Abstract: Research activities in nonlinear science over the past three centuries are reviewed, paying particular attention to the explosive growth of interest in chaos, solitons, and reaction-diffusion phenomena that occurred during the 1970s and considering whether this explosion was an example of a scientific revolution or Gestalt-like paradigm shift as proposed by Thomas Kuhn in 1962. The broad structure of modern nonlinear science is sketched and details of developments in several areas of nonlinear research are presented, including cosmology, theories of matter, quantum theory, chemistry and biochemistry, solid-state physics, electronics, optics, hydrodynamics, geophysics, economics, biophysics and neuroscience. It is concluded that the emergence of modern nonlinear science as a collective interdisciplinary activity was a Kuhnian paradigm shift which has emerged from diverse areas of science in response to the steady growth of computing power over the past four decades and the accumulation of knowledge about nonlinear methods, which eventually broke through the barriers of balkanization. Implications of these perspectives for twentyfirst-century research in biophysics and in neuroscience are discussed