Curtis T. McMullen

From the American Mathematical Society:

"Curtis T. McMullen has been awarded a medal primarily in recognition of his work in the fields of geometry and 'complex dynamics,' a branch of the theory of dynamic systems, better known perhaps as chaos theory. Curtis T. McCullen's conclusion was that there is definitely no such universal algorithm for equations above degree three; only a partially applicable method is possible. For degree-three equations he developed a 'new' Newtonian method and could thus completely solve the question of approximation solutions. … Curtis T. McMullen made a major advance, however, when he showed that it is possible to decide in part on the basis of the Mandelbrot set which associated dynamic system is 'hyperbolic' and can therefore be described in more detail. For these systems a well-developed theory is available. McMullen's results were suspected already in the sixties, but nobody had previously been able to prove this exact characterization of the Julia set."

"1998 Fields Medalist Curtis T. McMullen," AMS

Fields Medalist, 1998