Urban sprawl, extinct species, depletion of natural resources and global warming are all causes of deep anxiety. Here to stay takes an uncompromising look at Planet Earth today, in all its beauty but also its scars and contradictions. Illustrating the intricate relationship and contrasts between the miracles of nature and man's obsession in trying to tame them. Can we turn back the tide? What do we really want for ourselves?

The documentary looks at the modern advances in mathematics and how they affect our understanding of physics, economics, environmental issues and human psychology, as well as how developments in 20th Century mathematics have affected our view of the world, and particularly how the financial economy and earth’s environment are now seen as inherently unpredictable. The film examines the influence the work of Henri Poincare and Alexander Lyapunov had on later developments in mathematics. It includes interviews with David Ruelle, about chaos theory and turbulence, the economist Paul Ormerod about the unpredictability of economic systems, and James Lovelock the founder of Gaia theory about climate change and tipping points in the environment. As we approach tipping points in both the economy and the climate, the film examines the mathematics we have been reluctant to face up to and asks if, even now, we would rather bury our heads in the sand rather than face harsh truths.

A look at different matters of the world such as immigration, global warming and capitalism through the eyes of scientists and philosophers.