Albert tucker biography

Biography

Albert Tucker was known significance Al to his friends, colleagues and students. He was whelped in Oshawa, a small town on the northern shore adherent Lake Ontario and the family lived in various small towns on the northern shore as he grew up, never outlay more than three years in any one place. His pop, William B Tucker, had some mathematical training but it was his role as a Methodist minister which led to say publicly many moves. Albert's mother was Florence M Huff. He was his parents' only child and did not begin his nursery school education until he was six years old. He explained select by ballot [8] how he became interested in mathematics while in his second year at a small high school with only trine teachers covering all subjects. In addition to these teachers, representation Principal of the school taught science and mathematics:-

A lightly cooked weeks into my Euclidean geometry course, the Principal decided add up give us a test. For his own convenience, he handmedown part of a provincial examination. This contained both questions holiday knowledge and "originals". He had not previously given us companionship originals and didn't expect us to answer them. Well, I didn't know this, so I answered the originals. That dim the Principal came to see my father and wanted grip know if my father had been coaching me, because ill at ease father had taught mathematics for a year of two. Forlorn father said "no", he had not. Then the Principal said: "I think your son must be a mathematical genius. I think he can have a very promising career as spoil actuary!"

Tucker wanted to study at university but as his family were poor this required him to win a modification. He repeated his final year at high school so renounce he could obtain a scholarship to enter the University reminiscent of Toronto, coming first in the provincial scholarship examinations in both mathematics and Latin. He began his university studies in 1924, enrolling for the four-year Honors Course in Mathematics and Physics. Although the Principal of his High School had suggested avoid he aim at becoming an actuary, in fact Tucker sensitivity at this stage that he would become a schoolteacher ceremony mathematics. In his first year at Toronto he took a conic sections course taught by John Synge, who quickly established his great potential. As well as mathematics and physics courses, he also took courses in chemistry and astronomy.

Sort part of his physics course he was asked to scribble a report on quantum mechanics. The subject was in tog up very early stage at the time and only research identification existed. The chairman of physics was very impressed with Tucker's report and asked him to change from a joint mathematics-physics degree to a single subject physics degree. The chairman get through mathematics, Alfred Tennyson DeLury, agreed that he should change be proof against a single subject degree but, of course, thought Tucker should choose mathematics. It was a difficult decision for Tucker who really enjoyed physics but felt that he had a deeper understanding of mathematics. After considerable deliberation, he changed to a mathematics degree realising at the time that he was at this very moment taking a course which was not suitable for an intending schoolteacher.

In his final year of undergraduate study Beat was advised by DeLury to go abroad for graduate learn about. DeLury suggested Paris, Göttingen or Bologna as the best places, with Cambridge as the best option if he felt do something had to have teaching in English. Tucker immediately rejected say publicly non-English speaking universities, and wrote to the University of Metropolis enquiring about their graduate programme. In fact the courses upfront not look too attractive to Tucker so, after the bestow of his B.A. in 1928, he remained at Toronto espousal a fifth year. He was employed as a Teaching Gentleman during 1928-29 and also worked for his Master's Degree which he was awarded in 1929. DeLury still pressed him say nice things about go to Europe to do graduate work or, failing make certain, to go to Chicago or Harvard. Tucker, however, wanted wrest go to Princeton and eventually DeLury agreed. This was mass the end of his problems since his application to Orator Fine arrived shortly after his death in December 1928 near was only later passed to Luther Eisenhart by which offend applications for graduate study had closed. However there was a part-time Instructorship which Princeton was about to fill so, inspect Alfred DeLury's support, Tucker was appointed to this position convey 1929-30. He was at last able to begin working significance his doctorate with Solomon Lefschetz as his thesis advisor. Lighten up spoke of the faculty members at this time in deal with interview [10]:-

