或法律职业做准备。麦克兰恩的祖父William Ward McLane于1931年6月14日去世，即麦克兰恩从耶鲁毕业一年后。

1926年秋，麦克兰恩开始在耶鲁大学学习，但此时他的目标是专攻化学[3]：-

我既修了化学荣誉课程，也修了标准的新生数学课程。我觉得化学相当枯燥。我不喜欢实验室工作。我在新生数学课程中遇到了一位出色的老师，一位正在攻读博士学位的讲师，名叫Lester Hill。他给了我很多鼓励，说：“麦克兰恩，你为什么不参加Barge奖考试呢？”他们每年都给新生举行这个考试。于是我参加了考试，成功获奖，并决定也许数学是比化学更好的领域。

然而，他不仅修数学课程，在第二年还修了会计课程，觉得既然叔叔资助他的学业，他应该这样做。几周内他就对会计完全厌倦了，在一位同学说多么喜欢物理之后，麦克兰恩继续主修数学和物理。他1930年从耶鲁大学毕业，并在芝加哥获得了一份奖学金。在芝加哥大学，他受到伊莱基姆·黑斯廷斯·穆尔的影响，但他在那里的第一年，1930-31年，是[33]：-

……一个模糊地令人失望的研究生学习年份。

此时伊莱基姆·黑斯廷斯·穆尔已近七十岁，但他建议麦克兰恩去德国哥廷根攻读博士学位，这无疑说服了麦克兰恩去当时世界最重要的数学研究中心工作。当然，伊莱基姆·黑斯廷斯·穆尔年轻时自己也曾在德国学习，并基于他当时对德国数学的经验，在芝加哥创建了一个著名的数学研究学派。

麦克兰恩于1931年去了哥廷根[33]：-

大卫·希尔伯特已从教授职位上退休，但仍每周讲授一次“基于现代科学的哲学导论”。他的继任者赫尔曼·外尔广泛讲授微分几何、代数拓扑学以及数学哲学（我据此整理了讲课笔记）。从他的群表示讨论班中，我学到了很多（例如关于线性变换的使用），但我没有听从他的敦促，即代数学家应该研究李代数的结构。我也未被他的断言所说服，即集合论涉及太多“沙子”。埃德蒙·朗道（自1909年起任教授）以其惯有的精炼清晰向大量听众讲课——并有助手擦去用过的（滚动）黑板。理查·科朗特，研究所的行政负责人，讲课并管理许多为理查·科朗特-大卫·希尔伯特书稿工作的助手。古斯塔夫·赫格洛茨雄辩地讲授了他关于广泛主题的富有洞见的课程：索菲斯·李群、力学、几何光学、具有正实部的函数。费利克斯·伯恩斯坦教授统计学，但在1932年12月，在灾难降临之前离开了。这些就是当时哥廷根的‘ordentliche’教授。

然而，政治事件很快会扰乱哥廷根。麦克兰恩开始在保罗·贝尔奈斯的指导下攻读博士学位，但1933年纳粹上台。他们开始将顶尖数学家从哥廷根和其他大学中清除，这些数学家与犹太人有联系。麦克兰恩于1933年5月3日写信给他的母亲（见[33]）：-

如此多的教授和讲师被解雇或已经离开，以至于数学系几乎被彻底阉割。这对数学相当艰难，我们只有冷冰冰的安慰，即这对Volk是最好的事情。

麦克兰恩已经看到，他必须迅速完成博士学位，并尽快离开德国，以免事情进一步恶化。他于1933年7月19日答辩了他的学位论文Abbreviated Proofs in the Logical Calculus，赫尔曼·外尔作为考官。在论文末尾，他感谢他的导师保罗·贝尔奈斯“感谢他的批评”，“最感谢赫尔曼·外尔教授的建议和他讲座的启发”。麦克兰恩相当失望地得知赫尔曼·外尔只将他的论文评为“合格”。获得学位几天后，他与Dorothy Jones结婚，他是在芝加哥认识她的，她后来也来到哥廷根与他相聚（事实上她打字了他的论文）。这是一个小型仪式，随后在市政厅酒窖与几个朋友共进婚宴。这对新婚夫妇迅速返回美国。麦克兰恩的文章[33]对1933年哥廷根的事件给出了有趣的叙述。

