Mathematicae Lingua Franca: Bridging the Linguistic Gap Between the Mathematician and the Machine

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.