Analysis is only as good as your boundary conditions, I agree, and our uncertainty in these fields reflects the fact that they are areas where it is inherently difficult to isolate boundary conditions. Still, a lot of progress has been made in these subjects (except economics, arguably, I'll give you). Climatology is far from perfect, agreed, but we know much more about it than we did a half century ago.
Who fails in science?
People whose theories and findings are not vindicated by alternate lines of inquiry. A very recent case example, the search for pentaquark (5-quark as opposed to standard 3-quark particles), which was tentatively thought to exist, has not been found where it was expected to in recent experiments. The theory failed, and unless something new comes out to lend credence to its existence, it's likely to become a relic. An example of where enthusiasm ran high to look for something that was thought to exist but competition has driven the idea to lesser relevance. Sometimes the absence of a phenomena can be just as revealing as the presence of one, though (e.g. the null result of Michelson-Morley experiment?)
EXACTLY! That's what makes mathematicians the only ones who actually know what they're doing.
There's where you're wrong. Did a mathematician build the computer you're working on? Did a mathematician build the bridge you drove over to get to work? Did a mathematician invent the antibiotics you took the last time you were sick? There's inherent uncertainties in science, but that doesn't equate to complete uncertainty. (e.g. Someone who says the earth is flat is wrong. Someone who says the earth is a sphere is also wrong. They are not both equally wrong, however.) The bottom line in any science theory is, does it make predictions that are fulfilled, and does it continue to do so?
And math is HARD.
No joke. I've trudged my way through enough grad level physics courses to know that. Nothing I've ever done was more difficult. Anyone with the ability to make it as a mathematician has my due respect in that regard. Are you aware, though, that there are difficulties of comparable magnitude in experimental science, as well? The statistical end of it can be nightmarish, and has to be so to minimize the uncertainty in results.
In short, math is superior than science and if the scientist knew just a little more math (or paid a mathematician to do his thinking for him) he'd see that there's a lot that it can do.
Without science, math doesn't have any practical use, though. Scientists do consult mathematicians where necessary. Theoretical physicists are little more than mathematicians who deal with physical phenomena. Chemists and biologists work with statistics constantly. Mathematics is only 'superior' to science because it isn't inconvenienced by having to deal with real data. I'm not trivializing your field, I'm only stating that its importance is specific. Math is the language of science. Without somewhere to apply it, mathematics would be little more than an exercise in intellectual hedonism. (Don't take that the wrong way - I'm well aware of the importance of having pure mathematicians around - just pointing out that its real world applicability is the bulk of what makes it important to humanity.)
I read PH's article and I don't buy it. It's just an attempt to avoid the pejorative associated with the word "faith". No different from any other "my religion is better than yours" argument.
Call it what you want - my "faith" in science (as you term it) is based on its track record for success, though. Yes, I do have "faith" that the internal combustion process will get my car to work in the morning, so what? I have "faith" that beer and buffalo wings will taste good the next time I eat them. By your definition, I have "faith" in a lot of things. None of these things, including science, have to do with my religious "Faith", however - that is a completely different matter.
Economics is the art of finding the best-fit straight line to a single data point.
A very recent case example, the search for pentaquark
Physics is a bit more rigorous than the rest. There are a number of scientific fields in which you just report on the answer. But the interesting thing is that people make a living on just the search for the 5 quark. Mathematicians, if they can't make definite improvement on a problem, must throw out their useless non-answers.
There's where you're wrong. Did a mathematician build the computer you're working on?
Actually, yes. Boole. Or should the credit go to the kid at Dell who put it together?
Did a mathematician build the bridge you drove over to get to work?
Yep. Or does the credit go to the guy who put in the rivets?
Did a mathematician invent the antibiotics you took the last time you were sick?
Pretty much. Or does that idea go to the pharmacist? There's an intellectual food chain here. We are unthanked, forgotten and called "practical" only decades after we've died.
Are you aware, though, that there are difficulties of comparable magnitude in experimental science, as well?
They are all, at their root, mathematics.
The statistical end of it can be nightmarish, and has to be so to minimize the uncertainty in results.
See?
Without science, math doesn't have any practical use, though.
We thank you for doing the dirty work, but my point is that mathematicians see the whole forest. And the beach. And the mountains. The scientist, the practical scientist, is staring at the tree.
Theoretical physicists are little more than mathematicians who deal with physical phenomena.
Absolutely. They actually push the mathematics.
Mathematics is only 'superior' to science because it isn't inconvenienced by having to deal with real data.
Yep. Absolutely.
I'm not trivializing your field, I'm only stating that its importance is specific.
I disagree. It's general. Disgustingly general. Infinitely general.
Math is the language of science. Without somewhere to apply it, mathematics would be little more than an exercise in intellectual hedonism.
Mathematics is the language of the human mind. It is the only way we can understand the world. It will always be practical, no matter how hard you try. And I find it amusing that as a graph theorist (networks), I'm a "pure" mathematician.
Yes, I do have "faith" that the internal combustion process will get my car to work in the morning, so what? I have "faith" that beer and buffalo wings will taste good the next time I eat them. By your definition, I have "faith" in a lot of things.
No, what you describe is "expectation".