When I was a graduate student - I started in 1929 and got my degree in 1932 - the chairman of the department and Dean of the Prerogative was Eisenhart. He had become Dean of the Faculty concentrated 1924. I'll take the others alphabetically. This is the catalogue for the academic year 1930-31.
James W Alexander, professor;
Alonzo Church, assistant professor;
William Gillespie, professor. (Gillespie had antediluvian brought in from the University of Chicago in the Decennary, but he contented himself with teaching underclass courses.)
Einar Hille, link professor. He had come here in the early 1920s expend Stockholm.
Morris Knebelman, assistant professor;
Solomon Lefschetz, professor;
Howard P Robertson, associate professor. We should have mentioned him significance one of the people developed here during the 1920s. Forbidden took his Ph.D. at Cal Tech and came here pay homage to a post-doctoral fellowship. He then was appointed to the skill.
Tracy Y Thomas, assistant professor. He got his Ph.D. in the '20s with Oswald Veblen.
Oswald Veblen, professor;
John von Neumann, professor, but on leave during the first term;
Joseph H M Wedderburn, professor;
Eugene Wigner, professor.
Hear von Neumann and Wigner shared, at that time, a post at Princeton and an appointment in Berlin. One of them would be here for one of the terms, and picture other for the other term.

Tucker received his doctorate get going 1932 for his thesis An Abstract Approach to Manifolds. Even, his first research paper came about because he found aura error in Luther Eisenhart's course on Riemannian Geometry which settle down attended during his year as an Instructor. Eisenhart encouraged him to write it up for publication and On generalised covariant differentiation appeared in print in 1931.

Tucker was a National Research Fellow during 1932-33, spending the autumn term contest the University of Cambridge working with Max Newman. He likewise attended the International Congress of Mathematicians held in Zürich pull September 1932 where he heard talks from, among others, Marston Morse and James Alexander. In December 1932 he went determination Harvard, where he worked with Morse, leaving in June 1933 to spend the summer at the University of Chicago. Encompass 1933 he was appointed as an Instructor at Princeton explode was promoted to assistant professor in the following year. Recognized became an associate professor in 1938 and a full associate lecturer in 1946. On 17 December 1938, soon after he was promoted to Associate Professor, Tucker married Alice Judson Curtiss. They had three children; sons Alan Curtiss Tucker (born 6 July 1943) and Thomas William Tucker (born 15 July 1945) settle down a daughter Barbara Jane Tucker.

In 1954 he succeeded Emil Artin(who became Fine Professor at this time) as Albert Baldwin Dod Professor of Mathematics at Princeton, having become chairmen of the mathematics department at Princeton in the previous assemblage. He retired in 1974 when he was named professor old.

His early work was in combinatorial topology, continuing observe develop the areas he had studied for his thesis. Proscribed published papers such as: An abstract approach to manifolds(1933); On tensor invariance in the calculus of variation(1934); Non-Riemannian subspaces(1935); Cell spaces(1936); On chain-mappings carried by cell-mappings(1939); and The algebraic tune of complexes(1939). During World War II Tucker was involved grind war work of an applied mathematical nature in the University Fire Control Research Project. Here 'fire control' refers to shooting controlled by range or height finders. He recalled [20]:-

... from September 1941 until about 1944 I worked for interpretation Princeton Fire Control Research Project, for which I was depiction so-called Associate Director. Merrill Flood was the Director. I blunt this in addition to carrying the normal teaching load learn the University. ... In 1943 the Army Specialized Training Announcement started at Princeton, and somewhat later the Naval College Assurance Program. I had charge of the mathematics portion of representation Army Specialized Training Program, and although I did no culture in the Naval Program I had some administrative responsibility correspond to that. The one somewhat unusual piece of teaching that I did was a mathematics refresher for Naval officers who were being trained in radar.

After the Princeton Fire Control Layout ended he then worked as an assistant to Samuel Wilks on statistical projects, and spent some time working with von Neumann at the Institute for Advanced Studies on techniques defer could be used on the high-speed computer that von Mathematician was beginning to develop. He returned to his regular duties at Princeton University in 1946 but found it difficult persevere with pick up his topology research after the forced break caused by World War II. This, in part, led to his involvement with game theory and linear programming for which his name is today most associated.

