The 2018 Nobel prize in economics was awarded to Paul Romer and Richard Nordhaus for their contribution to the economic theory of growth. This theory still relies heavily on the one-good one-agent model introduced in 1928 by Frank Ramsey in Cambridge. Richard Nordhaus around 1990 introduced a damage function into the model to account for climate change. But surely there must be something wrong with a model that concludes that a global warming of 3°5 by the end of the century, way beyond the 2°C limit which is considered safe by the IPCC, is somehow "optimal" ? In this talk I will review some of the issues which face economic growth models as a way to understand our future on this planet, and the mathematical challenges which they open up.