Kurt Gödel's incompleteness theorems of 1931 are among the most iconic achievements of 20th century science. They showed that the aim of presenting mathematics as a closed, formal, and complete system is unachievable, and have been a cornerstone in logic, mathematics, and computer science. His discoveries about formal syntax and computability were crucial in the developments that led to our digital age.
There are thousands of pages of manuscripts by Gödel virtually unexplored, written in a forgotten stenographic script. They are extremely difficult notes on formal developments that require the skills of a working logician. The central aim of the project is to study the shorthand notes on incompleteness, from 1930 on. Secondly, related developments, called "the aftermath of incompleteness" will be studied, mainly the work of Gerhard Gentzen who in 1936 was the first one to gain a deep understanding of the incompleteness results, and Gödel's response to this line of work.