According to the word on the street, people REALLY hate math. Even Stephen Hawkin’s Brief history of time is math free:
Why do people hate math so much that half leave at every number? Is this more human stupidity, laziness, or just too cool for school? Explain.
How about, in addition to the negative reasons you listed, you include the idea that for a substantial portion of humanity math is hard. That doesn’t mean it can’t be mastered, and I’ve known some people who had little talent in math who, through hard work, acquired advanced math skills. However, many people who find math hard avoid except when necessary because they don’t find it fun or enjoyable.
Thus, when writing a book geared for the general public, if you include math you’re likely to make it less appealing to those who dislike math not through stupidity or laziness or “too cool for school” but rather because they find it hard. It’s one thing to exert the effort because your job requires it, or your life requires it, it’s quite another to expect people to do that for what is intended to be a popular book.
As an analogy, I have on occasion run a mile, but I detest running, I don’t enjoy it, and avoid doing it unless there is some underlying motivation. That motivation might “required to pass the gym course” or “Someone will pay me $100 to do this” or “someone is shooting a gun at me”, but it’s not something I’d ever do for fun. I don’t enjoy hot weather, either - I’ll work outside in hot weather for eight hours or longer if I’m getting paid to do so but unless you pay me I’m sitting indoors, in air conditioning, sipping a cool drink. I don’t run for fun, I don’t sit in hot weather for fun, and I don’t do math for fun.
I learned what math I actually needed to know, then some beyond that. I had to learn some additional formulas when I earned my pilot’s license, which I did, and committed to memory, and became quite good at them, but if it wasn’t for the fact that a hobby required that knowledge I never would have bothered to acquire it. For me, math is a strictly utilitarian subject. I only bother to learn what I actually need to know, because I just don’t like it.
I read Stephen Hawking’s book. I didn’t run screaming from the room when an equation appeared on the page. Then again, he did make an effort to explain as much as possible without math equations, and what was included was rather important to understanding what he was talking about. I found the subject sufficiently intriguing to wade through that. That’s all.
Bottom line, I hate math because I find it hideously difficult to master (though I did exert the effort to get what I need to get by in life) and in no way find it enjoyable or pleasant, although sometimes the results of math are sufficiently appealing so as to induce me to exert the effort to learn/perform math operations.
Most people get at least 6 years of math in school beyond the basic arithmitic that gets covered in elementary school. If you like math (as I do), thats a good thing, but if you start out not liking it, or being anxious about your abilities in it, then six years is a long time to have to suffer. And I imagine a little anxiety and distaste in early grades leads to poor performance on tests and homework, which leads to more dislike and anxiety, whcih leads to worse performance, etc. Plus, testing in math is a big part of SATs and similar tests, hence you can’t really just blow it off, and there’s that much more anxiety for people that don’t like it. If you want to do well in school, there’s no where to hide.
And all that is at a time in peoples lives when they’re still learning how to cope with stuff they dislike but can’t avoid.
So I don’t think its really surprising that a lot of people end up with a pretty visceral dislike of mathematics.
I agree with Broomstick and Simplicio. I was above-average at maths (as it should be spelt - from the root mathematics ;)) at high school but collapsed eventually. I’ve never needed more than basic arithmetic in my working lifetime.
Curiously one of my cerebral interests is astrophysics and quantum physics. I cannot follow any of the equations but nevertheless understand these areas in a broad sense. The only equation which has captured me is e=mc2 and that required an entire book to explain it. Fascinating.
I think a lot of the problem is that math is often taught with no context. Instead of explaining why this or that concept is useful, textbooks and teachers confront students with pages of equations that are completely stripped of any context or application. In my adult life, I’ve found some higher math useful, but had I known about possible applications in high school, I would have liked math more and found it easier.
In terms of why math is “harder”, I don’t think that’s necessarily true. I do think that many people (including me) just don’t think in the abstract way necessary to be successful at math as it is currently taught. This is not a bad thing, it just is. As more research is done (and it is a hot topic, so there is lots of this going on), and we learn more about how people learn math and how teachers can more effectively teach it, the situation will change. Until then, it’s job security for scientists and mathematicians. 
My wife as an elementary school student used to do math more slowly than her peers. That’s no problem. But she had to participate in “math races” in her math classes. Because she never won her race, her team often yelled at her.
In middle school, she had a math teacher who was a coach who yelled at her when she got problems wrong, and when she didn’t complete all of her homework, was made to put her nose on the chalkboard for several minutes. When she told her coah in private that others only completed theres because they were cheating in the hall before class and she refused to, his response was “Well you need to figure out something.” He was implying to her that she ought to be cheating to.
