Crazies say they validate and test their idea, but they actually suffer from severe confirmation bias where they summarily dismiss any counterexample or problem.
Would you be able to spot a Ramanujan from the dross?
You say that "they" ... something ... but ... they ... something ... disagree with the world. Care to flesh this out with an anonymised example?
Yes. We would do this by analyzing their arguments for logical errors, then testing their new theory, then hopefully proving their new theory. The difference between a crazy and genius is the results their new ideas produce.
In Ramanujan's words, "an equation for me has no meaning unless it expresses a thought of God". In mathematician circles of the early 20th century, this was an obscene statement. Even today, can you imagine a researcher in any field saying something like that, and being taken seriously?
Yet Ramanujan is probably one of the greatest mathematicians of all time. In Hardy's word, he had "never met his equal, and can compare [Ramanujan] only with Euler or Jacobi".
To think that "we" (whoever you mean by that) can recognize sheer talent of Ramanujan's type is, frankly, arrogant. If anything, the ivory towers are even more enclosed - research is more and more about the quantity of publications, not about the quality of ideas. A recent Nobel Laureate stated that if he had not received the Nobel Prize, his university would have probably fired him, for lack of a consistent publication record.
So no, I don't agree with your statement. While the scientific method you describe for approaching nature has worked tremendously well for understanding the world, it still completely fails to capture the core of what it is that makes a person a true genius.
After seeing Ramanujan's theorems on continued fractions on the last page of the manuscripts, Hardy said the theorems "defeated me completely; I had never seen anything in the least like them before", and that they "must be true, because, if they were not true, no one would have the imagination to invent them".
I'll agree that the costs don't come close to replicating work by LIGO or CERN.
it's much harder to skim the dross off a leonardo, to correct your mixed metaphor, because siege engines and flying machines require empirical testing, and that's expensive. within the hypothetico-deductive method you can tell whether someone's logic is incorrect (just as with ramanujan) but if they're proposing a different hypothetical basis, you often have to test it empirically
often you can proceed from their proposed hypotheses to obviously empirically false conclusions. but historically that hasn't been an especially good guide; in the 19th century kelvin proved that the sun was younger than the earth, demonstrating that something was wrong with his hypothetico-deductive framework, but it took quite a while to figure out what. and today relativity and quantum mechanics are widely considered irreconcilable
yes, because math has a logical flow and rules, and most errors would be noticed
After seeing Ramanujan's theorems on continued fractions on the last page of the manuscripts, Hardy said the theorems "defeated me completely; I had never seen anything in the least like them before",[76] and that they "must be true, because, if they were not true, no one would have the imagination to invent them".[76] Hardy asked a colleague, J. E. Littlewood, to take a look at the papers. Littlewood was amazed by Ramanujan's genius. After discussing the papers with Littlewood, Hardy concluded that the letters were "certainly the most remarkable I have received" and that Ramanujan was "a mathematician of the highest quality, a man of altogether exceptional originality and power".[74]: 494–495 One colleague, E. H. Neville, later remarked that "not one [theorem] could have been set in the most advanced mathematical examination in the world".
As for his results being checked, they were - after nearly a century in some cases:
As late as 2012, researchers continued to discover that mere comments in his writings about "simple properties" and "similar outputs" for certain findings were themselves profound and subtle number theory results that remained unsuspected until nearly a century after his death.