From Plato to Weil and beyond: Genericity through the history of mathematics

Abstract

At the end of the 19th century, genericity took an important step toward mathematical analysis, due to the developments promoted by the Italian school of algebraic geometry. However, its origins can be traced back to ancient mathematics in the work of prominent philosophers and mathematicians, such as Plato and Euclid. In this article, we will try to show how a key notion in the structuralist turn of algebraic geometry evolved from a vague linguistic phenomenon and became a precise and fruitful mathematical concept.