回到美国后，麦克兰恩在1933-34学年于耶鲁度过，同时他试图为下一年获得大学职位。他参加了1933年12月的美国数学会会议，并与乔治·戴维·伯克霍夫、Marshall Stone和约瑟夫·里特谈论了可能的职位。几周后，他收到哈佛的来信，提供他为期一年的本杰明·皮尔斯讲师职位。他还被要求教授一门高级课程。他欣然接受。至此，他一直从事数理逻辑研究，但这不是吸引数学系聘任者的主题。在哈佛被提供教授逻辑或代数高级课程的选择时，他选择了代数，并开始朝这个方向努力。他在哈佛度过了两年，然后离开，于1936-37学年在康奈尔担任讲师。接下来的学年他回到芝加哥，从事代数工作，并从亚伯拉罕·阿德里安·艾伯特那里获得很多帮助，之后接受哈佛助理教授职位，于1938年上任。

正是在哈佛的岁月（1938-47）里，他与加勒特·伯克霍夫写下了著名的教材A survey of modern algebra，该书于1941年出版。厄文·卡普兰斯基在[24]中关于这本教材写道：-

《现代代数综述》向美国本科生打开了此前在很大程度上只为数学家保留的领域，即巴特尔·伦德特·范德瓦尔登十年前出版的《现代代数》。乔治·戴维·伯克霍夫和麦克兰恩对学院和大学中代数的内容与教学的影响是直接而持久的。我们今天在本科代数课程中所认可的内容，很大程度上始于他们使之既易于理解又吸引人的抽象代数。

关于这份著名文本的更多信息，包括它是如何写成的细节，见THIS LINK。

第二次世界大战期间，麦克兰恩在哥伦比亚大学的应用数学组工作[3]：-

我们在做一些直接实用的问题，比如为火控计算曲线之类的。那是初等微分方程，我学会了更多关于它们的知识。但哥伦比亚大学的工作并不是真正有成效的应用数学研究方向。此外，它部分属于行政工作，我认定自己并不特别喜欢行政。我记得当时有意识地做了一个决定：如果你想进入商界并以此为职业，现在正是时候。我没有。我回到了哈佛，很高兴回到数学。

然后，在1947年，他被任命为芝加哥大学的数学教授。那里的研究中心有Marshall Stone、亚伯拉罕·阿德里安·艾伯特、厄文·卡普兰斯基、Otto Schilling和安德烈·韦伊在教职员中，由Stone领导。1952年，在被任命五年后，麦克兰恩从Stone手中接过了系主任的职位，后者卸任系主任，但又在教职员中留任了十六年。Wojciech Komornicki在1968-69年参加了麦克兰恩的代数课程，并在[27]中描述了这段经历：-

……这与我上过的任何数学课程都不一样。虽然用的是他自己的书教学，但麦克兰恩似乎会特意以不同于课本中的方式呈现材料。有时他会对同一个定理给出不止一个证明。他确保我们意识到这一点，解释说我们理解某事物的方式越多，我们的理解就越好。虽然我再次看到了我在NSF项目中记得的群的定义，但我听说群是一个只有一个对象的范畴，其中所有箭头都是可逆的。两个群的积是一个泛对象。我记得在这些新概念上挣扎，尤其是因为麦克兰恩的风格是给我们大局观，把大部分但并非全部的细节留给书和他布置的问题。然而，在麦克兰恩的讲解中，对数学的理解是最重要的。如果他认为有人没有理解一个证明，他会提供一个替代证明。而且从来没有暗示某个概念或证明对某人来说太复杂而无法理解。他教学的另一个让我印象深刻的方面是，他从不带笔记来上课。他会偶尔拿出一张索引卡，我猜上面有当天课程的主题，看一眼，放回衬衫或夹克口袋，然后继续讲课。尽管他的讲课在呈现我们所学内容的全局图景方面一丝不苟，但他非常注意回答问题。没有问题是太小的问题，他从不敷衍问题，也从不因学生提问而表现出任何恼怒。

麦克兰恩的工作涵盖了广泛的数学领域。他在整个职业生涯中时断时续地研究数理逻辑，这对保罗·贝尔奈斯的学生来说并不意外，他还做了一些关于平面图的早期工作。他研究了赋值及其到多项式环的扩展。在20世纪40年代，他研究了上同调，并引入了范畴论的基本概念。芝加哥大学数学教授Peter May说（见[28]）：-

