A mathematical couple solves a major problem with group theory – after 20 years of work

But one of Male’s graduates was the case. The Britta Spa.

“Our obsession”

In 2003, Spa arrived at the University of Cassel to start a doctorate with Male. It was almost perfectly suited to working on McKay’s assumption: even in high school it could spend days or weeks one problem. She is especially honest with those who tested her durability and courtesy recalls long hours spent in search of “tricks that are somehow not so deep.”

Spat spends his time studying group ideas as deep as he could. After graduating from her diploma, she decided to use this expertise to continue to stop at McKay’s assumption. “She has this crazy, really good intuition,” said Schaefer Fry, her friend and associate. “She is able to see that it will be so.”

With the kind assistance of Quanta magazine

Several years later, in 2010, Spa began working at Cité Paris University, where he met with Cabani. He was an expert in the larger set of groups in the center of the reformulated version of McKay Conject and Späth often goes to his office to ask him questions. Kabanes “always protested,” these groups are complicated, my God, “he recalled. Despite his initial hesitation, he also eventually fell in love with the problem. It became “our obsession,” he said.

There are four categories of lies groups. Together spat and cubans began to prove the assumption for each of these categories, and they reported several Basic results Over the next decade.

Their work made them develop a deep understanding of groups of a lie type. Although these groups are the most common building elements of other groups and therefore of great mathematical interest, their ideas are incredibly difficult to study. Cabans and Spa often had to rely on opaque theories from different fields of mathematics. But in the excavation of these theories, they have provided some of the best characteristics so far from these important groups.

As they did, they began to meet and continued to have two children. (In the end, they settled together in Germany, where they enjoyed working together in one of the three white boards in their home.)

By 2018, they had only one category of groups of the lie type. Once this was done, they would have proven McKay’s assumption.

This last case took them another six years.

“Grand achievement”

The fourth type of group is lying “There were so many difficulties, so many bad surprises,” said Spa. (This did not help that in 2020 the pandemic detained their two young children at home from a school, which made it difficult for their work. The last case was made. It followed automatically that McKay’s assumption was true.

In October 2023, they finally felt sufficiently confident in their proof to announce it in a room of more than 100 mathematicians. A year later publishes it online For the rest of the community to be absorbed. “This is an absolute spectacular achievement,” said Radha Caesar at the University of Manchester.