I think we are all "wired" differently. Some concepts are extremely difficult to grasp..not necessarily because of the way they are taught, but because of the way we perceive/receive the information. Right-brain dominance, left-brain dominance...ability to see patterns, connections..ability to "think outside the box"...some of us do better at this and some of us are not so good at it. I think teaching something like History, however, is more dependent upon having a good teacher..one who makes it lively and interesting. But when it comes to abstract thinking, I think it has more to do with the receiver (brain wiring) than the transmitter (teacher). :)

It depends on how advanced you're talking. I can do algebra, but past that, forget it. My husband can do trig almost in his head, and his son is a math wiz, too. There's some things I don't understand, like when you have an equation with two variables and you are supposed to put in any number so you can find the first variable, then you use that to find the second variable. I don't understand how you can just put in any number, when math is supposed to be so rigid...

Adavnced mathematics is difficult to comprehend because it has no application whilst taught, learning how to integrate formulae with more than one variable has no obvious use. As a result the concepts seem far more foreign than biology for example, at least with biology you can get a 'hands on' experience that really sinks in the information. Most higher mathematics actually has no use when created, only later do we find a use for it like complex numbers is used for electricity even though they were created in the 1st century by Heron of Alexandria! Also you do have the problem with any subject of how the information is taught. Because mathematics is already a difficult conceptual subject it is extremely hard to teach to those who simply cannot grasp it. When a question is asked sometimes it is very difficult to explain why, for example: A friend asked me why anything to the power of zero is 1. It took me about five minutes to even think up the answer, then I had to put it across in a way that he could understand. When I explained it he said that he never understood at school but I made him understand in a matter of minutes. Another reason of course is the language. Unlike practically every other subject we do not use words and conversation but characters and symbols. You derive an answer that is difficult to word, understand, let alone explain. If I wanted to say in words: (x^2)*5y -------- 4z^3 I would have to say "x squared multiplied by five y all divided by four z cubed." Looking at the two you see no correlation, one is the day to day manner of putting a point across whereas the other is a jumble of characters from a foreign language. At least with learning another language you see patterns and similarities with your own language but with mathematics there is no such similarity.

It wouldn't be called "advanced" mathematics if it was easy. That, along with the rest of the great answers already mentioned.

Maths isn't all that hard - it's about being able to exercise logical steps to achieve a certain result. I speak as a physicist whose 'advanced mathematics' go to vector calculus, advanced integration, basically physical mathematics, I don't know what you consider to be advanced mathematics... However, It can be conceptually hard, as alot of higher-end mathematics and physics is to do with derivatives (partial or full), rather than actual functions of systems, it gets hard to visualize del E for an electric field for example, or the curl of a B-field unless you're used to doing it... In my opinion once you get used to using maths to describe a system and to visualize it it gets much easier to really put your head around

I think mathematicians have unintentionally made the subject a lot harder than it needs to be. Here are two examples: 1) Many many concepts are represented by a single intrinisically meaningless symbol. For example, the Greek letter pi or the Hebrew letter aleph. There's nothing "mathematically" wrong with doing this, since math treats these as abstract concepts. But it makes the "language" of mathematics harder to grasp and harder to remember. Words are also a kind of symbol, but they convey more information, and had math chosen to use words to convey concepts, math would take longer to write, but I think it would be easier to grasp what's going on. This applies to the meaningless letters of "unknown quantities" like 'x', too. A specific example of what kind of quantity 'x' could be: like "plane_height" could make what's going on much clearer. 2) Mathematicians love to generalize. For example, they love to see how addition and multiplication are similar and thus in many ways, can be treated in the same way. This love of generalizing means they would rather have a theorem about a general abstract fuzzy concept that can be applied in many places, than one about a specific concept that can be used in one particular place only. "Mathematically" the general theorem can be applied in more situations, but at the same time, is much harder to grasp. The best of both worlds would be to say, look here's some specific easy cases which are the most useful, and by the way, it can be generalized like this, in smaller print.

I struggled mightily with math, until I had a teacher in college who was quite gifted at his task, and I received an unthinkable(for me) B in Calculus. Educators are salesmen, and vice versa. To the extent one can make his product understood, that is the degree to which he succeeds. A salesman achieves a sale, a teacher educates his student. I had a math background chock full of misunderstandings, and poor math grades in high school. And yet, I was still able to comprehend and succeed at Calculus at the college level, and I fully attribute it to the phenomenal skill of this singular professor at Niagara University. What was it about this guy that I remember? 1. An empathetic kindness for his students, he always seemed happy. I believe this has more to do with his life outlook; not a skill set normally taught to educators. 2. Patience and context. Like a good salesman, he made sure that the information was getting through. I have used this experience often in my career when explaining difficult concepts in my industry to customers. 25 years later, I realize how important math is, and am brushing up on it to help with my kids, rather than drift through in a state of confusion. But for me, I think an excellent teacher can make a difference despite one's poor math background.

Advanced mathematics can be difficult to comprehend because most of it cannot be based on the typical way in which people reason in everyday life. For the most part, people are used to extrapolating based on what they observe to be true. Math, on the other hand, is all about making "stereotypes" about things, and making sure that you don't make a wrong stereotype. In a science like physics, you usually use theory to predict results, and then test the results to see if the theory is accurate. In math, you must always be right, and you cannot make a false prediction. Because of this, it is important for mathmaticians to rigorously define all the terms that they use in an unambiguous way, sometimes in ways which aren't what your own intuition would tell you. It is somewhat offputting to use the various assumptions of math without knowing why they are chosen to be what they are.