Preserved among the papers of the late Max Wyman, '37 BSc, '82 LLD (Honorary), in the University of Alberta's archives is a draft of a letter dated 20 December 1945. Written in Wyman's own hand, it begins: "Dear Professor Einstein ..."
In the letter, Wyman informs Einstein that he had been asked to review the latter's paper on "The Influence of the Expansion of Space in the Gravitational Fields Surrounding Individual Stars," written with E.G. Straus. And then come these remarkable words:
"I believe that there is a rather serious error in the paper ..."
And there was. The paper had assigned a positive value to a term that should have been negative. It turned out to have been simply a mistake made when the paper was being reworked for publication, but Einstein responded to the correspondence with great interest because Wyman had included with his letter, "a rigorous solution of the field equations" underlying the paper. Not only had Wyman understood the work and spotted the error, he had solved the equations — something Einstein and Straus hadn't accomplished.
This was acknowledged in a letter Wyman received back from the Institute for Advanced Study at Princeton, New Jersey. Written for Einstein by Straus, it reads, in part:
"Professor Einstein and I were both very interested in your explicit solution to the field equations. We have since been able to show that all solutions of the field equation (2) can be transformed into the Schwarzchild solution, a fact of which we were not aware of at the time our paper was written. With this fact in mind your conclusion, that the explicit solution can be made to satisfy the boundary conditions (4), proves the same thing as part III of our paper."
Who was Max Wyman, this person who could correct Einstein's work and capture his attention? In 1945 he was a 29-year-old assistant professor of mathematics at the University of Alberta. He would later become the University's president — the first native Albertan and first U of A alumnus to hold that office.
Throughout his life he firmly believed that no group or individual had exclusive access to truth — it was important to listen to the voice of dissent, for great discoveries could emerge from the unlikeliest quarters.
As president of the University from 1969 to 1974 and as its vice-president (academic) before that, Wyman helped open up the University. When he died in 1991, he was saluted for his quiet dignity and the role he played in transforming the University into an institution where research flourished and graduate students became part of its communal life.
While Wyman's administrative contributions are well remembered, what is sometimes forgotten is his prodigious talent as a mathematician. For years a standing joke in the mathematics department was "What's the fastest way to solve a differential equation? Show it to Max Wyman." And the University's stature in the area of cosmology — a pursuit now identified as one of its areas of excellence — is a legacy that can be traced to Wyman's early interest in relativity theory.
In 1950 a bright young South African eager to understand Einstein's unified field theory was sifting through mathematical journals in the University of Cape Town library when he opened the latest Canadian Journal of Mathematics. In it he discovered Max Wyman's 1950 paper that unveiled the completely spherical symmetric solution of the theory. "It bowled me over," recalls Werner Israel, who would go on to become a world expert on black holes and a close collaborator with Stephen Hawking, the most celebrated physicist since Einstein.
In 1958 Israel accepted a position in the Department of Mathematics at the U of A. The magnet that drew him was Max Wyman. "He was doing things beyond Einstein," says Israel.
At that time not many people were working on the unified field theory. "It was a select group that included Schrodinger, the discoverer of wave mechanics, as well as Einstein himself," recalls Israel. "And in his mathematical penetration of the theory, Max went beyond everyone else," says Israel, who is now retired and living on the West Coast, where he's an adjunct professor at the University of Victoria. (For information about Israel's career see the Great Canadian Scientists Web site at fas.sfu.ca/css/gcs/.)
Wyman was the first to solve the equations underlying the unified field theory — and the results were disappointing. "Einstein must have felt very depressed," speculates Israel, for Wyman's solution proved to be a nail in the coffin for the theory which Einstein had hoped would effectively merge his theory of gravity with Maxwell's theory of the electromagnetic force and, in so doing, remove some of quantum theory's rough edges.
As brilliant as his contributions to relativity theory were, Wyman didn't confine his scholarly attention to the mathematics of relativity. His "beautiful" papers on Einstein's theory represented less than half of his research interest, notes Israel. "He was one of those rare scientists who establish international reputations in two quite separate fields."
Wyman's other research specialty was in the area of asymptotic expansions, the arm of mathematics that deals with equations too complex to yield an exact answer (chaotic systems, for example) — the best that can be done is to describe properties of their behavior after a long time.
Wyman's penchant for mathematics developed early. Born in Lethbridge he moved with his family to Edmonton where he attended Strathcona High School. There his grade 12 math teacher, recognizing his talent, brought in a first-year university calculus text to keep him occupied. By the time he graduated from high school, Wyman had worked through every problem in the book. And when he entered the U of A in 1932 at age 16, he was able to persuade the mathematics department to let him enrol in second year calculus.
