I dunno; we have access to all kinds of fascinating and exciting technologies today. You could get going with CRISPR for 5 large, if you do your research and buy secondhand equipment. We have 50F capacitors today in a package that would only fit a few mF in the past. You can order a few square inches of custom-designed PCB for about $1.00 these days, including shipping.

I guess that CRISPR requires extensive research and planning to target genes, pick out restriction enzymes, make gRNA, etc etc, but that's all freely available through public resources like the NCBI. When it comes to taking advantage of a global supply chain and centuries of incredible innovation, we are really standing on the shoulders of giants. And how long will it be before someone takes advantage of that low barrier of entry? History says: "not long."

I guess you are referring to Yitang Zhang who created the first bound on the twin-prime conjecture. These days mathematics has become so specialized that its rather difficult to come up with anything new that is noteworthy and not already discovered. Just browsing through the graduate math library the other day and the stacks and stacks of journals dating from the 1700's and from various parts of the globe made me realize just how much math is out there.

Still, like Ian Stewart said in his "Letters to a Young Mathematician", math is an inverted pyramid - when a problem is solved, it leads to more branches to be solved. So maybe breakthroughs are possible from a determined amateur.

New and novel ideas are often rejected.

One of the better examples is the theory of continental drift, now known as plate tectonics. The suggestion goes back a while, though it was a German meterologist, Alfred Wegner, who made the first serious proposal in 1912. He was rejected by a large part of the geological establishment, and died without seeing his ideas accepted. But the evidence mounted, both of the record that drift had happened (fossils, geological structures, magnetic reversals), and most importantly, a mechanism and sufficient time both made apparent by radioactivity and radioactive decay. By the 1950s the age of the Earth was known to be 4.5 billion years, and by the mid 1960s, Wegener's theory was geological fact.

It's now considered the central concept of geology, by at least one account I've seen, which is quite a feat.

Naomi Oreskes, recently known for her work on the disinformation campaigns against tobacco, lead, asbestos, CFCs, and now CO2 regulations, Merchants of Doubt, wrote several papers and two books on this subject in the late 1990s and early 2000s, specifically about the history of science aspect, and the long rejection (and eventual acceptance) of the theory. Recommeded reading.

I don't disagree with you on academia, though there may be reasons for that as well.

>Life, I fear, is no different than lord of the flies, except that the characters are rather a bit more polite.

Now that is depressing.