When ideas are actually being trafficked -- that is when they're new and struggling for breathing room, they're rarely clearly right or wrong. Consensus forms over a fairly long amount of time. With luck, and a lot of verification, over the course of a decade or three theories elide to the canon of science's best understanding of a given problem space. There we might broadly refer to theories as "true", but that's just everyday conversational shorthand, not the language of science.
The problem in the intersection with pop culture is that it's generally only well after those couple of decades of a theory working its way into the canon of scientific understanding that it begins working its way through pop culture. This is the critical point where there's a lot of naysaying from the general public and a lot of rolled eyes from scientists. It's at this point that science transforms into politics: each side hardens their positions, begins stating them in absolutist terms and tries to win the other side over, usually based on an appeal to authority.
Science itself is, in fact, a slow and reasonably democratic process. It is at times dogmatic, but far less than, say, American politics.
Does maths use the scientific method to answer questions? Do the questions maths can answer concern areas outside of just maths? Is maths something that is used _within_ the scientific method to answer questions, in a variety of different disciplines?
It's a lot easier to approach and attempt to answer questions (get consensus) when you have a generally accepted method for doing so. It seems like maths entusiasists, e.g. the kind who love computers, can take widely different approaches to answering the types of wide-ranging questions addressed in the sciences. They may even disregard the scientific method altogether.
If Usenet/WWW is any indication I'm guessing this leads to a lot of disagreement between maths devotees if the topic at hand is anything but pure maths and logic.
Not taking anything away from people who love maths. In fact, one of the major problems in the sciences is the lack of mathematical rigor by far too many scientists when analysing results.
tl;dr Scientific method + maths = good. Need both for solid analysis and reasoning.
See e.g. http://rationalwiki.org/wiki/Engineers_and_woo
I often think that while a purely technical background and education might be really powerful and enable one to analyze and predict well-behaved things better than others - which could lead to better decisions, it is extremely important to be receptive to the "inexplicable-until-experienced" stuff like music or business or relationships - to know that there are things that can't be controlled and shouldn't be controlled - that some things should evolve of their own accord - the chaotically evolved imperfect being more beautiful than the mathematically-designed perfect. (Edit: a combination of both works quite well, in my experience - some of the best businessmen, economic and political advisers I know of have engineering backgrounds - and no, they aren't unreasonably conservative or dogmatic).
In my opinion, the fear of "what will happen if I let go?" can lead to authoritarianism via technocracy (aside from the fact that anyone can get drunk on power) - not one's profession.
Funnily enough, in our media it was reported that of late, students receiving top-level government scholarships to the US/UK/elsewhere hardly ever choose engineering any more, but study economics instead (probably influenced by the dominance of the financial industry). So the next generation of Singapore leaders may very well be dominated by economics trainees - I wonder what sort of government we'll get, then? Certainly a more diverse one, but also one lacking in engineers and scientists.
Science may not be binary, but it's a heck of a lot more binary than Literary Criticism, Political Science, Law, or even Economics.
Consider the recently proposed ban on large servings of sweetened drinks. Do these promote diabetes costing the country lots of money in eventual treatment and lost productivity? Absolutely. Does the government have any business telling me what I drink with my Quarter Pounder and Large Fries? No.
I believe the answer to something like diabetes is more nuanced, such as the promotion of healthy eating habits in general, removing the massive grain subsidies that promote the existence of lots of cheap carbs and the availability of lots of meat. I'm sure a sociologist or psychologist could come up with better ideas for promoting health diets without being excessively coercive.
I in no way see how this applies to your fear of rule by scientists?
Speaking from the peanut gallery, more specifically, it's much more Bayesian than people would have you believe. Popular literature and most science instructors are not a very good source of context.
The hype does not equal the delivery.
I've tried having conversations explaining Bayes, general probability, and its relationship to scientific theories. Almost always falls on deaf ears. People are incredibly horrible at math--and I don't even consider myself to be that great at it. Their failures at being good with understanding maths flows into being horrible at understanding science, especially that which involves mathematics as integral part of its probabilistic standing in relation to alternatives.