Tom,
You have me on that. Beyond conversing over the internets, zip. Though I have followed the social aspects of science out of curiosity since the early 80's and mentally process the achievements better from that perspective, than from a more mathematical one.
It was really originally the observation in Hawking's A Brief History of Time, that Omega=1, which started me down this rabbit hole of questioning the Big Bang picture of cosmology.
That the expansion of the universe and the contraction of gravity are inversely proportional. Logically they would balance out to a larger cycle, not simply be coincidental. Thus making the redshift evidence of Einstein's cosmological constant.
It was in this further consideration that I started to see the issue of time and treating measures of sequence as foundational to the actual processes being measured, as being the focal point of this issue.
I would ask you a similar question; How many of the scientists and mathematicians, that you know, are human? Further, how many of them are intellectual products of a system of education stretching back centuries, in which each generation has gradually built on the foundations laid down by previous generations. Further, has it ever happened that within this system, it was discovered that assumptions, concepts, models and other such mental tools were found to be incomplete, misunderstood, lacking crucial insights, etc. which then required re-working and rethinking? By this, not only the physical sciences, but everything from history to geology.
In what reading I have done, rarely are new ideas accepted when first proposed and frequently the rejection is valid, but there are certainly enough examples of where the outsiders were eventually accepted as having been right, that the status quo cannot always be assumed correct.
As you state it; "Science is a rationalist enterprise. There aren't different practices and beliefs -- it is universally practiced the same way."
The consequence is that one frame emerges and while that frame logically considers itself to be universally objective, the fact remains "that no system of axioms is strong enough to prove itself."
Right now, some of those on the cutting edge of theory, strings and supersymmetry come to mind, who think some of the more formal proofs of science should be relaxed. That, as others have strongly objected, is not a good move.
There are a number of ideas out there that many people have devoted decades to, which could well prove to be intellectual dead ends. That is the nature of science. And civilization.
Regards,
John M