The Austrian Science Fund, opens an external URL in a new window (FWF) has launched the “excellent=austria” excellence initiative. This initiative includes the “Emerging Fields” funding scheme. In the second call (2026) of the programme, 6 different projects have been selected as Emerging Fields projects, one of which is the “UnAxiMa – Uncovering the Axioms of Mathematics, opens an external URL in a new window” project led by TU Wien.

In the UnAxiMa project, researchers are addressing one of the most fundamental questions in science: what should the rules of mathematics be? By addressing core questions regarding the relationship between axioms and computation, incompleteness, and necessity. UnAxiMa explores the axioms of mathematics taking into account aspects of mathematical logic (in particular, set theory, computability theory, and reverse mathematics), complexity theory, automated theorem proving, and philosophy. The aim: to uncover new rules that could forever change the way mathematics is practised, taught and applied, as well as our understanding of what mathematics actually is.

As early as 100 years ago, scientists in the Vienna Circle – a group of leading intellectuals from the fields of mathematics, philosophy and the natural sciences – explored the question of what the rules of mathematics should look like. 

“Axioms are the fundamental 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 arises. In this sense, axioms are the DNA of mathematics, which we want to understand even better,” says Juan P. Aguilera, project coordinator at TU Wien, describing the project’s objectives.

The project is led at the TU Wien by  Juan P. Aguilera, Sandra Müller, Michael Pinsker (Faculty of Mathematics and Geoinformation) and Laura Kovács (Faculty of Informatics). The team is completed by Vera Fischer and Georg Schiemer from the University of Vienna. 

The project will run for five years and has a total funding budget of 7 million euros.

Applications welcome

The UnAxiMa project is offering up to 12 postdoctoral positions and up to 12 PhD positions at TU Wien and the University of Vienna. Applications, opens an external URL in a new window are open until 22 May 2026.