AWT was born in 1905 and grew up in a small town in the province of Ontario in Canada. His father was a minister who had to retire early on a tiny pension when the two Methodist churches in his town were combined. AWT badly wanted to go to the one very good university in Canada, the University of Toronto. Because of his family's poverty, his only chance was to win one of two Toronto scholarships available each year to high school seniors in Ontario. Unfortunately, he did not do well enough on the scholarship exam as a senior and so he repeated his senior year to try again for the scholarship. Fortunately, the second time he won the scholarship. He planned to be a high school math teacher but, at the end of college, wanted to learn more mathematics before teaching and stayed on at Toronto for a Master's degree supported by a TAship (Toronto had no doctoral program). He excelled and was encouraged to go to a top European university such as Cambridge or Gottingen for a PhD. However, in a pile of books in the room he used for office hours, he found a graduate bulletin from Princeton and was captivated for the range of geometry courses offered there. He decided to apply in the form of a letter from his supervising professor to the Princeton Math chairman Nathan Fine. However, Fine had just died and the letter was in a pile of office materials that a University official gave to Fine's wife. She got around to opening the letter some months later and passed it to the new math chair Luther Eisenhart. All the admission offers and financial support had been committed then, but at the last minute a part-time math instructor left and the position was offered to AWT based on his TAship experience at Toronto. He arrived in Princeton in the fall of 1929 and never left. He died in 1995 in a nursing home near Princeton.

1. Soon after AWT became a faculty member in the Princeton Mathematics Department in 1933, the senior member of the department Solomon Lefschetz asked AWT if he were a member of the Mathematical Association of America (MAA), the mathematical organization focused on collegiate mathematics teaching. AWT replied that he was not an MAA member, only a member of the mathematical research organization, the American Mathematical Society (AMS). Lefschetz then demanded, "Don't you care about teaching, Tucker?" My father said he did and immediately joined the MAA.

2. When AWT was math chairman from 1952 to 1964, he had the same 2-course-a-semester teaching load as other tenured faculty at Princeton (the Dean of the College also taught 2 courses a semester). In addition, one semester each year he assigned himself to be the lead professor in the big calculus course that most Princeton freshmen took. When I asked him years later when I was a department chair why he assumed this extra duty, he looked at me like I was crazy and said, "The most important thing the Princeton Mathematics Department did was to teach freshman calculus, and so as department chairman it was obvious that I should led that effort." As chair, AWT felt it was also his job to get to know most of the math majors personally.

I later learned that Dean Eisenhart, who was the department chair (and Dean of the Faculty) when AWT was a graduate student, also led the freshman calculus course once a year.

3. As a child I once asked my father how he showed off his department to visitors (I knew then that the Princeton Mathematics Department was very famous for its brilliant professors). He thought a little and replied that he would invite them to sit in on one of Emil Artin's freshman honors calculus lectures (Artin was a world famous algebraist and a great teacher).

NOTE: Princeton used to be famous for enrolling high school senior class presidents (all-around students), not high school valedictorians. However, Artin's lectures converted a number of undecided students into mathematics majors and some into famous mathematicians, such as Hyman Bass.

4. One more story about Artin and teaching. An influential 1920 national report advocated some efforts at universities be devoted to research as an end in itself. Soon afterwards Princeton created two professorships in mathematics, the Fine Chair, and in mathematical physics, the Jones Chair, both endowed by the Jones family, with purely research obligations (no formal teaching required) and which came to be seen as the most prestigious professorships in the whole university. Oswald Veblen was the first Fine Chair (von Neumann and Eugene Wigner shared the first Jones Chair; they alternated years in Princeton and in Berlin). The next Fine Chair was Solomon Lefschetz. When Lefschetz retired, the mathematics faculty voted to give it to Artin. AWT loved to tell the story of when, as department chair, he had the pleasure of inviting Artin to his office to tell him he would be the next Fine Chair in mathematics. Instead of looking delighted, Artin looked concerned and finally said, "But the Fine Chair does no teaching. I will not give up my freshman calculus course and so I must respectfully decline the honor. AWT consulted with university lawyers about the exact terms of the Fine Chair endowment and it was decided that voluntary teaching by a Fine Chair was allowed. When so informed, Artin accepted the Fine Chair.

