Math, Mystery, and the Joy of Discovery at the College of Liberal Arts and Sciences
Sloan Research Fellow Philip Engel shares how a love of patterns and the unknown drives his work and shapes what he hopes for the next generation of mathematicians.
Interview with Philip Engel
Philip Engel, Ph.D., has always been captivated by patterns.
From a young age, he explored shapes and textures that piqued his interest, leading him to a summer program that introduced him to the world of abstract mathematics. “It was inspiring and beautiful,” Engel recalls. This experience solidified his desire to delve into the profound mysteries of mathematics.
Today, Engel’s research focuses on the Hodge Conjecture, one of the seven renowned Millennium Prize Problems. The conjecture aims to understand complex curved geometric objects, known as algebraic varieties, by examining simpler linear objects called Hodge structures.
“My area of research concerns how these curved geometric objects degenerate,” Engel explains, “similar to how a sphere can be pinched along its equator until it forms an hourglass and eventually pinches to a point.”
What keeps Engel passionate about his work is the continual sense of discovery. “I am always surprised in my research,” he says. “As you perform computations to understand the problem, an amazing tapestry is gradually revealed, weaving together all the disparate little facts you’ve learned.”
For him, mathematical research feels less like invention and more like uncovering something hidden, waiting to be understood. Engel hopes that students will experience this same sense of wonder. “I hope they acquire a sense of the beauty and wonder of math,” he says.
His advice for emerging mathematicians is to avoid specializing too quickly. Instead, he encourages students to “internalize the amazing discoveries of the past and rediscover them on their own terms.” Despite the increasing pressures of a career in mathematics, he believes that this deep exploration is invaluable.
Recently, Engel was named a 2026 Alfred P. Sloan Research Fellow in Mathematics, a recognition that energizes both his personal and professional life. He states that the fellowship “will provide the opportunity to pursue my research interests and discover beautiful new geometry, and hopefully, to share it with others.”
For Engel, the joy of mathematics lies in illuminating what has always existed—patterns and structures just waiting to be brought to light.