Kumar Murty, former director of The Fields Institute for Research in Mathematical Sciences, left, and Dr. Deirdre Haskell, interim director, are pictured at the institute in Toronto on Aug. 11.Laura Proctor/The Globe and Mail
One hundred years ago Toronto was temporarily the centre of the mathematical universe.
The cause was a history-making gathering that almost didn’t happen, and that heralded a key moment in Canada’s emergence on the international academic stage.
For the first time, the world’s most important mathematical meeting was held outside of Europe. Somewhat improbably, it came to Toronto.
“That was an important thing,” said Kumar Murty, former director of the Fields Institute for Research in Mathematical Sciences, located just a block away from where the 1924 conference took place. “At that time Canada was not regarded as a centre of mathematics for the world. It wasn’t on the map yet.”
This week mathematicians are once again converging on the city to mark the events of a century ago, but also to reflect on the nature of their work and communicate its enchantment.
“I hope the public will get a glimpse of what’s happening in mathematics,” Dr. Murty said of the present day gathering. “It’s an extraordinarily beautiful discipline.”
It was Dr. Murty who first had the idea of celebrating the centenary of the 1924 International Congress of Mathematicians, and its organizer and chairman, John Charles Fields.
Today, Fields’s name is associated with both the institute and with the Fields Medal, an international award commonly referred to as math’s Nobel Prize.
John Charles Fields, the University of Toronto professor who organized and was the president of the 1924 International Congress of Mathematicians, hosted at U of T.The Fields Institute
But in August of 1924, Fields was a 61-year-old professor at the University of Toronto looking to pull off one of the most prestigious academic meetings in the world. That month, the streets of Toronto were “overflowing with mathematicians” by the time the congress began, said Elaine Riehm, a historian and author who has written about the event and Fields’s role.
At a time when only a handful of academics were pursuing high level mathematics in Canada, more than 450 delegates converged on the city, making the trip by steamship and train, to present talks on algebraic geometry and group theory among other topics of the day.
Perhaps because the contents of the meeting were impenetrable to journalists covering the event, a report in The Globe fixated instead on the numbers and nationalities of those present, including “five Norwegians, five Russians, four Spaniards” along with assorted Danes, Poles, Czechs, Belgians and others.
The largest contingent was from the United States, followed by Britain and France. Conspicuous by their absence were any participants from Germany, a global powerhouse for the discipline.
Lingering bitterness over the First World War had sparked an impasse over whether German mathematicians should be invited to the gathering, which was supposed to have taken place in New York.
Toronto emerged as an alternate location, thanks to the efforts of Fields, a Hamilton native who was both an intellectual and avid world traveller with a Canadian aptitude for diplomacy. He would prove to be an ideal impresario for the meeting.
“Although not ambitious mathematically himself, he was ambitious for research,” Ms. Riehm said. “He thought he could do it and he thought he could raise the money.”
Fields also has another purpose in mind: to raise the profile of math and science in a country more preoccupied with harnessing its natural resources than with developing intellectual capital.
At the same time, Fields created a program that made room for applied science as a worthy partner to the more abstract and theoretical forms of mathematics that many of the delegates specialized in. The point, he said, was to show the public “that practice cannot be divorced from theory and that the pure scientist does his share in contributing to the well-being of the community.”
One hundred years later that distinction is far less sharp, said Deirdre Haskell, the Fields Institute’s interim director and host of this week’s meeting in Toronto.
As a case in point, Dr. Haskell cited the British mathematician G.H. Hardy who famously boasted in 1940 that nothing he had discovered was “useful” in the practical sense of the word, because it was purely an aesthetic pursuit.
“Nowadays, we know that a lot of what Hardy did in number theory is totally relevant to cryptography and it was very applied,” Dr. Haskell said.
Attendees at the 1924 International Congress of Mathematicians pose for a photograph outside of the University of Toronto's Convocation Hall, where the proceedings were held. Seated on the ground, third from the left, is John Charles Field, the organizer and chairman of the historic meeting who later helped to establish the Fields medal, the most coveted prize in mathematics.The Fields Institute
The same is true for the mathematics that undergirds the AI revolution. One panel at this week’s meeting will be dedicated to the topic, including the question of how future algorithms can be trained to prove theorems on their own.
No doubt such a possibility would astonish the mathematicians of 1924, and it raises the question of how mathematical achievements will be recognized in the future once machines are participating in the act of discovery.
Fields died in 1932. Four years later, the medal that bears his name was awarded for the first time and since 1950 it has been given at four-year intervals to recipients under the age of 40.
That tradition has probably helped to reinforce the image of elite mathematicians in popular culture as young geniuses – usually male – toiling in isolation.
This a stereotype Dr. Haskell said she would like to change, by showing that the profession is increasingly more diverse and collaborative.
It’s the prospect of collaboration that makes face-to-face meetings as important now as they were in 1924, said Martin Hairer, a Fields Medal winner based at the Swiss Federal Institute of Technology who is participating in this week’s event in Toronto.
For Dr. Haskell, another important reason – and another way in which this week’s meeting differs starkly from the 1924 congress – is the presence of women and people of diverse backgrounds in the mathematical community.
While strides have been made in this area, she said, there is still a long way to go.
“We lose girls, we lose recent immigrants just because they don’t see math as a way forward,” she said. “And that’s something that we have to change as a culture.”