[在他的研究中]他极具洞察力和独创性，尤其作为数学哲学家而格外突出。他与塞缪尔·艾伦伯格一起创造了一种思考数学的新方式。在1945年一篇具有里程碑意义的论文中，他们引入并命名了“范畴”、“函子”和“自然变换”的概念。他们在那里引入的语言改变了现代数学。事实上，自那以后，非常多的数学若没有那种语言，简直就无法想象。

麦克兰恩是七本书的作者：(与加勒特·伯克霍夫合著) A Survey of Modern Algebra(1941)；Homology(1963)；(与加勒特·伯克霍夫合著)Algebra(1967)；Categories for the Working Mathematician(1971)；Mathematics, Form and Function(1985)；(与Ieke Moerdijk合著)Sheaves in Geometry and Logic: A First Introduction to Topos Theory(1992)；以及Saunders Mac Lane: A Mathematical Autobiography(2005)。

关于A Survey of Modern Algebra的信息见THIS LINK。

关于其他六本书的信息见THIS LINK。

在麦克兰恩获得的众多奖项和荣誉中，我们提及肖维勒奖（1941年）：-

……因其著作《Modular 约翰·查尔斯·菲尔兹》和《Some Recent Advances in Algebra》……

以及 Leroy P 凯瑟琳·斯蒂尔 奖（1986年）：-

……因其对代数和代数拓扑学的许多贡献，特别是其在同调代数和范畴代数方面的开创性工作。

他于1989年获得国家科学奖章：-

因通过在同调代数与范畴论领域的创建与发展中的合作，革新了现代数学的语言与内容，因对数学教育的杰出贡献，以及因对数学与科学界的敏锐领导。

因他对美国数学协会的贡献，麦克兰恩获得了该协会1975年杰出服务奖。他曾任该协会理事（1943-45年）、副主席（1948-49年），并于1951-52年任主席[10]：-

他的主席任期给当时活跃于该协会的人留下了持久的印象。他视这一职位与其说是荣誉，不如说是机会，以他特有的想象力和精力攻克大学数学的问题，并使协会走上此后一直遵循的积极道路。

他于1949年当选为国家科学院院士，并于1973年至1981年担任其副主席。他还在1949年当选为美国哲学学会会员，并于1968年至1971年担任其副主席。他于1973-74年任美国数学会主席[10]：-

作为美国数学会主席，麦克兰恩为该学会提供了人们所期待的那种充满活力的领导，发起新活动并大力延续旧活动。学会的许多成员尤其珍视他管理的开放性和他与会员之间新的沟通渠道。他以堪称典范的技巧处理棘手问题，我们许多人都有幸亲眼目睹。他担任该学会主席，如同他担任该协会主席一样，将被人们怀着钦佩之情铭记。

在他的其他荣誉中，我们注意到他于1972年被选为爱丁堡皇家学会的名誉会士。他获得了许多大学的荣誉学位，包括普渡大学、耶鲁大学和格拉斯哥大学。

麦克兰恩和多萝西麦克兰恩有两个女儿，格蕾琴和辛西娅。多萝西于1985年去世，麦克兰恩于次年与艺术家奥萨·斯科廷尔文·席格（她于1977年与尔文·席格离婚）结婚。麦克兰恩的爱好包括滑雪、徒步旅行和写诗。他会大声朗读拜伦、雪莱、济慈和华兹华斯等诗人的作品。奥萨说[55]：-

所以当他临终躺在床上时，我给他读诗——就是那些诗人。

凯利在[25]中写道：-

没有人能如此激励他人，除非他除了敏锐的才智之外，还拥有热情和温暖，对同胞的深切关怀，以及一种因不感伤而更加真实的同情。那些自豪地称自己为他的朋友的人知道这些事情：其他人将在阅读[他的作品]时推断出这些。