So for her, however unconsciously, math is about people yelling at her and demanding she betray her own integrity.
Of course that’s just one person’s story, but bad education is a pervasive problem so I’m guessing there are stories simillar to these behind a lot of people’s seemingly visceral dislike of math.
(Wife probably also has dyscalculia, based on our own amateur diagnostics, but that didn’t have to mean she disliked math.)
If music were taught the same way maths is – by introducing scales, sheet notation, chords, harmonics, memorizing all of the above, subjecting it to mindless manipulations according to seemingly arbitrary rules, all before ever actually listening to a single piece of music – I’m sure people would hate it just as much. It would seem to be just a complicated jumble of rules for manipulating funny marks on paper. Oh, sure, you’d have heard about some people doing beautiful things with music, but all of that would sound far too complicated to ever really get into and grind through all those chord progressions and meters. Plus, what’s it good for, anyway?
But luckily, that’s not how things are. We’re exposed to music all the time, and while few ever truly dig deep into the foundations of music, there’s probably hardly anybody that can’t enjoy a nice tune.
And it’s actually similar with maths – there’s hardly anybody that doesn’t enjoy a puzzle, and at bottom, that’s all maths really is. It’s just that this tendency isn’t furthered, and the connection most often remains unexplored. Maths is introduced upon unsuspecting students in the form of some fixed edifice of arcane rules, set in stone by the ancients, to be followed without fault, rather than just as a way of figuring things – making up stuff and rules and see where they take you, trying out different ways to arrive at a solution, just because it’s fun. That anybody at all ends up doing maths for maths’ sake is almost a miracle, and just speaks to how ingrained that puzzling tendency is within us.
Well, I could go on, but really, Paul Lockhart said it better in his A Mathematician’s Lament (pdf). Anybody at all interested in the teaching of mathematics should read this, I believe.
I pretty much agree with Broomstick. I’m no dummy but I really struggled with math throughout my school years, and in high school - the last time I took a math course - I ended up in the remedial class, even though everyone was too polite to identify it as such. I had some very good math teachers over the years but math never came easily to me. Row after row of numbers, rules that didn’t make intuitive sense, knowing with despair that it would only get harder, year by year. Gah. Now I’m 46 and in a nontechnical field - I never need math more complicated than addition and subtraction when I’m writing a check or figuring out a tip.
For those who love math, relish complicated equations and find elegance in the march of numbers, more power to them. I gladly acknowledge that math is vitally necessary for scientific and engineering advancement. It’s just not for me.
Though more time consuming, math should be taught in an applied manner as much as possible. It is the abstraction of figuring with numbers rather than working with real problems and solutions that drives many people, myself included, absolutely batshit insane. Simple algebra, geometry and even some trig can all be logically explained using real world examples and puzzles to help it make sense to people. Instead we use endless repetition, arcane formulas, strange rules, and the rare, boring word problem.
But what about those that prefer it more abstract?
I have a Pure Maths degree, so I guess I am classed as “ok” at Maths 
Having to apply everything to real world ideas when doing these things at school would have driven me insane. Abstraction by definition hides a lot of the important stuff from you.
I think the music argument is overly simplistic. Why should it be applied to Maths and not other subjects? I learnt Swedish as an adult (I had my first lesson at the age of 25) and it was done in a more “modern” way of just using the language from the off instead of the repetition. It was nuts. We spent class after class after class just not knowing what the hell was going on as the important basics just were not drilled in to us.
Language and maths are not music. With music you can fiddle until something sounds nice, no matter if it breaks musical rules or not (). There is no concept of “sounds nice” in maths and languages, there is simply “getting it right”.
() On that note, I had a housemate at University that was an exceptional pianist. He couldn’t listen to “Don’t Look Back in Anger” by Oasis as it broke some hideous musical rule. I’d hate to be so good at music that I couldn’t listen to things because it broke the rules. In music rules are there to be broken. Not so in Maths.
I think there’s two issues at work here. One is educational and one is cultural. For education, as some touched on upthread, math isn’t taught in the same way that a lot of other subjects are, and without context it gets separated and too theoretical. I think word problems try to address that problem, but the just end up presenting unrealistic scenarios. It seems like a lot of math basically just gives you the formula for how to turn plug in some values and get other values out, but if people don’t understand WHY they’re doing what they’re doing, they’re just plugging numbers into magical formulae. And, worse, because math builds upon the simpler concepts to create more complex ones, the moment one gets lost on a concept, anything that builds on that concept is also impossible to understand.
