Starting Year: 2016
Title: Hilbert’s 24th Problem
Abstract: 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.
Funding Source: FCT – Fundação para a Ciência e a Tecnologia, I.P.
Typology: R&D Project
Reference: PTDC/MHC-FIL/2583/2014
Principal Investigator (PI): Reinhard Kahle
PI’s institution: FCT NOVA
NOVA Math members involved: Reinhard Kahle, Alan James Cain, António José Mesquita da Cunha Machado Malheiro, João Jorge Ribeiro Soares Gonçalves de Araújo, Manuel Almeida Silva, Paulo Guilherme Domingos Canha Moreira dos Santos, Serena Delli, Gabriele Pulcini, José Francisco de Vasconcelos Teodósio Nunes dos Reis, Mirko Engler, Guilherme Miguel Teixeira Rito, Isabel Oitavem