Gender equality is a fundamental human right, considered essential for the creation of a just society and a key ingredient of the United Nations Sustainable Development Goals. A key determinant of gender inequality in terms of the gender wage gap and other dimensions are the attitudes and stereotypes associated with women. Here, we investigate the evolution of gender norms for 160 years in the US. Socioeconomists have posited two fundamental and widely debated theories on the evolution of cultural norms across time. One school argues that cultural norms (including gender norms) should converge across time as economies become more advanced and globalised and technological progress allows for easier information sharing. The other school states that cultural traits are highly persistent, passed down from generation to generation and will remain divergent across regions. To test these theories quantitatively, researchers need data on attitudes measured at appropriate levels of granularity, at a high frequency and over a long time series. However, no such data currently exists. Here we propose an unsupervised machine learning methodology to measure attitudes at the document level. We apply this methodology to 193 million pages of local newspaper text to produce localised attitudes towards women on four different dimensions: career vs family, attitudes towards abortion, attitudes towards feminism/suffrage, and violence against women. We establish five novel facts on the evolution of attitudes across time with these measures. (i) Attitudes are less persistent than the existing literature hypothesises. (ii) The persistence of attitudes varies considerably across different regions and dimensions. (iii) Attitudes exhibit cyclical patterns. (iv) Regional variation in attitudes decreases considerably over time and has fallen between 64% to 79%. (v) A decrease in transport costs that allows for easier information sharing is associated with a homogenisation of the norms. Our paper calls for more research on whether similar patterns exist across countries and the causal factors that make culture converge.