Uncovering the Axioms of Mathematics is an interdisciplinary research project that combines mathematics, computer science and philosophy to answer one of the most fundamental questions in science: What should the rules of mathematics be? A hundred years ago, the Vienna Circle – a group of leading intellectuals from the fields of philosophy and natural sciences – explored this question. Their work culminated in Gödel's incompleteness theorems, one of the most significant achievements in the foundations of science. These theorems show that there are questions that cannot be answered using the known rules of mathematics. In this Emerging Field, researchers are looking at the phenomenon of incompleteness from a modern perspective, taking into account modern developments such as computers and AI. The aim is to reveal the axioms of mathematics.

‘Axioms are the basic rules of mathematics – and thus its most important component. They are, in a sense, the atoms of the universe or the bits of a computer: the elementary building blocks from which everything is created. In this sense, axioms are the DNA of mathematics, which we want to understand even better,’ says Juan P. Aguilera, coordinator (TU Wien), about the goals of the project.

The funding volume amounts to 7 million euros.