Web3 Platform for Formal Mathematics

Project Information

FormalWeb3

Grant agreement ID: 101156734

DOI

10.3030/101156734

Project closed

EC signature date 26 January 2024

Start date 1 February 2024

End date 31 July 2025

Funded under

• European Research Council (ERC)

Total cost

No data

EU contribution

€ 150 000,00

Coordinated by

UNIVERSITAET INNSBRUCK
Austria

Periodic Reporting for period 1 - FormalWeb3 (Web3 Platform for Formal Mathematics)

Reporting period: 2024-02-01 to 2025-07-31

Summary of the context and overall objectives of the project

Mathematics is today on the verge of a revolution. Formal, computer-verified proofs become ubiquitous and largely adopted as the new means of communication and collaboration. This led to landmark proofs, such as Hales's verification of the Kepler conjecture and Scholze's condensed mathematics recently validated by computers, generating considerable momentum in the mathematical community. Simultaneously, there is growing industrial demand for formal proofs of software and hardware. Similarly, Web3 constitutes a transformation of how data and collaboration are realized in a decentralized, intelligent, and interconnected way.

In this project, we develop a Web3 platform for formal proofs, designed to establish connections between mathematicians, researchers in formalization, communities, and businesses. This platform will also integrate state-of-the-art verification, AI, and autoformalization tools to assist in the creation of computer-understandable proofs. The proposed work will include the development of a Wiki for formal mathematics with integrated blockchain-based tokens that reward users for their contributions. We experiment with translations for various logics and proof systems, and investigate the safety and security of the protocols.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The work done in the project focused on the technical tool development
and experiments with more advanced features.

In particular:
- We proposed and implemented payment channels with proofs
- We have developed a blockchain explorer for formal mathematics
- We have developed several improvements to automated reasoning
systems, including better Prover9 strategies and automated
proofs of confluence, and for set-theoretic problems.

On the more theoretical side we have worked on stronger logics
and their encoding in a blockchain for for formal mathematics
focusing on dependent higher-order logic.
- We have proposed how to extend it with the Hilbert choice operator
- And proposed automated reasoning tools for it.

We have also investigated how the developed tools can be used for
practical formalizations.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The improvements to the platform developed in the project include
all the basic components needed to develop proofs in a distributed
platform, and upload them or even place bounties and collect them.
The developed blockchain explorer can be used to explore theories,
proof documents, individual proofs, as well as upload proofs
completed offline. Further work on providing the services requiring
tokens online would be necessary meaning that substantial further
development and investigation would be required to make the platform
into a business product.

One of the most important achievements of the project has been
the development of payment channels with proofs. However we only
managed to provide rather rudimentary interfaces to these and they
are still at the proof-of-concept stage with further work required
to allow non-experts to use these.