Objective
Irrational and transcendental numbers, such as √2 and π, have fascinated mathematicians since ancient Greece. Despite this enduring interest, substantial progress in this field remains rare: classifying numbers according to their arithmetic nature is notoriously challenging, and understanding how some of them combine to produce remarkable identities, such as e^{iπ}-1=0, is even more so.
A cornerstone result in the field is the Hermite-Lindemann-Weierstrass theorem (Theorem HLW), which establishes a fundamental criterion for the algebraic independence of values of the exponential function at algebraic points. Throughout the 20th century, much research in transcendental number theory focused on generalising this theorem, leading to landmark contributions by Siegel, Gelfond, Schneider, Shidlovskii, and Baker.
In recent years, substantial advances have been achieved for other classes of transcendental numbers and in the closely related domain of functional transcendence. Mêtis seeks to build on this momentum by revisiting several longstanding problems--including a new generalisation of Theorem HLW--some of which have remained unresolved for nearly a century.
A distinctive feature and recurring theme of the project is its ambition to combine different types of functional equations in innovative ways to obtain fundamentally new results. While the motivation and perspective are rooted primarily in number theory, the methodology draws on a rich constellation of areas within mathematics and theoretical computer science. These include differential algebra and the Galois theories of linear differential and difference equations, combinatorics, model theory, automata theory, and algorithmics.
By integrating these diverse perspectives, the project represents a unique opportunity to establish the first research programme dedicated to tackling these problems within a unified framework.
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.
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.
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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.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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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 - HORIZON ERC Grants
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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-2025-ADG
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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.
75794 Paris
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.