Project description
Proof assistant technology for use by mathematicians
Proof assistants have seen growing adoption among researchers and scientists in recent years, thanks to their ability to efficiently formalise large bodies of mathematics. They have been used to certify major results such as the Scholze liquid tensor challenge and the Kepler conjecture. However, current proof assistants are limited to formal settings and cannot process the flexible, semi-formal language commonly used by mathematicians. The ERC-funded MALINCA project aims to develop a new proof assistant technology that preserves the precision of formal language and mathematical meaning while incorporating greater versatility. It will be designed to understand and represent the dynamic linguistic structures mathematicians use in practice.
Objective
In the recent years, proof assistants have shown their astounding ability to tackle the complete formalisation of large pieces of mathematics, with the celebrated certifications of the Feit-Thompson theorem, of the Kepler conjecture, and more recently, the resolution of Scholze liquid tensor challenge. We believe that the time is ripe to demonstrate that they can tackle mathematics in the flexible and semi-formal way it is created and exchanged by the mathematicians. To that purpose, we aim to develop proof assistant technologies of an entirely new nature, including a formal language and a foundational approach to mathematical meaning, with the versatility necessary to represent the dynamic linguistic structures to be found in the daily practice of mathematics. The result will be a linguistic front-end that will allow mathematicians, and scientists in general, to express in proof assistants their proofs and computations the semi-formal way they think of them. Three research tracks stand out: the mathematical and linguistic foundations; formalisation of real-world vernacular mathematics into a high-level language of representation (Godement challenge); new techniques and software tools, based on natural language processing, to automate the formalisation process. The translation in the machine of semi-formal mathematics needs to go beyond the traditional view that reduces reasoning to logic, and requires to understand the dynamics of the discursive linguistic process which underlines mathematics. Building on advances of linguistics, mathematical logic, programming language semantics and machine learning, we will contribute significantly to the rise of a new generation of proof assistants, integrating at their heart a linguistic layer and automated guidance tools for mathematical proofs, theorems and definitions. The resulting high-level manipulation of concepts will lead to novel research outcomes supporting the daily activity of mathematical scientists.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project's classification has been human-validated.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project's classification has been human-validated.
- humanities languages and literature linguistics
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
- natural sciences computer and information sciences data science natural language processing
- natural sciences computer and information sciences artificial intelligence machine learning
- natural sciences mathematics applied mathematics mathematical model
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
-
HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC-SYG - HORIZON ERC Synergy Grants
See all projects funded under this funding scheme
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2024-SyG
See all projects funded under this callHost institution
Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
78153 Le Chesnay Cedex
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.