Job offer

European Commission; France; Sur place; EUR 30 000 - 45 000; Plein temps

Résumé du poste

Dans le cadre du projet Malinca, une opportunité de recherche est offerte pour un doctorant en mathématiques au sein d'une équipe internationale. Le postulant sera impliqué dans le développement d'une nouvelle technologie de preuves formelles, avec un accent sur l'automatisation des processus de création de preuves à partir de textes mathématiques. Ce rôle clé nécessite des compétences en recherche et une connaissance approfondie des théories mathématiques.

Qualifications

• Compétence démontrée dans la recherche mathématique.
• Compréhension des technologies de vérification formelle.
• Capacité à travailler sur des projets de recherche interdisciplinaires.

Responsabilités

• Travailler sur la recherche pour améliorer l'automatisation des preuves formelles.
• Annoter et organiser les informations pour passer d'un raisonnement textuel à une preuve formelle.
• Collaborer avec des centres de recherche partenaires.

Connaissances

Recherche en mathématiques

Automatisation

Formalisation

Formation

Doctorat en mathématiques ou domaine connexe

Description du poste

Organisation/Company CNRS Department Laboratoire Jean-Alexandre Dieudonné Research Field Mathematics History » History of science Researcher Profile First Stage Researcher (R1) Country France Application Deadline 1 Jul 2025 - 23:59 (UTC) Type of Contract Temporary Job Status Full-time Hours Per Week 35 Offer Starting Date 1 Sep 2025 Is the job funded through the EU Research Framework Programme? Horizon Europe - ERC Is the Job related to staff position within a Research Infrastructure? No

Offer Description

The Malinca project (ERC Synergy, http://malinca.org ), with centers in Paris, Nancy, Nice and Madrid, aims to develop a new generation of proof assistant technology capable of understanding the dynamical linguistic structures found in current high-level mathematical texts. The project includes the study of interpretation mechanisms for logical foundations, a new linguistic layer representing the intermediate steps between natural language texts and formal proof documents, and the automatisation tools for the efficient construction of definitions, theorems and proofs.

We would like to apply this to make the use of computer formalisation practical and current for mathematical research writing.

The co-direction and co-supervision of this thesis are placed in the context of the association of other centers within the project, the Comillas Pontifical University in Madrid and INRIA in Paris.

Computer verification of mathematical proofs furnishes a way for mathematicians to concieve, save and transmit complex mathematical theory developments while keeping the required high level of rigour. Nevertheless, the use of these technologies is slowed by the difficulty of furnishing the large set of details needed to obtain a fully formalised proof. Several approaches have been proposed and are under active consideration.

The framework defined by the Malinca project consists, starting with a text written in natural language and containing textual reasoning in a classical way, to annotate and organize the information in successively more precise layers, to arrive at a level ready for translation into a formal proof. In this process, there are many questions that need to be resolved, for example filling into a proof the small steps that are considered as easy by the author, looking for intermediate statements that will be useful for a longer proof, or searching for the relevant definitions and lemmas in a database.

The question for the thesis will be to work on computational search for structures, strategies and information in the context of a mathematical development, in order to improve the automatisation of the process of creating formal proofs for a given mathematical topic.

Co-directed by David Alfaya (Comillas, Madrid) and co-supervised by Hugo Herbelin (INRIA, Paris).