Is scientific research a good use of government funding when hospitals, schools and social services are suffering from tight budgets??

There is a certain irony in seeing such a question posted online, typed in via a computer (or, for all I know, maybe some even more cutting-edge piece of handheld technology). Because, if wise men and women, the best part of a century ago, hadn't developed the principles of quantum mechanics, there could be no such things. At least not in anything like their current form: we'd still be on valves and transistors, or even cogs and pulleys... themselves the off-shoots of yet earlier scientific research. As for those hospitals you mention, had it not been for scientific research into human biology, they wouldn't have any treatments to offer their patients (in which case, it really wouldn't matter if their budgets were to be taken away altogether!). Gene therapy, for instance, clearly would not have been able to get off the ground if its developers had not possessed any conception of a 'gene' or understood the structure of DNA. But that is something that we owe to state-funded scientific research. It is...

How do we account for the weird coincidence of math and science (e.g., physics)?

Given that mathematics is a body of universal and necessary truths, how could science (or anything else for that matter) not coincide with it? If the physical world was to violate the principles of mathematics, now that would be weird.