Saunders Mac Lane came from a Scottish family who fled from Scotland after the Battle of Culloden in 1746. His grandfather, William Ward McLane was born in Lewisville, Pennsylvania in 1846, became a Presbyterian Minister but was forced to leave the Church after preaching the theory of evolution. He became a pastor in the Congregational Church and the eldest son from his second marriage, Donald Bradford McLane, was born 19 January 1882 in Steubenville. Donald married Winifred Saunders, the eldest daughter of George Aretas Saunders, in 1908. Winifred was a graduate of Mount Holyoke College and taught English, Latin and Mathematics at High School before her marriage. After his marriage, Donald became a Congregational Minister in Taftville, Connecticut and his eldest son Leslie Saunders MacLane, the subject of this biography, was born in Norwich, close to Taftville. When he was only one month old his parents decided they did not like the name Leslie and from that time on he was known as Saunders MacLane. The change from MacLane to Mac Lane only came about many years later after his marriage. Saunders had two brothers, Gerald R MacLane, who became a mathematics professor at Rice University and Purdue University, and David Tyler MacLane, born 20 January 1922, in Utica, New York, who became a school teacher and businessman. Mac Lane's early years were spent in several different small towns but he did live in one large city, spending a few years in Boston when aged around seven.

Mac Lane's High School education began in Utica, New York but was interrupted in 1924 when he was 14 years old for, at that time, his father died. After his father's death, Mac Lane moved to Leominster, Massachusetts, to live with his grandfather who, as we noted above, was also a Congregational Minister. Saunders graduated in 1926 from high school and, in that year, he entered Yale University. It had been his half-uncle, John Fisher MacLane (born 1878), who had visited him and explained that he and several of his relations had gone to Yale University. He offered to provide Mac Lane with sufficient funds to cover his expenses at Yale but he expected Mac Lane to train for a career in either business or law. Mac Lane's grandfather, William Ward McLane, died on 14 June 1931 a year after Mac Lane graduated from Yale.

In the autumn of 1926, Mac Lane began his studies at Yale but at this time his aim was to specialise in chemistry [3]:-

I took both an honours course in chemistry and the standard freshman mathematics course. I found the chemistry rather dull. I didn't enjoy laboratory work. I had a wonderful teacher in the freshman mathematics course, an instructor working for his Ph.D., named Lester Hill. He gave me lots of encouragement and said, "Mac Lane, why don't you take the Barge Prize examination?" They gave that examination to freshmen every year. So I took the examination, succeeded in winning the prize, and decided that maybe mathematics was a better field than chemistry.

However, he did not take only mathematics courses but, in his second year, he took an accounting course, feeling that he should do that since his uncle was financing his studies. Within weeks he was completely bored by accounting and, after one of his classmates said how much he was enjoying physics, Mac Lane went on to major in both mathematics and physics. He graduated from Yale in 1930 and took up a fellowship at Chicago. At the University of Chicago he was influenced by Eliakim Moore but his first year there, 1930-31, was [33]:-

... a vaguely disappointing year of graduate study.

By this time E H Moore was nearly seventy years old but his advice to Mac Lane to study for a doctorate at Göttingen in Germany certainly persuaded Mac Lane to work at the foremost mathematical research centre in the world at that time. Of course Moore had himself studied in Germany as a young man and had created in Chicago an eminent research school of mathematics based on his experiences of German mathematics at that time.

Mac Lane went to Göttingen in 1931 [33]:-

Hilbert had retired from his professorship, but still lectured once a week on "Introduction to Philosophy on the Basis of Modern Science". His successor, Hermann Weyl, lectured widely on differential geometry, algebraic topology and on the philosophy of mathematics (on which I wrote up lecture notes). From his seminar on group representations, I learned much (e.g., on the use of linear transformations), but I failed to listen to his urging that algebraists should study the structure of Lie algebras. I also was not convinced by his assertion that set theory involved too much "sand". Edmund Landau (professor since 1909) lectured to large audiences with his accustomed polished clarity - and with assistants to wash off used (rolling) blackboards. Richard Courant, administrative head of the Institute, lectured and managed the many assistants working on the manuscript of the Courant-Hilbert book. Gustav Herglotz delivered eloquently his insightful lectures on a wide variety of topics: Lie groups, mechanics, geometrical optics, functions with a positive real part. Felix Bernstein taught statistics, but left in December 1932 before the deluge struck. These were then the 'ordentliche' professors in Göttingen.

However, political events would soon disrupt Göttingen. Mac Lane began to work for his doctorate under Paul Bernays' supervision but in 1933 the Nazis came to power. They began to remove the top mathematicians from Göttingen, and other universities, who had Jewish connections. Mac Lane wrote to his mother on 3 May 1933 (see [33]):-

So many professors and instructors have been fired or have left that the mathematics department is pretty thoroughly emasculated. It is rather hard on mathematics, and we have but the cold comfort that it is the best thing for the Volk.

