Brian Carey Goodwin (25 March 1931 – 15 July 2009) (Sainte-Anne-de-Bellevue, Quebec, Canada - Torbay, Devon, UK) was a Canadian mathematician and biologist, a Professor Emeritus at the Open University and a founder of theoretical biology and biomathematics. He introduced the use of complex systems and generative models in developmental biology. He suggested that a reductionist view of nature fails to explain complex features, controversially proposing the structuralist theory that morphogenetic fields might substitute for natural selection in driving evolution. He was also a visible member of the Third Culture movement.

Brian Goodwin was born in Montreal, Quebec, Canada in 1931. He studied biology at McGill University and then emigrated to the UK, under a Rhodes Scholarship for studying mathematics at Oxford. He got his PhD at the University of Edinburgh presenting the thesis "Studies in the general theory of development and evolution" under the supervision of Conrad Hal Waddington. He then moved to Sussex University until 1983 when he became a full professor at the Open University in Milton Keynes until retirement in 1992. He became a major figure in the early development of mathematical biology, along with other researchers. He was one of the attendants to the famous meetings that took place between 1965 and 1968 in Villa Serbelloni, hosted by the Rockefeller Foundation, under the topic "Towards a theoretical Biology".

Thereafter, he taught at the Schumacher College in Devon, UK, where he was instrumental in starting the college's MSc in Holistic Science. He was made a Founding Fellow of Schumacher College shortly before his death. Goodwin also had a research position at MIT and was a long time visitor of several institutions including the UNAM in Mexico City. He was a founding member of the Santa Fe Institute in New Mexico where he also served as a member of the science board for several years.

Brian Goodwin died in hospital in 2009, after surgery resulting from a fall from his bicycle. Goodwin is survived by his third wife Christel, and his daughter, Lynn.

Shortly after François Jacob and Jacques Monod developed their first model of gene regulation, Goodwin proposed the first model of a genetic oscillator, showing that regulatory interactions among genes allowed periodic fluctuations to occur. Shortly after this model became published, he also formulated a general theory of complex gene regulatory networks using statistical mechanics. In its simplest form, Goodwin's oscillator involves a single gene that represses itself. Goodwin equations were originally formulated in terms of conservative (Hamiltonian) systems, thus not taking into account dissipative effects that are required in a realistic approach to regulatory phenomena in biology. Many versions have been developed since then. The simplest (but realistic) formulation considers three variables, X, Y and Z indicating the concentrations of RNA, protein and end product which generates the negative feedback loop. The equations are

and closed oscillations can occur for n>8 and behave limit cycles: after a perturbation of the system's state, it returns to its previous attractor. A simple modification of this model, adding other terms introducing additional steps in the transcription machinery allows to find oscillations for smaller n values. Goodwin's model and its extensions have been widely used over the years as the basic skeleton for other models of oscillatory behavior, including circadian clocks, cell division or physiological control systems.

In the field of developmental biology, Goodwin explored self-organization in pattern formation, using case studies from single-cell (as Acetabularia) to multicellular organisms, including early development in Drosophila. He proposed that morphogenetic fields, defined in terms of spatial distributions of chemical signals (morphogenes), could pattern and shape the embryo. In this way, geometry and development were linked through a mathematical formalism. Along with his colleague Lynn Trainor, Goodwin developed a set of mathematical equations describing the changes of both physical boundaries in the organism and chemical gradients.

By considering the mechanochemical behaviour of the cortical cytoplasm (or cytogel) of plant cells, a viscoelastic material mainly composed of actin microfilaments and reinforced by a microtubules network, Goodwin & Trainor (1985) showed how to couple calcium and the mechanical properties of the cytoplasm. The cytogel is treated as a continuous viscoelastic medium in which calcium ions can diffuse and interact with the cytoskeleton. The model consists in two non-linear partial differential equations which describe the evolution of the mechanical strain field and of the calcium distribution in the cytogel.