The Proof Manifesto

Wherever there is communication, there are proofs. For how else can one convince oneself that the information presented by another party is reliable? Everyone uses proofs, though some may do so without knowing it (somewhat like a hero of Molière who realized one day that he was speaking prose for fifty years).

The mathematical study of proofs emerged in the bold program by David Hilbert who coined the term Beweistheorie (Proof Theory). In this program, the role of proof theory was to provide a formal model of a rigorous mathematical proof and to show, by analysing this model, that no contradiction in Mathematics can ever arise. Even though Hilbert’s dream did not materialize in its full extent, through groundbreaking insights of Kurt Gödel and Gerhard Gentzen, for the first time the concept of proof was put in the center of a mathematical study. Through a progress that followed, in the course of the second half of the XXth century, proof theory reached the status of one of the cornerstones of modern logic.

In the recent years, formal methods that originated in mathematical logic and in proof theory itself have witnessed a tremendous growth in applications. This included the quick progress in the areas of Computer Science such as formal verification, automated proof search, proof assistants, proof complexity, and new applications in mathematics such as proof mining. On the other hand, formal proofs also infiltrated into other areas previously not prone to formal analysis, be it formal epistemology or logic in law. All these exciting developments lead to a much more varied landscape of research around the notion of proof than the world had previously seen and lead to a rapid diversification of the field.

We believe that the time has now come for a consolidation of knowledge accumulated in the study of formal proofs and of the community of proof researchers. We thereby proclaim the organization of the Proof Society whose main aims are:

  • To support the research on the notion of “proof” in its broadest sense, through a series of suitable activities;
  • To be therefore inclusive in reaching out to all scientific areas which consider “proof” as an object in their studies;
  • To enable the community to shape its future by identifying, formulating and communicating its most important goals;
  • To actively promote “proof” to increase its visibility and representation in the larger scientific community and society.