Nonlinear Thinking

Credit: Grant Sanderson (@3blue1brown)

Partial differential equations help researchers to explain a wide range of phenomena. But when it comes to fluctuating stock prices, the flow of blood through the body, the movement of oil through a pipe or the shape of space-time, complicated dynamics and features enter in. With them comes the need for a specific type of equation, known as nonlinear partial differential equations (PDEs). 

Earlier this year, University of Texas at Austin professor and leading expert in nonlinear PDEs, Luis Caffarelli won the Abel Prize. Considered the Nobel Prize of mathematics, the prize recognized Caffarelli’s work that “transformed our understanding of nonlinear PDEs,” as his UT colleague Francesco Maggi explains it. 

For example, Navier-Stokes equations relate to fluids in motion but aspects of the equations remain poorly understood. Consequently, the Clay Mathematics Institute offers $1 million to anyone who can solve these aspects of the equations. Caffarelli and his colleagues are considered to have come closest to doing so; they provided new insights into what mathematicians call singularities. It’s just one of many examples where his work opened up new thinking and directions that other mathematicians could build upon. 

The first person of Latin American origin to win the prize, Caffarelli holds the Sid W. Richardson Foundation Regents Chair in Mathematics #1 and is the second University mathematician in five years to win the prize. Due to his win, no public research institution in the world has had more Abel Prizes than UT Austin.