[Job-offers-cs] PhD and Postdoc positions in UnAxiMa: Uncovering the Axioms of Mathematics (Logic / Philosophy / Computer Science; PIs Aguilera, Fischer, Kovács, Müller, Pinsker, Schiemer)

[Pekka Orponen]

The FWF Emerging Fields project UnAxiMa (Uncovering the Axioms of 
Mathematics) is offering up to 12 postdoc positions and up to 12 PhD 
positions at TU Wien and the University of Vienna, Austria. The goal of 
the 5-year project is to explore 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 project is jointly led by 
six principal investigators: Juan P. Aguilera (TU Wien), Vera Fischer 
(University of Vienna), Laura Kovács (TU Wien), Sandra Müller (TU Wien), 
Michael Pinsker (TU Wien), and Georg Schiemer (University of Vienna). 
The project website is


https://unaxima.com/>
We are looking for highly motivated and creative candidates, and in 
particular encourage female researchers to apply. The applicants should 
have a strong background in at least one of the following fields: 
mathematical logic, theoretical computer science, universal algebra, or 
philosophy of mathematics. For the PhD positions the requirements are a 
Master's degree or equivalent in mathematics, computer science, or 
philosophy. For the postdoc positions the requirements are a PhD or 
equivalent in mathematics, computer science, or philosophy. Successful 
candidates will be based at either TU Wien or University of Vienna, but 
will collaborate with all of the 18-24 team members intensively.

Instructions for how to apply will appear at unaxima.com in early May 2026.
Applications will be accepted until the positions are filled. For full 
consideration, we encourage applications by May 22th, 2026. Successful 
applicants will start in October 2026 or as soon as possible thereafter, 
but not later than October 2027. The duration of the positions will be 
up to 4 years (for PhD positions) and 3 years (for postdoc positions), 
with initial contracts offered for one year, and prolongation subject to 
evaluation. The positions carry no teaching load; however, participation 
in teaching might be arranged if desired. There is sufficient funding 
for conference and research exchange trips.

Applicants will be required to submit a motivation letter, a CV 
(including list of publications, if applicable), and a statement of 
research experience and interests (2 pages maximum). In the case of the 
PhD positions, a transcript of records as well as a copy of the Master's 
thesis should be included if available (otherwise, any other written 
work such as a draft or Bachelor's thesis are welcome). Applicants 
should moreover arrange for at least two recommendation letters to be 
submitted directly to UnAxiMa. Formal applications will be submitted 
through a system to be announced on

https://www.unaxima.com/careers>
in early May 2026. Informal inquiries about these posts may be directed 
to Professor Michael Pinsker, chair of the Hiring Committee, at 
jobs at unaxima.com.

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About UnAxiMa:

UnAxiMa is an interdisciplinary project integrating mathematics, 
computer science, and philosophy to address one of the most fundamental 
questions in science:
What should the rules of mathematics be?
This question was investigated already 100 years ago by the Vienna 
Circle, a group of leading intellectuals from mathematics, philosophy, 
and the natural sciences. Their work culminated in Gödel’s 
incompleteness theorems, one of the most significant achievements in the 
foundations of science. According to Gödel’s theorems, there will always 
be mathematical questions which cannot be answered using the rules of 
mathematics. Such questions have appeared in algebra, analysis, 
combinatorics, topology, information theory, game theory, machine 
learning, and other fields. This ever-growing list compels us to seek 
more powerful rules which extend mathematics beyond its current reach. 
In UnAxiMa, we aim to identify new rules which could change forever the 
way that mathematics is done, taught, and applied, as well as our very 
conception of what mathematics is.

Adequate rules for mathematics must reflect current scientific 
understanding, which has changed dramatically since Gödel’s time: 
mathematical disciplines have become increasingly specialized and the 
world has seen radical technological advances. For the first time, 
UnAxiMa addresses both phenomena by uniting six disciplines towards 
distilling new rules which are theoretically sound and practically 
viable. The fields of Reverse Mathematics, Complexity Theory, Forcing, 
and Inner Model Theory evolved in the second half of the 20th century, 
and nourish our insight into the axioms of mathematics and their limits. 
Automated Theorem Proving, as part of artificial intelligence, is now 
seeing accelerated progress, thereby challenging our rules by the 
practical need of efficiency. Philosophy of Mathematics serves as the 
guiding light in our quest for rules that reflect our understanding of 
truth.

UnAxiMa isolates core questions on the relationship between axioms and 
computation, incompleteness, and necessity. The answers to these 
questions require interdisciplinary collaboration and have the potential 
to lead to a paradigm shift in the foundations of mathematics.

UnAxiMa gathers, in a single geographic location, world-leading experts 
from each of the six fields necessary to realize its collaborative 
vision. The project emerges as the culmination of 100 years of research, 
which have created an unprecedented scientific landscape where the 
momentum to rethink our scientific foundations is centered in Vienna 
once again. In a historic effort, UnAxiMa shall uncover the axioms of 
mathematics.