Below I shortly site two posts arbitrarily picked up from few more, where the authors are discussing reasons why the offer of Mathematica as a tool for analytic calculations is often rejected.
All these reasons are, of course, solid, and I know at least one more such reason, if not a few.
However, there is the fact that Mathematica cannot make some simple analytical operations that are easily done by hand. As one of multiple examples one can have a look at the recently discussed problem of custom ordering of elements of expression. One can follow the thread initiated here: http://forums.wolfram.com/mathgroup/archive/2013/Apr/msg00198.html.
Alternatively, one can do some such operations with Mathematica, but this requires a good knowledge of Mathematica programming to achieve things that could be easily achieved by hand, the knowledge being far beyond the elementary one. I am making such calculations and have lots of examples requiring such a programming. I know by experience that using Mathematica pays off, and each of us knows that, of course. But why do we think that a newbie also knows that?
I believe that the outcome is that a new user (let it be a student, an engineer, or a professor) will be rejected by his first (second, third,... tenth) experience. I observed several such cases.
And this actually is a very serious reason. Important that it is not in society or psychology, but in Mathematica itself.
I think that at least partially the situation depends upon the incompleteness of the analytical sub-package of Mathematica. I believe, it misses several easy-to-use functions to make some common elements of calculation. The examples of some of such functions (but not limited to) may be found in the Presentations/Manipulations sub-package of David Park. For example, such as bringing a custom factor out of parentheses, multiplying of numerator and denominator by the same factor, completing the square and others. Especially important are the functions addressing parts of expressions and enabling one making transformations there, leaving the rest of expression untouched. Important, that they all should be as intuitive as possible.
The second point is that examples shown in the Menu/Help for operations on analytics are often too elementary. A certain number of examples should, indeed, be simple in order to guide a newbie, but there should also be more complex ones covering different aspects of use of the function in question alone and in combinations. Their complexity should increase gradually. There should also be lengthily tutorials on analytics.
Mathematica is great already as it is. However, I believe that until this is not fixed, Mathematica will not become a common tool of choice for making analytics, though it has all potential for that.
But that was exactly my point...I tried so hard with our Community College and University to get Mathematica into the curriculum....or, as I said, to give some lectures and examples on the use of Mathematica....and ALL of them, Engineering, Math and Physics Depts said 'Thanks but No Thanks', as if they have something against Mathematica....It seemed that the idea that students would not use pencil and paper in as laborious a manner as possible really bothered them....Not once did they think perhaps this might lead to a real enjoyment of technical subjects and perhaps to much better understanding of their course work......even when I was working I was affectionately known as 'The Mathematica Nut'...although, I'm reminded of something that Nietzsche said....
"Overzealousness on the part of one person can lead the others to Apostasy".....
...Similarly, too many mathematicians cannot see why their students should
not learn how to carry out long and complex symbolic calculations, e.g.,
symbolic integration, with paper and pencil; after all, they had to do
it. Oddly enough, some of these same mathematicians use powerful
symbolic programs to do their own research in number theory, algebraic