Mac Lane had seen that he had to work quickly for his doctorate and leave Germany as soon as possible before things deteriorated further. He defended his thesis Abbreviated Proofs in the Logical Calculus, with Weyl as examiner, on 19 July 1933. At the end of his thesis he thanked his advisor Paul Bernays "for his criticism", "and most of all Professor Hermann Weyl for his advice and for the inspiration of his lectures". Mac Lane was rather disappointed to learn that Weyl had only rated his thesis "sufficient". A couple of days after getting his degree, he married Dorothy Jones whom he had met in Chicago and who had joined him in Göttingen (in fact she had typed his thesis). It was a small ceremony followed by a wedding dinner with a couple of friends in the Rathaus Keller. The newly married couple quickly returned to the United States. The article [33] by Mac Lane gives an interesting account of the events at Göttingen in 1933.

On returning to the United States, Mac Lane spent the session 1933-34 at Yale while he tried to get a university position for the following year. He went to the American Mathematical Society meeting in December 1933 and talked with George Birkhoff, Marshall Stone and Joseph Ritt about possible positions. A couple of weeks after this he received a letter from Harvard offering him an appointment for a year as Benjamin Peirce Instructor. He was also asked to give an advanced course. He gladly accepted. Up to this time he had worked on mathematical logic but that was not a topic that was attractive to those making appointments to mathematics departments. Offered the option of giving the advanced course at Harvard on logic or algebra, he opted for algebra and he began to move in that direction. He spent two years at Harvard and left to take up a post of instructor at Cornell for session 1936-37. He spent the following session back at Chicago, working in algebra and getting much help from Adrian Albert, before accepting an appointment as an assistant professor at Harvard which he took up in 1938.

It was during the years at Harvard (1938-47) that he wrote his famous text A survey of modern algebra with Garrett Birkhoff which was published in 1941. Kaplansky writes in [24] about this text:-

"A Survey of Modern Algebra" opened to American undergraduates what had until then been largely reserved for mathematicians in van der Waerden's "Moderne Algebra", published a decade earlier. The impact of Birkhoff and Mac Lane on the content and teaching of algebra in colleges and universities was immediate and long sustained. What we recognise in undergraduate courses in algebra today took much of its start with the abstract algebra which they made both accessible and attractive.

Further information about this famous text including details of how it came to be written are given at THIS LINK.

During World War II Mac Lane worked in the Applied Mathematics Group at Columbia [3]:-

We were doing some immediately practical problems of calculating curves for fire control and such. It was elementary differential equations and I learned to understand more about them. But the work at Columbia was not in really profitable directions of applied mathematical research. Also it was partly administrative and I decided that I didn't especially like administration. I remember making a conscious decision at that time: if you want to go into business and make that your career, now is the time to do it. I didn't. I went back to Harvard, happy to go back to mathematics.

Then in 1947 he was appointed professor of mathematics at Chicago. The research centre there had Marshall Stone, Abraham Albert, Irving Kaplansky, Otto Schilling and André Weil on the staff and was led by Stone. In 1952, five years after being appointed, Mac Lane took over the chairmanship of the department from Stone who stepped down as chairmen but remained on the staff for another sixteen years. Wojciech Komornicki attended Mac Lane's algebra course in 1968-69 and describes the experience in [27]:-

... it was nothing like any mathematics course I had ever taken. Though teaching from his own book, it seemed that Mac Lane would go out of his way to present the material differently than what was in the text. Sometimes he would give more than one proof of the same theorem. He made sure that we were aware of this, explaining that the more ways we understood something the better our understanding. Though I once again saw the same definition of a group that I remembered from my NSF program, I heard that a group was a category with one object in which all the arrows were invertible. The product of two groups was a universal object. I remember struggling with these new concepts especially since Mac Lane's style was to give us the big picture leaving most, but not all, of the details to the book and to the problems he assigned. However, the understanding of the mathematics was paramount in Mac Lane's presentations. If he thought that someone did not understand a proof, he would provide an alternative proof. And there was never any hint that a concept or a proof was too complex for someone to understand. Another aspect of his teaching that struck me was that he never came to class with notes. He would every once in a while pull out an index card on which I assume he had the subject matter of the day's class, look at it, put it back in his shirt or jacket pocket and continue the lecture. Though his lectures were meticulous in presenting the global picture of what we were learning he took great care to answer questions. No question was too small and he never blew off a question nor showed any irritation by student asking questions.

