Mathematics professor receives Frontiers of Science Award
Matt Stoffregen, an assistant professor of mathematics at Michigan State University, has been honored with a Frontiers of Science Award from the International Congress for Basic Science (ICBS) for his work in knot theory and topology. The Frontiers of Science Award, established in 2023, honors top research, with an emphasis on achievements from the past 10 years which are both excellent and of outstanding scholarly value.
Stoffregen was a co-author of the paper, “The (2,1)-cable of the figure-eight knot is not smoothly slice,” which was one of 86 mathematics papers selected for the award. Overall, 148 academic papers were honored by the ICBS. The other co-authors honored with Stoffregen included Irving Dai from the University of Texas at Austin, Sungkyung Kang from the University of Oxford, JungHwan Park from the Korea Advanced Institute for Science and Technology and Abhishek Mallick from Rutgers University. Mallick received his Ph.D. from MSU in 2021 and is now a tenure-track assistant professor at Dartmouth College.
In the paper, the five mathematicians disproved one of the most fundamental questions about four-dimensional topology. Posed over 60 years ago by Ralph Fox, the slice-ribbon conjecture is the claim that all slice knots are ribbon.
In math, a knot is like taking a loop of string, tangling it up any way you want, and then gluing the ends together so that it forms one closed loop. A knot is called “slice” if it can be flattened into a smooth disk without tearing or crossing over itself in four-dimensional space. A ribbon knot is a special knot that that twists and folds in space, but in a way that it always looks like it came from something flat. The slice-ribbon conjecture asks the question, “is every slice knot a ribbon knot?”
Mathematicians have asked this question for decades as they work to understand 4D space and how shapes work in higher dimensions. In 1980, Akio Kawauchi showed that the (2,1)-cable of the figure knot is almost slice, and in 1994, Katura Miyazaki proved that it was not ribbon. That left the knot as a good candidate for Stoffregen and the team of researchers to show that the slice-ribbon conjecture was false.
The quintet is continuing to develop tools for proving that knots are not slice. The problem, according to Stoffregen, is not the knots in question, but developing machinery powerful enough to certify that the knot is not slice.
The Frontiers of Science awards were presented at the 2025 meeting of the ICBS, held July 13-25, 2025, in Beijing, China. The annual event brings together leading experts to celebrate basic sciences – mathematics, physics, information science and engineering.
- Categories: