Rather than inventing a solution from scratch, let's take what we know works and add a little cryptographic magic. Here are some things that we know work:
- The Arxiv system for holding academic papers and for tracking changes to them.
- The mathoverflow system (and similar) for asking questions and for rating questions and answers and participants.
- Polymath style cooperative projects.
- Khan Academy and similar systems of self-paced learning.
- Repositories of knowledge such as Wikipedia and ncatlab.
- Math Olympiad and other competitions.
The proposal will have the following features:
- You can play the game at any level, starting with K-12 mathematics, and up to new research.
- Participant IDs are linked to unique real world individuals. However you can play with pseudonyms, then claim the credit if you do well, but never need to own up to mistakes. Reviews can also be pseudonymous, freeing the reviewer to be honest.
- Abusive pseudonyms can be unmasked. Subsequent pseudonyms by that user will, for some time, have an elevated "abuse level" that users and software can take into account. Fair but tough reviews need to be endorsed by others as non-abusive to prevent abuse of the abuse system.
The system runs on various sorts of points and the interactions between them. The stackexchange folk (who run mathoverflow and similar sites) are experts on this and their advice should be sought. A possible scheme might be:
- Mathcoins are earned in various ways (including doing moocs and accompanying tests), and can then be spent to allow the participant to attempt higher level actions which can allow them to move up on a more permanent basis.
- Achievement points are earned by well-regarded actions and they accumulate. This is rather like masterpoints in Bridge and encourages the enthusiast as much as the skillful. This is important because there will be lots of work (such as marking middle level participation) needed to keep the wheels ticking over.
- Levels are more like the rankings in Tennis, though more blurred. At the top it is the judgement of peers. At the bottom it is mostly automated. In between the judgement of people above is the key. Moving up the levels is the objective of the game, and hopefully those at the top become stars, though they can, if they like, hide behind a pseudonym.
To start with, every participant would have an authenticating public key. The player can then generate as many additional public keys as necessary to represent pseudonyms. The activities (Arxiv/etc) would need to be modified to support this (or replaced), including supporting the authentication of all actions.
The easy thing will be for the participant to link from pseudonym to themself (or other pseudonym). All that is needed is to generate a "certificate" claiming that the public keys represent the same person, and have the certificate be signed by both public keys.
There are lots of other things that need to be done. They can all be done with a Trusted 3rd Party solution. Many of them can be done more elegantly and securely with cryptographic cleverness. It can also sometimes be possible to divide information between trusted 3rd parties so that compromise of only one doesn't reveal important information.
- Proving that a pseudonymous identity has sufficient points/etc to participate in high level activities.
- Identifying the abusiveness status of pseudonyms without identifying the real participant.
- Transferring mathcoins to, from and between pseudonyms.
- ... and much more
I think that the idea of Mathematics as a vast interconnected system, with no insurmountable barriers from the bottom to the top, would be very powerful and productive.