**Research and Undergraduate
Teaching are Compatible**

1. AWT's initial teaching load at Princeton in 1933, like that of other Instructors, was 5 courses a semester, yet he said that this period was the most productive research time in his life. He had no other University duties except to teach. He had typically had about 3 different courses to teach, with multiple sections in two, and the courses varied little from semester to semester. Classes had 20 to 25 students. He taught in the mornings (six days a week), with minimal preparation needed; graded homework himself as well as held office hours in the early afternoon; and from 3 pm on into the night he could pursue his research uninterrupted. Future departmental and professional duties and graduate supervision took up more time throughout the day than the time gained from a reduction in teaching and grading duties.

2. When AWT was studying for a Master's degree at the University of Toronto, he was offered a TAship to teach a course in advanced calculus. However, when the two MS students offered TAships dropped out at the last minute, AWT was asked to teach the other TAs' two courses-- one a brand new course in mathematical economics and the other a course in PDEs for engineers-- in addition to his own course, at no increase in salary. Still, his expanded teaching experience subsequently earned him a part- time instructorship at Princeton when his application for graduate study was received too late for a TAship.

**Tea at Fine Hall**

1. During AWT's last year as a graduate student, he was asked by Professor Veblen to oversee the creation of a daily tea around 4pm in the Fine Hall Lounge. Veblen had been in Cambridge the year before and liked the English tradition of daily tea. Other graduate students were enlisted to share the duties of making tea and providing cookies. Over time, the Fine Hall tea became the center of department life, and eventually many other U.S. mathematics departments copied the Fine Hall tea. When I went to graduate school, my father's only advice was to be sure to attend tea regularly. The next vignette explains the hidden meaning of this advice.

2. "Grading through Tea": By the time AWT was chairman, most incoming graduate students already knew the material in standard first-year graduate courses and research seminars were the only graduate courses offered. Students formed informal seminar groups to learn and review the first- year graduate course content that appeared on the PhD qualifying exam. I later asked my father how, without graded graduate courses, the department monitored the academic progress of students before they was working with a professor on the thesis. I told him that I knew the students were very bright but still sometimes even one of these students surely did not make good progress. AWT said that from time to time, he took attendance at tea in an informal fashion. If a student was not regularly at tea talking mathematics with other students, then AWT or another professor would call the student into their office and examine the student on what he had been doing mathematically. AWT said, "We never had a problem with any student who was regularly in mathematical conversations with fellow students at tea."

**AWT
version of a teacher's obligation for his students' welfare.**

AWT's father was a minister. Although AWT had enough religion as a child and never went to church, he treated his students and junior faculty the way a minister treats his congregation. In the fall of his second year as a graduate student at Princeton, he was assigned to teach two sections of the freshman calculus course and the professor in charge was T.Y. Thomas. Thomas taught a specially chosen section of strong students. The weekly syllabus that Thomas gave to all instructors seemed too fast to AWT for his students, although he knew that Thomas's class could probably handle it. AWT complained to Thomas about this. Thomas then called a meeting of all the instructors in the course and asked if anyone else thought the syllabus was too demanding. No one else was willing to. Then Thomas announced that all TAs commit themselves to follow his syllabus. My father was the only one who refused. As AWT knew would happen, Thomas went to the Dean of the Graduate School to demand that AWT be expelled for insubordination. A friend of AWT's informed Lefschetz, AWT's advisor, and Lefschetz spoke to the chairman Eisenhart. After he heard AWT's side of the story he reassigned AWT to sophomore calculus sections. When AWT recounted this story to me when he was retired, I was very moved and asked him, with all the hurdles he had getting into college and then into Princeton, where did he find the courage to stand up to Prof. Thomas. His response set a morale standard that I will always inspire me as a teacher. He said, "As long as I was the instructor of those students, their academic welfare was paramount to me. Nomatter what the consequences to me, I had to fight for what was right for them."

**Miscellaneous**

1. Great Lefschetz quote: AWT overhears a discussion between Lefschetz and Oscar Zariski in which Zariski was asking for advice on how to categorize an algebraic geometry paper submitted to Annals of Mathematics—should it be classified as algebra or geometry. Lefschetz responded:"If the paper consists of a lot of symbol manipulation, then it is algebra. But if there is an idea, then it is geometry."

For more information about the Princeton Mathematics Department, readers should refer to Oral History of the Princeton Mathematics Community in the 1930s. (The oral history covers much of the first half of the 20th century despite its restrictive title.)

The vignettes on this webpage have been translated into Swedish by Valeria Aleksandrova, See http://www.pkwteile.de/wissen/awtucker-vinjetter . And into Portuguese by Artur Weber; see https://www.homeyou.com/~edu/vignettes-awtucker .