Have you ever read a research paper and found a mathematical mistaken in it? Indeed I have, and perhaps you are not skilled or knowledgeable on the topic, but there are mistakes, and they do exist. Often these peer-reviewed papers do not get the adequate time necessary to hash out all the issues or find the mistakes. Further, often research papers have a lot of math in them, but they are solving the wrong problem, or attacking the problem the wrong way, and yet they publish the paper anyway.
Of course, I've also seen mistakes in college textbooks, supposedly written by the professor, and a group of grad students. Yes, it happens, and sometimes the professor points it out to the students along the way, or the correction will come about the next year. This seems unfortunate when you are paying $225 that college textbook in the first place, and so perhaps I might shed some more light on this problem, I'd like to tell you about something I recently read.
There was an interesting post on SlashDot on March 4, 2012 titled; "Math Textbooks a Textbook Example of Bad Textbooks," by Samzenpus, where the words of Keeghan were reiterated, namely that;
"There may be a reason you can't figure out some of those math problems in your son or daughter's math text and it might have nothing at all to do with you. That math homework you're trying to help your child muddle through might include problems with no possible solution. It could be that key information or steps are missing, that the problem involves a concept your child hasn't yet been introduced to, or that the math problem is structurally unsound for a host of other reasons."
Now then, in the future I suspect that math textbooks will be holographic, give it five more years and they will project holograms of the shapes, and images which you are trying to figure out. Putting things in three and four dimensions with a projected hologram makes a lot of sense. Imagine the advantages for a student who can visualize the math problem using holographic imagery. You see, in solving these problems in this way they will be using the spatial part of the brain, and not the language part of the brain were they are trying to determine what all the symbols mean.
Indeed, I bet that the students learn math better, quicker, and go on to enjoy it more, therefore do better at the subject and get better grades. Perhaps, we are just a few technologies away right now from having all the math and science engineers, scientists, and future generation of mathematical intellectual superstars graduating from our high schools and colleges. I wouldn't be surprised, and I hope that if you are involved in any of these types of technologies, that you will be thinking here, please consider it.