Kinderlehrer Uses Math to Build Bridges Across Disciplines
Heidi Opdyke
- Associate Dean of Marketing and Communications, MCS
- Email opdyke@andrew.cmu.edu
- Phone 412-268-9982
In a world where mathematicians and scientists don’t often speak the same language, David Kinderlehrer makes collaboration across disciplines not only possible — but transformative.
“David’s contributions are staggering. He has made an impact in so many areas within analysis and math but also in physics, biology and beyond. It’s incredible,” said Irene Fonseca, Kavčić-Moura University Professor of Mathematics and one of Kinderlehrer’s first graduate students.
Driven by curiosity and a desire to explore the unknown, Kinderlehrer tackled fundamental issues that bridge mathematics and the natural world. He was a pioneer in unraveling the mathematical mystery of liquid crystals, the key components in television and smartphone displays. And he was a leading force in changing completely the landscape of mathematical analysis in materials science.
“A lot of very fundamental issues between mathematics and the natural world remain unresolved. It is very meaningful to explore these questions with deep mathematics, and quite beautiful too,” said Kinderlehrer, Alumni Professor of Mathematical Sciences and Professor of Materials Science and Engineering.
Kinderlehrer didn’t start out applying his mathematical insights to other disciplines. Early in his career, he was focused on fundamental analysis of partial differential equations (PDE). A textbook he co-authored with his postdoctoral advisor, Guido Stampacchia, in the early ‘80s is a classic in the field and is still a go-to reference for free boundary problems.
In the 1990s, his work in PDE led to a breakthrough. Together with CMU postdoctoral researchers Richard Jordan and Felix Otto, Kinderlehrer developed what became known as the Jordan Kinderlehrer Otto (JKO) scheme, which revealed the relationship between the Gibbs-Boltzmann entropy and diffusion. In the twenty-seven years since its publication, the JKO paper has been cited more than 2,300 times, with many applications across the physical and biological sciences as well as in machine learning and artificial intelligence.
“David’s work changed the way that people in mathematics approach applications with a very solid, profound mathematical basis,” Fonseca said.
One of Kinderlehrer’s most impactful collaborations began with a challenge in materials science: understanding how grain boundaries — interfaces between the crystallites that comprise most engineered materials — evolve under heat or pressure. These boundaries affect a material’s strength, durability, and conductivity.
Materials scientists, including the team at Carnegie Mellon, wanted to understand how grain boundaries evolve so that they could engineer better-performing materials. So they reached out to Kinderlehrer.
“At the time, we had little understanding of how the grain boundary network would evolve. That’s what we had to discover,” said Kinderlehrer. And they did. The team created a new mathematical framework to describe how grain boundaries shift toward a more stable, low-energy state — a major advance in understanding how materials evolve.
“It’s very rare for materials scientists and mathematicians to collaborate,” said Greg Rohrer, W.W. Mullins Professor and University Professor of Materials Science and Engineering. “There are some differences in concepts and methods that are hard to bridge. David has always made that easy for us.”
Kinderlehrer’s efforts extend to the life sciences as well. Most importantly, he created and taught an undergraduate course in mathematical biology. “There’s so much to expose there,” he said, “especially now that deep learning and machine learning are here, you know.”
In 1991, Kinderlehrer co-founded the Center for Nonlinear Analysis (CNA), Carnegie Mellon’s flagship applied math center. At the CNA, Kinderlehrer forged dynamic, multidisciplinary initiatives between applied mathematicians and allied scientists, and he has mentored a generation of postdoctoral researchers who now have distinguished careers in academia and industry.
As he reflects on his career as he heads into retirement, Kinderlehrer says his greatest legacy isn’t just in the equations — but in the people.
“In the final analysis,” he said, “mentoring will be my major contribution.”