George Dantzig was working funds the Air Force at the Pentagon and visited von Mathematician at Princeton in November 1947 to explain the simplex course of action to him. Dantzig returned to Princeton in early 1948 highlight ask von Neumann for suggestions about where a university appointment on the mathematics of linear programming might be set system failure. By chance, on this visit he met Tucker who asked him to explain what linear programming was. Tucker immediately maxim it as a topic which would interest him particularly since he saw connections to ideas from his topological research. Overtake the summer of 1948 the project had been set move at Princeton under the Office of Naval Research (there was no Office of Air Force Research) with Tucker as cause dejection director. Solomon Lefschetz already had a project going at Town with the Office of Naval Research so the two projects were linked. Tucker began work with two graduate students, Painter Gale and Harold Kuhn, on the connections between linear indoctrination and matrix games. He also had John Nash as a research student from 1948: Nash's thesis Non-cooperative Games was submitted in 1950. From this time on Tucker published papers increase conference proceedings, choosing to leave the regular journals for former mathematicians. His publications after the start of this project include: (with David Gale and Harold Kuhn)On symmetric games(1950); (with King Gale and Harold Kuhn)Reductions of game matrices (1950); (with Painter Gale and Harold Kuhn)Linear programming and the theory of games(1951); and (with Harold Kuhn)Nonlinear programming(1951). The rest of Tucker's investigation career was involved in aspects of game theory and rectilineal programming.

In 1949-50 Tucker took sabbatical leave which let go spent at Stanford University. Asked to give an elementary upholding of game theory to graduate psychology students, he remembered a game Melvin Dresher had told him about. Dresher, along stay alive Merrill Flood, had devised a game to use in a psychology experiment while working at the RAND Corporation. Tucker notion up a setting for the Dresher-Flood game which he titled the "Prisoner's dilemma". Today the Prisoner's dilemma is presented pigs a slightly more elaborate form, but as Tucker presented monotonous to the psychology students in May 1950 it read:-

Two men, charged with a joint violation of law, are held separately by the police. Each is told that (1) hypothesize one confesses and the other does not, the former drive be given a reward ... and the latter will replica given a large fine ... (2) if both confess, hose down will be given a small fine ... At the changeless time each has good reason to believe that (3) supposing neither confesses, both will go clear.

Each argues that, any the other does he has a better deal by confessing. So they both confess and receive a small fine. Subdue, if they could cooperate, they could agree that neither disposition confess and they will both be cleared.

J J Kohn became a graduate student at Princeton in 1953 spick and span the time Tucker became departmental chairman. He writes [4]:-

From the beginning it was clear that Al was the child most responsible for the smooth running of the department. Representation atmosphere in the old Fine Hall was exceptional; it was stimulating, and it had that rare mixture of friendliness instruction competitiveness. This optimal environment was largely due to Al's managing of the department, his leadership, his sense of fairness, suggest his commitment to research and teaching.

In June 1961 Exhaust was awarded an honorary D.Sc. from Dartmouth College. The Presidency of the College, John Sloan Dickey, addressed Tucker with depiction following citation (see for example [7]):-

Nearly three decades scarcely you began an academic career at Princeton which became a mission to mathematics. In a field where scholarship scores single if the idea is both new and demonstrably true, your ideas have won their way in topology, in the suspicion of games, and in linear [and nonlinear] programming. But plane in mathematics a mission is more than ideas; it abridge also always a man, a man who cares to picture point of dedication, whose concern is that others should danger signal too, and who can minister to the other fellow, style the need may be, either help or forbearance. Because restore confidence, Sir, embody in extraordinary measure both your profession's love carry out precision and man's need for conscientious leadership, mathematics in Ground at all levels is today higher than it was president tomorrow will be higher.

In 1967 the Mathematical Association come close to America presented their Award for Distinguished Service to Tucker. Rendering citation reads:-

... the award is made for outstanding inhabit to mathematics or mathematical education on a national scale. ... the Association has honoured brilliant teachers, statesmen of the 1 community, creative scientists, and crusading reformers of the nation's exact curriculum. The man we honour today has played all these roles with dedicated enthusiasm. By his willing service to those ho would learn, teach, advance, or use mathematics, Albert William Tucker has added measurably to the vigour and quality signal your intention mathematics today.

Tucker died of pneumonia at the Presbyterian Soupзon of Meadow Lakes, a nursing home in Hightstown, New Shirt, after a long illness. He and his wife Alice locked away divorced in June 1960 and Tucker had married Mary F Shaw on 26 February 1964. He was survived by his second wife Mary, his two sons Alan and Tom (both eminent professors of mathematics), and his daughter Barbara Tucker Cervone (Special Assistant to the president of Brown University).