Could someone explain how increasing number of agents help? Is each agent researching a potential solution space where there's many potential solution spaces? I'm struggling to conceptualize how a large agent swarm can be used to solve a research problem.

I don't think it's nearly as relevant as the total amount of compute being used. I just think they like talking about swarms because it sort of anthropomorphizes them.

Feel like this might still apply to multi-agent programming:

I have earlier argued that the sheer number of minds to be coordinated affects the cost of the effort, for a major part of the cost is communication and correcting the ill effects of miscommunication (system debugging). The Mythical Man-Month Frederick P. Brooks Jr.

By collaborating and division of labour.

I am just as clueless as you are, but I think it having each agent work on the problem mostly individually in parallel, likely sharing their breakthroughs for the next wave of agents. I'm reminded of infinite monkey's writing Shakespeare; suggesting if you have an infinite amount of agents, they will end up solving a Millenium Prize Problem.

Here is OpenAI's blog post about Navier-Stokes; [1] which suggests they used smaller connected swarms given the different prompts, then the findings were used to write further follow up prompts for a new group of agents.

[1] https://openai.com/index/navier-stokes-solution/

Actually, I think Microsoft just posted the results of research the other day that would be relevant. They were looking at self-organized AI swarms instead of centralized orchestration, and found that just starting up thousands of SOTA models really can precipitate a natural hierarchy and work toward problem solving.

At the very least, the swarm would be able to set up a means of claiming avenues of thought, then verifying the solutions (or lack thereof) of other agents.

It's quite clear this process - whatever it may be - works, given the results we've seen in the past few weeks.