How Student Math Research Connects to Modern Science

Connor: Dr. Wei, that idea of reduction feels central to scientific discovery. How do you see it show up in your work?

Dr. Wei: In biology and medicine, we’re constantly working with incredibly complex systems such as how proteins fold, how diseases progress, or how treatments interact with the body.

The challenge is making those systems understandable. When you can reduce complexity in a meaningful way, you move from approximation to something more precise. That’s where mathematics becomes essential. It gives us a way to focus on what actually matters.

Dr. Wei: Connor, you’ve said the methods behind your work may be more important than the result itself. Why is that?

Connor: A lot of mathematics ends up being useful in ways you can’t predict at the time. For this project, the key idea is connecting different areas of math like discrete geometry and algebraic geometry and using that connection to solve problems more effectively.

That kind of approach could apply to many different problems, anywhere you have structure, symmetry, or a large number of possibilities that need to be narrowed down.

Connor: Dr. Wei, can you share an example of how that kind of thinking applies to biomedical science?

Dr. Wei: One example is protein structure. Proteins can take on an enormous number of possible configurations, but only a small number are stable or biologically meaningful. The challenge is figuring out which ones matter.

Mathematics helps us reduce that complexity. Instead of trying everything, we can focus on a much smaller set of possibilities. That’s critical in areas like drug discovery.

Connor: Your conversation also touched on the idea of moving from approximation to exact solutions. Why does that matter?

Dr: Wei: In many areas of science today, especially with machine learning, we rely on approximation through models that can be very good, but never exact. Mathematics gives us another pathway. When you can describe a system precisely, you can sometimes solve it directly rather than estimate it.

That shift—from approximation to deeper understanding—is where breakthroughs can happen.

Dr. Wei: How do you think about the role of mathematics in solving larger challenges?

Science gives us the concepts, but math allows us to formalize them and apply them. When we’re solving big problems, the key is breaking them into smaller pieces that math can address.

Often, breakthroughs happen when someone connects ideas across disciplines.

Dr. Wei: What advice would you give to future scientists?

Connor: Follow what you’re genuinely interested in. The most meaningful work comes from curiosity, not outcomes. Find people who share your interests and focus on small contributions—they build into something bigger over time.