Srinivasa Ramanujan springs to mind as the most famous example. This is an interesting question to me because while the answer is probably none or predates the modern definition of academia, there's a hidden circular definition embedded in the problem.

Fundamental science is defined by its acceptance through the peer review process, and not by its applications or results. These undiscovered geniuses sending papers to professors are looking for inter-personal validation and acceptance as a peer. They want a benediction to become something (or to redeem or reinvent as something) and they think the blessing of a prof will give that to them. More cynically, a few want to be able to front the conversation like they do in sales, where they can say, "well, we're in talks about it with <high profile client> right now and here's the opportunity to get in before this thing gets really big." Substitute client for institution or professor, and it's the same play. Fronting an institution is also the easier problem to solve than actually applying their own ideas to build the time/perpetual-motion/free-energy/anti-gravity machine, and blaming an ossified bureaucracy for getting in their way seems plausible because it gets in everyones way.

However, some monograph authors are solving an important problem, which is finding analogies and abstractions that scale their minds and (albeit, incomplete) knowledge to others faster than the official rate of publication. Sure, it's probably misleading at relevant levels of detail and the map is not the territory, and it creates a signalling and noise problem for practitioners - but knowledge is not so precious. I'd propose we need more maps for hackers to use for free exploration with the understanding that the governance and prestige systems are their own games. We need more people actually doing math and physics on their own and with better cognitive tools, and perhaps fewer gatekeepers. Now with the internet, what was once a necessary filter is now mostly a bottleneck.

Every elite competency has a funnel and pipeline problem and papers like this (and authors like James Gleick, John Gribbin, Douglas Hofstadter, Roger Penrose, Simon Singh and other popular writers with varying credentials) bring people into the field.

Dismissing this author for a lack of affiliation is probably accurate, but it is a lazy argument that forfeits the opportunity (and an implied responsibility) to improve the public discourse with engagement with ideas that arrive in it. Many respected academics believe and openly advocate stupider things than this paper, and offering it just a fraction of what they have applied to more ridiculous ideas would go a long way to scaling knowledge to new minds, imo.