This work explores the combination of free cloud computing, free open-source software, and deep learning methods to analyse a real, large-scale problem: the automatic country-wide identification and classification of surface mines and mining tailings dams in Brazil. Locations of officially registered mines and dams were obtained from the Brazilian government open data resource. Multispectral Sentinel-2 satellite imagery, obtained and processed at the Google Earth Engine platform, was used to train and test deep neural networks using the TensorFlow 2 API and Google Colab platform. Fully Convolutional Neural Networks were used in an innovative way, to search for unregistered ore mines and tailing dams in large areas of the Brazilian territory. The efficacy of the approach is demonstrated by the discovery of 263 mines that do not have an official mining concession. This exploratory work highlights the potential of a set of new technologies, freely available, for the construction of low cost data science tools that have high social impact. At the same time, it discusses and seeks to suggest practical solutions for the complex and serious problem of illegal mining and the proliferation of tailings dams, which pose high risks to the population and the environment, especially in developing countries. Code is made publicly available at: https://github.com/remis/mining-discovery-with-deep-learning.