Mathematics is a dynamic and ever-evolving field. Each advance is the result of persistent effort, creative thinking, and a willingness to learn from setbacks. In this section, I spotlight recent mathematical breakthroughs that inspire me, and I share reflections on the essential role of resilience and embracing uncertainty in discovery.

I follow Quanta Magazine for its engaging coverage of recent advances in mathematics.

Reading about these breakthroughs reminds me that every major advance is preceded by countless failures. In my graph theory research, I initially overcounted configurations that looked distinct but were actually equivalent. The cyclic structure of the graphs made it especially difficult to spot overlapping cases and subtle symmetries. That experience taught me to be more meticulous with casework, more aware of structural equivalence, and more willing to question assumptions. I’ve come to see persistence and learning from mistakes as essential, not just for progress in mathematics, but for discovery itself.

Mathematics rewards resilience. Setbacks lead to learning, and small insights build toward breakthroughs. Progress comes through persistence, steady effort in uncertainty, and a willingness to explore the unknown.