> For example I can't help but think of what would happen if some random (not PhD) engineer came up with a new and highly innovative mathematical construct and

> For example I can't help but think of what would happen if some random (not PhD) engineer came up with a new and highly innovative mathematical construct and published it on their blog... I doubt their idea would get any attention at all; no matter how useful or impressive it is. It would be lost in the noise because scientists are not going to review it Anecdote: as an undergrad I worked part-time for a physics research group, and once my address got added to their staff web page, I started receiving "highly innovative" new theories via email about once per week. They were generally long and involved; it would have taken me hours to pore through one and figure out what it was trying to argue or whether it made any sense. And this was circa 1995, when only a small portion of the world had access to email, let alone web pages. I wonder what it's like now...