The problem with the current system of science contributions via the publications is inherently flawed:

It incentivises only additions to the general public knowledge by writing more articles and gives little to no credit to those who review mostly anonymously, those who spot mistakes or those who actually fix mistakes. To advance in one’s career, researchers are generally measured by the number of publications and the reputations of their journals

Furthermore, journals make a profit while authors, editors and reviewers either do their work for free or even have to pay to publish (e.g. for an open access licence).

In the special case of mathematics, all scientific results are self-contained and can, in theory, be verified by anyone knowledgeable in the field (e.g. no special equipment is necessary).

Wouldn’t it make more sense to craft a knowledge tree instead of a linear journal, that would semantically link to previous results?

For illustration, let’s consider a new paper in mathematics, that publishes, e.g. three theorems. In the proof, several older results are used and quoted via citation.

The reader then has to either trust the author or the peer review process, that these older results have been indeed been proven correctly in the other papers (as well as their quoted results) or she has to verify the cited results and their quoted results until arriving at the axioms.

In some cases, mistakes happen, and a quoted result does not (yet) exist or is even provably false. However, there is no immediate incentive (apart from the author’s honor code) to correct mistakes. Thus, some unsuspecting grad student might continue to quote a wrong or only partly-proven result having either to figure out the mistake themselves or falling into the trap and building on top of this possibly false assertion.

I propose to instead build a semantic knowledge graph, in the following style:

As a researcher, you can contribute in several ways:

1. You can add a new node, that is a new theorem by submitting the statement of the proof as well as the links for the correct quoted parent theorem nodes.
2. You can challenge an existing edge of the graph if you spot holes in a proof or have a counter example.
3. Formalize existing results into the knowledge graph.

Item 3 could be a nice source for students’ theses. The role of editors and reviewers could be to function as administrators for new additions to the graph.

Advantages:

1. The knowledge graph becomes crawlable. Issues with a parent node can automatically be inherited to child theorem nodes.
2. Contributions to rectify issues with papers can be acknowledged by the scientific community as valuable contribution.
3. Automatic proof checking becomes an option if the proofs are formalized (se. e.g. Lean).
4. Researches might become quicker in discovering related results.
5. AI can function as a proof-helper, either auto-completing (like chat gpt for coding) or even suggest noteworthy theorems that are corollaries to current knowledge.

Disadvantages / Challenges

1. There needs to be software and infrastructure to run the knowledge graph.
2. Change Management in the scientific community would have to take place.
3. Commercial journals might oppose this heavily.
4. The graph might become quickly “unreadable” due to complex combinations. One would need a suitable filtering / tag structure in order to be able to see only relevant content.