Cities with larger populations tend to produce more patents, showing that bigger cities are better at generating new ideas and inventions. This is because the social environment in big cities allows for more interactions among people, leading to more innovative ideas being shared and developed. The relationship between urban population size and patenting is superlinear, meaning that as the city grows, the number of patents generated grows even faster. This pattern holds true not just in the U.S. but also in cities around the world, showing that the link between population size and innovation is consistent across different urban and economic systems.