Sketching the Future - Profile Luis Caffarelli

In mathematics, as in any other field, there are those rare individuals who quietly dedicate themselves to the art of collaboration and the pursuit of understanding. Professor Luis A. Caffarelli is one such figure, whose humility and commitment to teamwork have given him the unique reputation of being more likely to share an insight across the water cooler than to publish it in a journal. 

Rather than chasing personal glory, he has made a career out of embracing the banality of progress. In an ironic but inarguably well-deserved twist, it is likely this quality that has built him into one of the most lauded mathematicians of our time. 

As he transitions into retirement, Caffarelli remains deeply connected to the mathematical community. "I still feel that I'm engaged in the community, and students continue to seek guidance from me." This highlights his enduring influence on the next generation of mathematicians and his ongoing commitment to fostering mathematical endeavors.

Throughout his career, Caffarelli's primary focus has been on non-linear partial differential equations, particularly the Monge–Ampère equation and equations that describe flow in porous media. These complex mathematical challenges had stymied mathematicians for years, but in 1990, Caffarelli embarked on a series of papers that brought fresh insights and opened new avenues for understanding the existence and uniqueness of solutions. His work in this area has become a cornerstone for researchers worldwide.

Caffarelli's journey through mathematics commenced in his hometown of Buenos Aires, Argentina. His academic path led him to the University of Buenos Aires, where he pursued his undergraduate and graduate studies. His formative years in the field laid the foundation for a career marked by innovation and contributions to the world of mathematics. Today, Caffarelli is a professor emeritus of mathematics at the University of Texas at Austin where he held the Sid W. Richardson Foundation Regents’ Chair in Mathematics. 

In addition to his remarkable career, Caffarelli's personal life is enriched by his enduring relationship with his wife, Irene Gamba. Both faculty members at the Oden Institute for Computational Engineering and Sciences, they have been married for 40 years and have raised three children. Their partnership is a testament to the power of love and support that has allowed them to flourish both personally and professionally.

In 2012, Caffarelli was awarded Israel's Wolf Prize. This prestigious recognition is reserved for individuals who have significantly contributed to various fields, including mathematics, and underscores the profound and lasting impact of his work on the world of mathematics. In May of this year, Caffarelli was awarded the Abel Prize from the Norwegian Academy of Science and Letters, a renowned award considered the Nobel Prize equivalent in mathematics. Caffarelli is the first Latin American mathematician to have received it. 

Reflecting on his lifelong passion for mathematics, Caffarelli remarked, "I have a deep affection for mathematics. I started with a strong foundation, and my love for the subject has grown over the years." 

He believes in the power of collaboration and interaction, stating, "Advances in our field often arise from interactions and the cooperative efforts of research groups, not from competition." He values the contributions of different individuals, asserting, "Progress is not about competing. It's about interacting and cooperating to create something new."

Caffarelli's contributions are documented in more than 250 scientific publications, but beyond his well-known accomplishments lies a hidden trove of unpublished work. 

“A few months ago, just after Luis’ official retirement date had been decided, I looked around his office and started thinking about what to do with all his papers,” reflected Gamba. “Well, on the top of a cabinet, I found a collection of folders full of his past lectures. It’s an amazing collection of conference speeches he gave and the drawings he made to visualize the mathematical concepts just for his own use. None of these drawings are in any of his publications, but everyone who has seen them comments about their incredible power in explaining these complex ideas."

Together with a handful of her and Caffarelli’s colleagues at the Oden Institute, Gamba plans to publish the sketches. These writings and mathematical visualizations are a testament to his creative process and the depth of his exploration. They offer a rare glimpse into the mind of the researcher, revealing the creative instincts that have been instrumental in his groundbreaking discoveries.

Luis A. Caffarelli's journey through free-boundary problems for nonlinear partial differential equations has illuminated the discipline. His legacy extends beyond his own equations and theorems to the minds he has inspired and the modes by which his work will undoubtedly shape the future of mathematics.