Notre Dame Mathematics

10/12/2026

10/11/2026

T-minus one week until fall break! Go Irish, Beat Midterms ☘️

10/07/2026

What do math and astronomy have in common? More than you might think!

From understanding the elements that make up stars to exploring how those elements are formed, mathematics gives us the tools to uncover the patterns and processes behind our universe. 🔭📐

For our physics PhD students, math isn’t just about numbers—it’s a way of asking bigger questions about how the universe works.

10/03/2026

What is Topology? 🔵🍩

Meet Juanita Pinzón-Caicedo, Assistant Professor of Mathematics in Notre Dame Science, whose research explores topology and the mathematics of shapes and spaces across dimensions.

From understanding when two spaces are fundamentally the same to asking what information survives when a space is transformed, topology gives mathematicians a different way to think about geometry.

So what exactly is topology, why does it matter, and what do donuts have to do with any of this? Watch to find out.

10/02/2026

What is Topology? 🔵🍩

Meet Juanita Pinzón Caicedo, Assistant Professor of Mathematics in Notre Dame Science, whose research explores topology and the mathematics of shapes and spaces across dimensions.

From understanding when two spaces are fundamentally the same to asking what information survives when a space is transformed, topology gives mathematicians a different way to think about geometry.

So what exactly is topology, why does it matter, and what do donuts have to do with any of this? Watch to find out.

09/26/2026

Game day fun meets the joy of math! 🧮☀️ Math Fest and Astro Fest brought interactive games, hands-on activities, and big smiles to campus on football Saturday. Thanks to all the little mathematicians and future scientists who joined us! 🍀

Join us next time on Friday, October 9th (12-3pm) for Insect Fest at the Eck Visitors Center Backyard before the Stanford vs. ND game!

Comment below what famous mathematicians you can spot in these photos. 🧠

09/14/2026

What are Partial Differential Equations? 🌊📐

Meet Matt Novack, Associate Professor of Mathematics in Notre Dame Science , whose research focuses on fluid mechanics, kinetic theory, and the equations that help us understand how complex systems evolve.

Matt, as a Domers On A Bench ☘️ , shares how PDEs show up everywhere from waves and fluids to some of the deepest questions in analysis.

So what exactly is a partial differential equation, and what makes these equations so interesting to mathematicians? Watch to find out.

Along the way, Matt also touches on the Navier-Stokes Millennium Prize Problem and shares some thoughts on what AI could mean for the future of PDE research.

08/31/2026

08/29/2026

08/28/2026

Hello! My name is Camilo Nunez-Reyes, and I am an undergraduate Physics and Math major here at Notre Dame! Throughout this past summer, I had the opportunity to research the Borsuk-Ulam Theorem via Topology. I would describe Topology as the study of Mathematics where shapes and spaces are made out of clay and rubber bands! A common joke in Topology is that Mathematicians can’t tell the difference between a donut and a mug, because they are homeomorphic. This means there exists some function that can grab the mug and transform it into a donut without losing any information, and vice versa without losing any information about the mug or donut! We can say many shapes are homeomorphic if they follow this criterion, for example it is provable that a diamond and a circle are topologically identical! Where Topology becomes particularly powerful is in recognizing that we can prove shapes are homeomorphic in any number of dimensions, allowing for great generality. Because of this trait, Topology plays an important role in many areas of Physics, such as Quantum Field theory, String theory, and even General relativity!

To best understand the Borsuk-Ulam Theorem itself, I invite you to consider a function that flattens a circle onto a number line, like squishing a hula hoop onto the ground. What the Borsuk-Ulam Theorem argues is that, no matter how you flatten this circle onto the number line, two points on this circle when flattened must meet at the exact same point. Of course, being Topology, the Borsuk-Ulam Theorem works with any sphere of dimension n being mapped onto a real space of dimension n. Overall, researching the Borsuk-Ulam Theorem as a sophomore was intellectually challenging, but it was an amazing experience! I would like to give a special thank you to my teammates, Liviu Nicolaescu, mentors, and the Galvin Scholars Program and Notre Dame Science for assisting with the research process!