The title is a bit misleading, but the insistence of people on commenting -- and ostensibly refuting -- established science through use of pseudoscience. For example, your average American layperson doesn't believe the theory of evolution, believes himself capable of refuting the combined expertise of every biological scientists (well, 99.99% of biologists; see the "Scientific Method" essay for why the distinction is immaterial). The problem is, next to any given biologist, a layperson knows almost literally nothing. This extends to beliefs such as astrology, Star-Trek-educated physicists, and pretty much every form of pseudoscience.
Mathematicians don't really encounter this sort of resistance, although I've met one man who insists that division by zero is possible and doesn't realize that it would break the ring structure of the integers. I suspect this is because math is presented as impenetrable from the very first, and it's, frankly, difficult to wrap your head around the concepts. Have you ever seen the definition of a topology, for example?
So, I'll illustrate the point first with mathematics, and an anecdote, at that. As of this writing, I'm nearly three-quarters of the way to an undergraduate degree in mathematics. I've seen and understood more mathematics than probably a good 99% of the American population. However, I'm just beginning to comprehend the sheer magnitude of all the information mathematicians have discovered over the past three centuries. Men since Fermat and Newton have been working day and night to advance mathematical knowledge for hundreds of years; it's taken the equivalent of three years of study to get me to the point where I'm only beginning to viscerally understand just how little I know in comparison to everything out there. If I am only beginning to intuitively understand just how little my mind's candle illuminates in the cathedral of human knowledge, how does someone who hasn't studied any math since trigonometry (and that's not real math, for the record) realize just how miniscule his knowledge of actual mathematics is?
Math isn't really an issue for people, because they figure that they won't need to know any of the incredibly complex beauty and structure of the interconnecting theorems between, say, a family of functions on the complex plane and its continuity, convergence, and the different ways it can converge and be continuous. In fact, the average person probably won't need to know anything beyond simple applied calculus (of course, I imagine the life of someone who only learns things he needs to know to function in society is boring, cold, and incredibly confusing), and so won't bother trying to refute a mathematician on the topics he's spent years studying; instead, he'll simply accept the mathematician's word, roll his eyes, go on with life, and completely forget what the mathematician said. The stakes are slightly different in different fields of science: evolutionary theory, for example. Inevitably, deeply religious people feel the need to refute the theory of evolution, refusing to treat an evolutionary biologist with respect as they would a mathematician (although the level of expertise both accrue in their respective fields is similar). Pseudoscientists and their ilk treat their various fields of science similarly: astrologers, new-age, and all that. Creationism is only, frankly, the most prominent offender, so I'll be picking on it in this essay nonetheless.
So, let's start to illustrate the differences between the education of your average layman in the sciences and the education of an expert in the field. To master a particular field and so receive a doctorate, it takes roughly a decade of constant extra education in the topic beyond that which the candidate received in high school. This is just about the time elapsed between beginning elementary school and finishing high school. So, the layman needs to realize that the difference between his knowledge of a given scientific field and the knowledge of experts in that field is similar to the difference between the knowledge of a senior in high school and the knowledge of a first-grader.
To try a different analogy, consider the inner workings of a nuclear reactor. You know that it's got lots of rods with uranium in them, that it starts a reaction by lifting graphite out so neutrons can instigate nuclear reactions, that it's cooled with water, that it's surrounded by a big concrete shell. So, can you, from scratch, build a nuclear reactor? Do you know how to mine the material for the concrete, manufacture the concrete, build the building? Do you know how to mine, refine, and manufacture the fuel and material for the fuel rods and cooling system? Do you know the first thing about the nitty-gritty of the electronics that go into the control room, the safeties in place to prevent a meltdown or explosion?
Or think about a computer. We all know how computers work in principle: electricity runs through circuits on the motherboard, runs the fan, processor, hard drive, and various chips. However, could you build from scratch even a single chip, let alone an entire motherboard even equivalent to an old 1980s computer? Do you have the knowledge of dielectric constants, capacitive coupling and crosstalk, inductive losses, timing issues, proper grounding, and a million other things I couldn't even begin to list off the top of my head because I've got no idea about how a computer really works?
Finally, to wrap it up with a mathematical example, an analytic complex function at any point in a simply connected domain is completely determined by its value on the boundary of the domain. Could you prove that theorem? (It's called the Cauchy Integral Formula, by the way.) To even begin, you'd have to first know what a function is, what it means for a function to be complex, what it means for a complex function to be analytic, and this isn't even beginning to touch all the local integral theory required to build up to the global formula.
The point of all of these analogies is to demonstrate that even though you think you know and understand a principle, that doesn't mean that you actually understand the field around it, let alone well enough to refute experts who have spent as much, and more, time studying it as you spent going from the first grade to the twelfth grade. One of the great failings of the modern primary and secondary educational systems is the failure to communicate just how little high school graduates actually know and understand; this, in turn, has contributed to and aggravated the anti-intellectual atmosphere brewing in modern America. Why trust the scientific community's consensus on, say, global warming? Because, quite simply, they know what they're talking about. Why trust the scientific community on evolution? Because evolutionary biologists are well-deserved, qualified experts in their fields. Why trust the scientific community on mathematics? Because mathematicians have spent years studying math, years that have been spent toward understanding the material. That level of expertise ought not be lightly dismissed.
Thanks to the fine ladies and gentlemen of the Stardestroyer.net message boards who posted in this thread, especially "aerius", "kheegan", "FSTargetDrone", "Darth Zod", and "Darth Wong".