The ideas I present are a continuation on the proposal here: Digital People.
I highly recommend giving it a read.

Perhaps you’ve heard of the Millenium Problems, a collection of 7 of the hardest unsolved problems in mathematics, physics, and computer science with a 1 million dollar reward for any potential solver. But that mere one million isn’t really a reward nor is it any kind of incentive. Rather it’s a compensation for the years or perhaps lifetime spent determining if a fancy sounding sentence is true or not. In this article, I’ll investigate a new resource for problem solving that could at best advance or even solve one of the Millenium problems, and at worst be yet another tool in our problem solving toolkit.

Optimizing Problem Solving:
Let’s move away from the Millenium problems to a more general case: At the core, what really is problem solving? From what I’ve observed in CS and olympiads (and life), it’s the ability to utilize previously understood experiences to draw novel conclusions. The exceedingly difficult kind of problems either require little familiarity with fancy concepts–their simplicity defines their difficulty, or they require copious amounts of background knowledge but, once that’s achieved, are still shockingly simple. Thus the limiting factor of problem solving isn’t how much knowledge a system has, but rather the different perspectives used to gain that knowledge. Aside from the difficulty of the Millenium Problems, I think the lack of perspective is a primary reason why 6 of the 7 remain unsolved. The ubiquity of mathematics curricula (but really any subject) is the cause of this perspective drought. It’s a lot more efficient to teach the same material in the same way rather than to investigate new ways of teaching the same thing. I believe this explains the success and lifelong progress of autodidacts. Teaching oneself forces you to create your own perspective–which is by no means easy–but reaps rewards greater than never having an uncertainty about learning.

Premise for Digital People:
Above I proposed that one roadblock to solving a Millenium Problem is the perspective drought. This is true, but fails to acknowledge something important. Any society would be bound to suffer from a perspective drought if their population was few no matter how information was taught. This is quite obvious, it takes a conscious to come up with a new way of doing something. More consciences = more perspective and vice versa, but herein lies the main reason why little progress has been made on the Problems: compared to the number of graduate math students, the number of those actively working on solving an MP is small. Thus we face a perspective drought of the population size kind in the subset of those working on them, and because of this, a true perspective drought.

Send in the Cavalry:
The watered down abstract of the article at the top is that the impact of virtual simulations of human-like beings would be revolutionary to many fields and life in general. I’ll add just one more droplet in the pool of digital people uses particularly in the context of, you guessed it, problem solving. Let’s create a virtual world of only highly-motivated digital peoples (perhaps artificially ensuring this) who are determined to work exclusively on the MPs. Now let’s assume each one of these individuals have been taught or self learnt almost all of our knowledge of math in a way that minimizes the chances of a perspective drought. That is, each individual has learned or applied the same topic in an almost unique way so that the insights they’ve gained are also pretty much unique. A threshold exists so that if the number of individuals exceeds that threshold, the differences in perspectives becomes almost nonexistent. Adding another digital person would then just be inefficient. In other words, perspectives are vast but still finite. If we start to see too many similar thought-processes among digital people then we know we’re close to the threshold or we need to spend more resources to find newer insights. Lastly, our simulation should have a large number of people, and exactly how large is bounded by whether the marginal perspective gained on a problem from a new person is a unique perspective.

From the Entscheidungsproblem and the Incompleteness Theorem, the truth value of a particular problem could be impossible to find so there is a chance this proposal is completely useless. So if little progress is made, when do we pull the plug? As long as the flow of new perspectives is continuous, I don’t think we ever should. We should store (for future retrieval) and then remove old perspectives from our simulation in order to keep the energy used relatively static. I think this setup is our best chance of proving an MP or at least showing it’s undecidability.

Conclusion:
Earlier, I said this “each individual has learned or applied the same topic in an almost unique way so that the insights they’ve gained are also pretty much unique”. But this is really a black box abstraction, in theory there is a way to make digital people learn in unique ways, but how? Rewind the clock. Simulate all of human academic progress with digital people and see what new things or approaches are discovered. More on this later.

Check this out too:

https://www.metaculus.com/questions/1048/when-will-the-next-millennium-prize-problem-be-solved/