Incremental science happens because of data; leap science happens because of creativity and intuition to explore the areas data hasn't 'gapped to'. And it is the difference when 'the data does not yet lead there, so we can't think there' that I refer to for social conformity.
Once in a blue moon one of these outsiders turns up something genuinely impressive.
There is no reason whatsoever to assume that is the case here.
Actually no.
Theories of this ilk which demonstrate their consistency with laws of physics to the level of observations already made and significantly beyond, tend to end up studied more, by more people.
Especially ones that take an unusual angle, and end up deriving existing laws of physics almost as a surprising side effect. It suggests a useful insight.
Even better if they take an unusual angle, predict some differences from assumed existing laws but only in unusual circumstances nobody has tried to observe so far, and are consistent with those laws in areas already observed.
Or ones which explain existing laws better than current explanations. Notably the inconsistencies between general relativity and quantum mechanics mean that anything which can explain both at the same time and give correct answers to both is quite interesting.
The ones that get dismissed quickly are those which aren't consistent with laws of physics that are already assumed, especially at the level of existing observations.
What new predictions (ie. not covered by existing theories) does this theory propose that are testable?
> Especially in areas requiring higher mathematics
I just don't recognise this at all. Why do you say this? The journals are full of new discoveries, my experience with mathematicians is they're a very open and accommodating bunch (ok, it's not my field, but still)
Recently: transgenerational epigenetics was considered a violation of the Central Dogma of biology, but since then evidence has piled up and it's now considered a legitimate area of research.
The jury is out in high energy physics where SUSY and string theory elbowed some (possibly) more interesting competitors out of the way. It's too early to tell how that will work out - but it is clear that some approaches get a lot more funding and attention than others, and this seems to be for political rather than objectively scientific reasons.