This paper presents a new dataset on educational attainment (primary, secondary and tertiary schooling) at the world level since 1870. Inequality in years of schooling is found to be rapidly decreasing, but we show that this result is completely driven by the decline in illiteracy. Then, we turn to inequality in human capital and focus on Mincerian production function that accounts for diminishing returns to schooling. It explains the negative cross-country correlation between Mincerian returns to schooling and average schooling contrary to other functional forms. As a result, we show that world human capital inequality has increased since 1870, but does not exceed 10% of world income inequality. Next, we analyse the relationships between the national distributions of income and schooling. We show that human capital within countries exhibits the inverted U-shaped curve with respect to average schooling, namely a "Kuznets curve of education." We find that the usual Kuznets curve of income inequality is significant both in pooled and fixed-effects regressions over the period 1870-2000, and is robust to the inclusion of other variables in the regression such as schooling and human capital inequality. However, the "Kuznets effect" associated to GDP per capita is 4 times smaller in magnitude than the externality of average schooling favouring the decrease of income inequality within countries since 1870.