ELI5: Explain Like I'm 5

Timeline of abelian varieties

Okay kiddo, let me explain what a timeline of abelian varieties means.

First, let's start with what an abelian variety is. An abelian variety is a type of mathematical object that is a special kind of algebraic variety that has a finite number of holes or singular points. Think of it like a doughnut that can have a certain number of missing pieces.

Now, a timeline of abelian varieties is a list of when different abelian varieties were discovered or studied by mathematicians throughout history. For example, the first abelian variety was studied by a mathematician named C. F. Gauss in the early 1800s. He was interested in studying the number of solutions to a particular equation and discovered this new type of mathematical object.

Then, throughout the 1800s and 1900s, other mathematicians like C. G. J. Jacobi and E. E. Kummer continued to study abelian varieties and discovered new properties about them. They found that abelian varieties were very important in number theory, which is a branch of mathematics that involves the study of whole numbers, prime numbers, and fractions.

Later in the 1900s, mathematicians like André Weil and Alexander Grothendieck developed new methods for studying abelian varieties and were able to prove some very important theorems about them. They found that abelian varieties could be used to solve very difficult mathematical problems, and their work led to the development of a new field called algebraic geometry.

So, a timeline of abelian varieties is basically a list of all these different discoveries and developments by mathematicians throughout history, showing how our understanding of abelian varieties has grown and evolved over time.