Abstract
Scientific research, and particularly research in mathematics, is arguably one of the crowning achievements of our collective human intellect. Its creation increasingly requires collaboration between multiple researchers with different and sometimes complementary backgrounds. On the other hand, its verification requires a careful matching between the expertise of reviewers and authors. Unfortunately, errors do occur and sometimes are only corrected many years after they appear in print, if at all. Nevertheless, at least when it comes to mathematical research, computer-verified formalized proofs are possible as a final arbiter of mathematical truth. Formalization of mathematics is the process of digitizing mathematical knowledge, which allows for formal proof verification of not only mathematical results, but computer programs as well. However, they are not easy to produce even for relatively simple statements. Hence, such approaches typically lack far behind the current research frontier. Aimed at addressing the above-mentioned issues, the three main contributions of this thesis are as follows: 1. To promote collaboration and expert reviewing within mathematical research, we propose a novel blockchain-based system that allows mathematicians to collaborate by sharing their partial pen-and-paper proofs (proofs written in natural language), and for reviewers to review thereafter. 2. To close the gap between the set of formalized and unformalized (i.e., pen-andpaper) mathematical knowledge, we propose a blockchain-based system that allows mathematicians, computer scientists and even automated artificial intelligence (AI) tools to collaborate by sharing their partial formalized proofs (proofs in program code). 3. To ensure the quality and correctness of each partial proof, we propose a proof of concept of incentive mechanisms that incentivize mathematicians to share their partial results immediately and expert reviewers to review.