It wasn't a move the department would regret: when he graduated in 1937 he took with him the department's top award, as well as the Governor General's Gold Medal. Along the way Wyman had also claimed prizes in English and chemistry and a handful of scholarships. But not all his accomplishments during his University years were academic: he also won an Alberta junior golf championship. (An avid golfer and passionate curler throughout his life, Wyman was also fond of testing his analytical abilities at the race track.)
Only three years after leaving the U of A, Wyman received his PhD magna cum laude from the California Institute of Technology — a remarkable accomplishment made even more so because he had finished all of the requirements for the degree in two years and one quarter: he had to wait two academic quarters to graduate while fulfilling his residency and teaching requirements.
Wyman's PhD thesis was in the area of abstract spaces and he had also done original work in the area of complex analysis during his first years at Caltech. It wasn't until he had completed his PhD requirements and was waiting to graduate that he developed his interest in relativity theory. It was an interest encouraged by Richard Chace Tolman, a Caltech professor who wrote the 1934 text Relativity, Thermodynamics and Cosmology.
Tolman wasn't the only inspiration Wyman found at Caltech. Among his teachers and fellow students were some of the greatest mathematicians and physicists of this century. From the beginning, Wyman's interests tended to straddle mathematics and physics, and he often joked that neither side would claim him: the mathematicians considering him a physicist, the physicists regarding him as a mathematician.
At Caltech he attended classes and lectures given by such scientific luminaries as Wolfgang Pauli, who in 1930 postulated the existence of the neutrino; J. Robert Oppenheimer, later director of the Manhattan Project; Enrico Fermi, who would one day have a chemical element named after him; Paul Adrian Dirac, who shared the 1933 Nobel Prize in Physics with Schrodinger; Fritz Zwicky, who discovered more than 120 supernovas; and Henry Norris Russell, famous for his theory of stellar evolution.
Two of Wyman's good friends at Caltech were William A. Fowler and Charles Townes. Fowler, with whom Wyman attended football games, shared the 1983 Nobel Prize in Physics for his work establishing how chemical elements are formed in nuclear reactions, especially in the evolution of stars. Townes received the Nobel Prize in 1964 for his role in the invention of the laser.
When he left Caltech, Wyman accepted a wartime position with the National Research Council in Ottawa. He spent two years there — with a year lecturing at the University of Saskatchewan sandwiched in between — before returning to Alberta in 1943 to teach at the U of A. Teaching loads at the University were heavy in those years. The demands of the classroom left little time or energy for original research. During the school year Wyman kept abreast of developments in his areas of interest the best he could, and each summer he turned his attention to problems that interested him.
It was an unsatisfactory arrangement, however. The complexity of his work was such that each year he would have to painfully regain much of the knowledge he had acquired the summer before, and he saw the need for change. As head of the math department, then dean of science, then vice-president (academic), and later as president of the University of Alberta, he was instrumental in modifying teaching loads, allowing the University to evolve into a modern research university.
In assessing Wyman's contributions to the University, the late Henry Kreisel, who succeeded him as vice-president (academic), acknowledged Wyman's role in transforming the University. "No person has had a greater role in the development of the University of Alberta from the mid-1950s to the mid-1970s, and in the quantum leap that transformed it from a relatively small institution to one of national, and in some areas of international, significance, than Max Wyman," said Kreisel at the memorial service held for Wyman in February 1991.
But Kreisel believed that Wyman had made an even greater contribution: When all is said and done, it may well be that his greatest achievement will have been that he opened the University. In a public institution there were to be no secrets . He believed passionately that people should be able to express themselves freely and without fear. He believed that no one had a monopoly on truth and that great discoveries often emerged from the most unexpected quarters.
When he left office as president of the U of A, Wyman became the first chair of the Alberta Human Rights Commission. Later, he served on the Kirby Commission, which was charged with looking at the state of Alberta's lower courts.
But he was always a mathematician at heart. Jean Forest, a former chancellor of the U of A who now sits as a member of the Canadian Senate, tells of Wyman phoning her early one morning — he knew she was an early riser — when they both served on the Human Rights Commission. He had exciting news, he told her: he had just woken up with the solution to an equation that had baffled mathematicians for years. When she laughingly informed him that the only news that normally caused that sort of excitement in her home was the birth of a baby, Wyman had a quick rejoinder: after 20 years of gestation, this was a baby worth writing home about.
When he died just weeks short of his 75th birthday, Wyman had a lifetime of accomplishments in which he could take pride. In recognition of his contributions to science he had been made a fellow of the Royal Society of Canada in 1951 — at the time, the youngest person ever elected to the Society — and many other honors had followed. But he never forgot his pride in that letter written when he was not yet 30 years old. It is perhaps his best memorial. "Dear Professor Einstein ..."
Published Winter 1997/98.