Short answers, pulled from the story.
Italian statistician and sociologist Corrado Gini developed the Gini coefficient and published it in his 1912 paper Variabilità e mutabilità. He built on the earlier work of American economist Max Lorenz, proposing the difference between the perfect-equality line and the actual income distribution curve as a measure of inequality.
A Gini coefficient of 0 reflects perfect equality, where every person has the same income or wealth. A Gini coefficient of 1 reflects maximal inequality, where a single individual holds all income or wealth and everyone else has none.
South Africa has the world's highest income Gini coefficient. Estimates place it between 0.63 and 0.7 on a pre-tax basis. After social assistance it drops to approximately 0.52, and after taxation it falls further to approximately 0.47.
The world income Gini rose steadily from 0.43 in 1820 to a peak of 0.71 in 2002, according to estimates by Milanovic. After 2002 the trend reversed, reaching 0.68 by 2005 and 0.65 by 2013, a decline attributed to rapid economic growth in China, India, and other large developing economies.
The Gini coefficient measures relative distribution, not absolute wealth, so two countries with very different living standards can share identical scores. It cannot be added across populations, is sensitive to how households versus individuals are counted, and struggles to capture income earned through informal economies, which account for an estimated 31.2% of world GDP according to a 2010 study.
Yes. The Gini has been applied in ecology to measure biodiversity, in astronomy to classify galaxy shapes, in engineering to assess Internet router fairness, in health science to measure inequality in quality of life, and in credit risk management to evaluate how well rating models separate defaulting borrowers from non-defaulting ones.