  Breakthrough discoveries and inventions involve unexpected combinations of
contents including problems, methods, and natural entities, and also diverse
contexts such as journals, subfields, and conferences. Drawing on data from
tens of millions of research papers, patents, and researchers, we construct
models that predict next year's content and context combinations with an AUC of
95% based on embeddings constructed from high-dimensional stochastic block
models, where the improbability of new combinations itself predicts up to 50%
of the likelihood that they will gain outsized citations and major awards. Most
of these breakthroughs occur when problems in one field are unexpectedly solved
by researchers from a distant other. These findings demonstrate the critical
role of surprise in advance, and enable evaluation of scientific institutions
ranging from education and peer review to awards in supporting it.