To this end, I think I was fortunate to have some good math teachers through high school who understood this and made a point to really explain the derivations of the formulae we used and exactly how they’re applicable. For instance, in high school I learned calculus by starting with the physics principles, seeing how a concept like instantaneous velocity would be useful, and then going about figuring out how to derive that. From then on, even if some of the formulae got a little fuzzy, I at least had an intuitive concept of what that meant, so I could still meaningfully build on that.
The problem is, a lot of kids get lost a lot sooner. Take long division for example. I just remember being taught that that was how you do it. When we asked why it worked or anything like that, our teacher couldn’t explain why, so it was just a magical algorithm that worked. So that meant we had no intuition behind why it worked, and when things went wrong, we really couldn’t understand why. I suspect that some of those kids never got it, and pretty much anything from then on just seemed even more complicated.
As for the cultural aspect, I think it’s a lot simpler. Somehow it seems socially acceptable to be bad at math. If someone fumbles some relatively simple arithmetic, they can just say “oh, well I’m bad at math” and everyone gets a snicker out of it and no one thinks worse of that person. But then imagine if someone has trouble reading just a few simple lines, you’ll NEVER hear anyone jest with “oh, well I’m bad at reading”. I think this cultural divide reinforces the idea that math is hard and not necessary in every day life.
And, of course, as technology continues to improve, the applications of math become less and less obvious. Where people used to be able to say you needed it to balance your checkbook or whatever, that just isn’t needed anymore. Instead, a lot of the applications of math in everyday life are a lot less obvious. OTOH, compared to other basic skills we learned in elementary school like reading, we make use of it constantly. So I think that the use of it isn’t as obvious, it somehow gets stuck in the realm of academia and nerds and, well, that sort of stuff is hard, right?
Unlike dyslexia, which is quite commonly known (if perhaps at times misunderstood) it is much less well known that there is a learning disability called dyscalculia and it affects, among other things, the ability to perform basic arithmatic distinct from comprehension of underlying theory. It is a spatial and sequencing problem that also affects the ability to physically sequence your body (as in “klutziness” learning dance steps or following an aerobics instructor) and overall manner of understanding spatial orientation, leading to a characteristic manner of reading a map (always orienting the map in the direction you are facing), and endemic problems with differentiating left and right. Many people have no idea that these are part of a constellation of related issues, that also express themselves in math class.
Like dyslexia, dyscalculia can be found in people with normal to exceptional intelligence in other areas, including accelarated verbal/reading/writing ability.
That depends entirely on your conception of mathematics. If you want to see it as a set of fixed rules according to which operations are to be carried out, then yes, there is only one right way. Thing is, there is no central authority that has decreed what is proper maths and what isn’t; rather, it’s an evolving conceptual framework delineated mostly by what people find interesting – what ‘sounds good’ to them. Rules are broken (or rather, changed and amended) all the time: it used to be that taking the square root of negative integers was considered the devil’s work, but nowadays, people are quite comfortable with it.
Of course, if you have settled on a set of rules, you must be consistent within it (otherwise, there would be no point in setting down rules at all), but the same goes for music – if you play a note that does not fit into the scale you’re using, for example, it just won’t sound right.
And as with dyslexia the numbers with it will be small, but the numbers that have parents that think their child has it as their special little baby couldn’t possibly just be bad a counting will be much, much higher.
When you’re dealing with arithmetic - and let’s face it that’s mainly what we’re talking about here - there may not be one path, but there is definitely one destination. It is called “the right answer”. You can do 702/13 whichever way you want, but there’s only ever going to be one right answer when dealing with basic school arithmetic.
There is no one destination with music.
Only because that’s the way it’s taught, which is where I think the problem lies. You could analogously teach music by just harping on about the sonata form, where there’s probably as much of a possibility of being right and wrong.
Read what I wrote about “sounding right”. Music can “sound right” despite it not being absolutely correct as far as musical theory goes.
There is no “sounding right” in arithmetic. There is “right” and “wrong”.
Check the distain with which you utter “bad at counting” and you’ll understand how people end up with math anxiety (which can be just as debilitating, if not more so, than a learning disability).
No, I recognise that, along with dyslexia, it is a real problem that some people really, really struggle with and I feel for them.
However, it is also used as an excuse for lazy and/or not bright kids. Like “it is glandular” for obese people. Yes, some have that issue but there are also a lot of people that are just fat because they don’t exercise and eat too much cake.