As of late I've been coming across a lot of people online who are convinced that, without much (or any) formal training and often without any collaboration, they have solved a major unsolved problem in the quantitative sciences. They are incredibly attached to the correctness of their solution. They often talk about their god-like cognitive abilities and act as if the scientific community is dogmatic (One guy said he has a "vulcan-like" mind, which I thought was hilarious). Often their "quantitative" theory doesn't even have any real math in it, and they almost never make any experimental predictions.
As someone who has and probably will continue to tutor kids in math and science, I'd like to know what kinds of events at what stage of development lead people to this insane level of hubris and confirmation bias.
Some requested examples:
This youtuber thinks he's proven the Collatz conjecture and other famous problems.
This youtuber solves a bunch of made up problems in fluid dynamics and has a few uncontrolled experiments on video to demonstrate the effectiveness of his model.
Many examples are people my age (undergrad) who have approached me in real life and, once we discover a common interest in quantitative science, they start throwing around technobabble about a "major" problem that they've contrived.
There's also a pretty good example of the pretentiousness exhibited by these people in the stack exchange posts linked in the comments.