**Financial support through the following projects:**

PEst-OE/MAT/UI0297/2011

PEst-OE/MAT/UI0297/2014

UID/MAT/00297/2013

- In 2000, a draft note of Hilbert was found concerning a
*24th problem*for his Paris problem list. - This problem concerns simplicity of proofs.
- The aim of the project to reassess Hilbert’s 24th problem as a philosophical challenge (rather than a purely formal exercise).
- We take a closer look at the specifically mathematical examples that concerned Hilbert himself, in particular syzygies (the modern understanding of which is subsumed by the notion of Gröbner bases).
- Syzygies are, however, just a starting point for looking at Hilbert’s problem in other suitable mathematical contexts.
- Special emphasis is put on the potential impact of Hilbert’s 24th problem on contemporary philosophy of mathematics.

**Research Groups**

**Thematic Lines**

**Project Grant**