Caroline Turnage-Butterbaugh featured as keynote speaker at 2026 Joint Mathematics Meetings

In early January, Caroline Turnage-Butterbaugh, associate professor of mathematics, gave an invited address at the 2026 Joint Mathematics Meetings (JMM) in Washington, D.C. Organized by the American Mathematical Society (AMS), this event is the largest annual gathering of mathematicians worldwide, attracting over 5,000 attendees. While approximately 3,000 researchers give short talks at the conference, only around 40 are invited to deliver keynotes. Turnage-Butterbaugh was one of four mathematicians who spoke in the AMS Current Events Bulletin Session. 

“The Current Events Bulletin Session at the Joint Mathematics Meetings, begun in 2003, is an event where the speakers do not report on their own work, but survey some of the most interesting current developments in mathematics, pure and applied,” according to the AMS.

Speakers for this session are selected by their peers for their research expertise and excellence in exposition. In addition to their talk at the JMM, the speakers also write an accompanying expository paper on the topic. 

Last June, Turnage-Butterbaugh received the invitation to speak on the recent breakthrough work of MIT professor Larry Guth and Oxford University professor and 2023 Fields medalist James Maynard. Their work is in Turnage-Butterbaugh’s research field of analytic number theory, which studies the prime numbers using techniques from complex analysis. Reflecting on her preparation method, she described how she studied the history of progress leading up to Guth and Maynard’s result, and what it took to come to their conclusion, rather than just the conclusion itself.

“The type of result [Guth and Maynard] proved is something called a ‘zero density result.’ Instead of starting with how the earlier such results are proved, I thought to myself, ‘Okay, if I was going to start from scratch, what would I try?’” she said.

“When I give talks on my own research, my goal is to invite people in and have them say, ‘Maybe I’ll go read her paper,’” Turnage-Butterbaugh said. “Then you get to the paper and it’s more technical, but you’ve already got the essence of what’s going on.”

Turnage-Butterbaugh is now in the process of publishing her paper in the Bulletin of the American Mathematical Society. While she acknowledges that the process has been a “big lift,” she doesn’t think hard work and enjoyment can’t go hand in hand — a belief she also carries when teaching undergraduates at Carleton.

“I think [the keynote address] really aligns with a lot of what I like about Carleton,” she said. “We do really good, interesting mathematics here, but we also have fun!”

Turnage-Butterbaugh was quick to thank those who have supported her along the way, including the wider mathematics community and her mentors. From them, she has learned the importance of making connections and asking questions, a lesson she passes on to aspiring mathematicians.

“Talking to other people, getting to know them, and asking questions is my number one piece of advice, and I thank my PhD adviser for teaching me that,” she said. “He was the one who told me, ‘You need to give talks so people know who you are.’ He was right.”

Being selected as a keynote speaker at the Joint Mathematics Meetings is an honor that signifies the wider mathematics community appreciates one’s work and presentation skills. In her lecture, Turnage-Butterbaugh used curiosity and excitement to emphasize that celebrated mathematics is not just about results, but about how ideas are shared.