Kirby has historically been a skeptic of the existence of structural biases in mathematics, including regarding the field’s gender imbalance. In the 1970s, about 10% of mathematicians were women; today almost 30% are, according to a 2020 report by the International Science Council.

In an article that he wrote in the 1990s, and which was submitted for publication in the Notices of the American Mathematical Society but never published, Kirby made the case that these dismal numbers were not the result of any bias in the field. “In my view, the smaller number of women in math is not due to discrimination by men nor to any inherent inferiority in women, but rather is due to the simple fact that more men than women choose to enter mathematics,” Kirby wrote.

To many mathematicians, the reality that few women enter the field is anything but a simple fact. “Evidence suggests that there is a feedback effect here: because there are so few female professors, female students can’t see a clear career path through mathematics, so they decide not to pursue a Ph.D.,” wrote four prominent female mathematicians in 2022 in the Times Higher Education Supplement. As the International Science Council report put it, after analyzing a dataset of hundreds of thousands of published mathematical papers, “various structural and systemic factors must have affected the careers of female mathematicians in ways different from those of men.”

Kirby’s views are well known within the low-dimensional-topology community. I asked Kirby if he thought that made it harder for women to participate in settings like the recent conference where he had a prominent role. He said he didn’t know because, with the exception of one mathematician, no one had ever brought it up with him.

Ray, who serves as the gender equality officer at the Max Planck Institute, said “I don’t think it shaped the way the conference felt. I do think it shapes how he is viewed in the field of mathematics, but I think in general we do separate the mathematics from the mathematician.”

A Communal Effort

Just as it had after K1, low-dimensional topology advanced quickly following the release of K2. One major development was the elaboration of Seiberg-Witten theory, which used ideas from physics to distinguish between four-dimensional manifolds. By the late 2000s, the Kirby list was ready for updating again.

“The thing is, the field became much bigger since the 1990s, it became huge,” Baykur said.

This time the impetus for creating a new list came from Ruberman and Baykur. They began collecting problems around 2013. But between their other obligations and the pandemic, it wasn’t until October 2023 that they managed to gather a group of topologists to meet in person. They wanted the third version of the list to be more of a communal effort.

“The initial list was wonderful, I’m so glad it was there, but this new format is commendable in making that a bit more open,” Ray said.

In late 2022, Kirby joined Baykur and Ruberman as a co-organizer of the conference. They invited experts from the major areas of low-dimensional topology — corresponding to the same five-chapter structure Kirby had used in earlier versions of the list — but tried to avoid inviting so many specialists that no one had anything in common with anyone else.

Baykur and Ruberman did most of the organizing while Kirby took on more of a titular role.

“It’s kind of like Rob’s baby, you know, like he’s emotionally in charge. But Danny and Inanç handled all the logistics,” Miller said.

On Monday, October 30, the group began work on the K3 list (as it was called for obvious reasons and also in reference to K3 surfaces, which are important objects in topology).

The list reflected ways in which low-dimensional topology had grown since K2. In the early 1990s the work of Andreas Floer gave rise to new methods for sorting three-dimensional manifolds. By the end of that decade those methods had blossomed into an entire area of study, Heegaard Floer homology, and within that area there are now a number of different approaches to distinguishing manifolds. Those approaches should all be consistent with each other, but it’s not known for sure that they are, and K3 will include questions that aim to settle the matter.