Can you provide examples for the ideal case for you? What would you like to see in Mathematica to make it easier?
As a heavy user of both, my experience is that Mathematica is more difficult initially when writing your code, but is ultimately easier than Excel because the thing you would be doing in Mathematica would be very hard to do in Excel (it is both a technical as well as maintenance nightmare).
I typically use Mathematica to prototype ideas. When they pan out, I integrate them with existing code written in c or Python. That Mathematica excels at symbolic manipulation as well as numerical solutions while having excellent visualization tools makes it invaluable.
In particular I love to build up some complicated function of many variables and wrap a Plot[] command in a Manipulate[] command so that I can drag the slider bars around and see how the shape of the function changes. This allow for me to get an intuitive understanding of the problem.
I use it mostly for exploratory data analysis. I'm pretty quick with making plots in it (I've used it since v1.2), so I tend to use it for reading in a data set, and them playing around with it. It can handle datasets in the hundreds of thousands of points (still in memory) pretty quickly. You can plot 200k points a series without it slowing down.
On those rare occasions I need to solve equations or do some calculus, there's nothing better.
Me too. I still use it quite frequently. One example where I've used it many times is to debug encryption algorithms. Mathematica can usually handle the most natural form of the Algorithm allowing you to compare the results with optimized low level code.
Given symbolic manipulation, Mathematica allows you to frame your problem without stating how to solve it, even though it would nearly always need some help. I often do the math by hand anyways beforehand for the purpose and to understand what is going on, but Mathematica subsequently allows automating and easier maintenance.
While this could be an extensive debate, I prefer Mathematica to Matlab whenever there is an option. I am a heavy user of both, though have never used Symbolic toolbox in Matlab. It starts a lot more complex in Mathematica, but becomes significantly more powerful shortly thereafter.
The ulterior goal of infrastructure is consumption. The goal of everything you suggest is consumption. Infrastructure supports businesses and employees. All these crazy R&D projects are only a success when consumption has been increased. There's not much difference between consuming reality series or some high pretentious art, a lot of people will prefer the former.
All these cheap lunches together, one for the plantage worker, the transporter, the designer, the real estate holder, the taxman, etc. etc. is the clockwork of the (global) economy.