Mac Lane's work covered a wide range of mathematics. He worked on and off throughout his career on mathematical logic, no surprise for a student of Bernays, and he did some early work on planar graphs. He studied valuations and their extensions to polynomial rings. In the 1940s he worked on cohomology and introduced the basic notions of category theory. Peter May, Professor in Mathematics at the University of Chicago, said (see [28]):-

[In his research] he was extraordinarily perceptive and original, and he was especially strong as a philosopher of mathematics. With Sammy Eilenberg he created a new way of thinking about mathematics. In a landmark 1945 paper, they introduced and named the concepts of 'categories,' 'functors' and 'natural transformations.' The language they introduced there transformed modern mathematics. In fact, a very great deal of mathematics since then would quite literally have been unthinkable without that language.

Mac Lane was the author of seven books: (with Garrett Birkhoff) A Survey of Modern Algebra (1941); Homology (1963); (with Garrett Birkhoff) Algebra (1967); Categories for the Working Mathematician (1971); Mathematics, Form and Function (1985); (with Ieke Moerdijk) Sheaves in Geometry and Logic: A First Introduction to Topos Theory (1992); and Saunders Mac Lane: A Mathematical Autobiography (2005).

Information about A Survey of Modern Algebra is given at THIS LINK.

Information about the other six books is given at THIS LINK.

Among the many prizes and honours Mac Lane received we mention the Chauvenet Prize (1941):-

... for his writing 'Modular Fields' and 'Some Recent Advances in Algebra' ...

and the Leroy P Steele Prize (1986):-

... for his many contributions to algebra and algebraic topology, and in particular for his pioneering work in homological and categorical algebra.

He received the National Medal of Science in 1989:-

For revolutionizing the language and content of modern mathematics by his collaboration in the creation and development of the fields of homological algebra and category theory, for outstanding contributions to mathematics education, and for incisive leadership of the mathematical and scientific communities.

For his contributions to the Mathematical Association of America, Mac Lane received the Association's Award for Distinguished Service for 1975. He was a Governor of the Association (1943-45), a Vice-President (1948-49), and President for 1951-52 [10]:-

His presidency made an enduring impression on those who were active in the Association at that time. He saw the office less as an honour than as an opportunity, attacked the problems of collegiate mathematics with characteristic imagination and energy, and set the Association on the active course that it has followed ever since.

He was elected to the National Academy of Sciences in 1949 and served as its vice-president from 1973 to 1981. He was also elected to the American Philosophical Society in 1949, and served as its vice-president from 1968 to 1971. He was president of the American Mathematical Society in 1973-74 [10]:-

As President of the American Mathematical Society, Mac Lane has given that Society the dynamic leadership that one would have anticipated, initiating new activities and vigorously pursuing old ones. Many members of the Society especially valued the openness of his administration and his new lines of communication with the membership. He handled difficult problems with exemplary skill which many of us have enjoyed observing at first hand. His presidency of the Society, like his presidency of the Association, will be remembered with admiration.

Among his other honours we note that he was elected an Honorary Fellow of the Royal Society of Edinburgh in 1972. He received honorary degrees from many universities including Purdue University, Yale University and the University of Glasgow.

Saunders and Dorothy Mac Lane had two daughters, Gretchen and Cynthia. Dorothy died in 1985 and Mac Lane married the artist Osa Skotting Segal (who was divorced from Irving Segal in 1977) in the following year. Mac Lane's hobbies included skiing, hiking and writing poetry. He would read aloud the works of poets such as Byron, Shelley, Keats and Wordsworth. Osa said [55]:-

And so I was reading poetry to him - those same poets - when he was lying there at the end of his life.

Kelly, in [25], writes:-

No man could so stimulate others unless, alongside an incisive intellect, he was possessed of enthusiasm and warmth, a deep interest in his fellow man, and a sympathy the more real for being unsentimental. Those who proudly call themselves his friends know these things: others will infer them in reading [his works].