If you believe what Wolfram Research say, there are several million Mathematica 
users. See for example

http://www.wolfram-media.com/products/mathematicabook.html

where it says about a book:

"The definitive reference and tutorial for several million enthusiastic 
Mathematica users around the world"

There are several things that make me question the truth of this. One, 
admittedly not very sophisticated metric, suggests the number of *active* 
Mathematica users might be only 1.71 that of Sage!

First, why do I not believe this several million number?

1) As an engineer, working in several companies over the years, I've seen very 
little usage of it. Plenty in academia, but little outside.

2) Do a job search on monster.com and see how many jobs require Mathematica 
knowledge. Then compare it to MATLAB, and you will find far more companies want 
MATLAB skills than want Mathematica. If there were several million users, I 
would expect to be able to find lots of jobs requiring Mathematica skills.

3) WRI come out with a lot of ****, like for example that publishing a 
'Demonstration' on

http://demonstrations.wolfram.com/index.html

counts as an academic publication! See the FAQ at

http://demonstrations.wolfram.com/FAQ.html

where it says:

---------------------------------------------------
Question. Do Demonstrations count as academic publications?

Answer. Yes. Every Demonstration undergoes a rigorous review process that 
checks 
for quality, clarity, and accuracy, so you can count them as academic 
publications.

---------------------------------------------------

It sure would be easy to get a lot of publications and a chair if one could 
write papers as simple as this demo!

http://demonstrations.wolfram.com/SineAndCosineGraphGenerator/

So how can one judge the popularity of Sage vs Mathematica? Well, given they 
both have one main public support forum:

Sage - sage-supp...@googlegroups.com
Mathematica - comp.soft-sys.math.mathematica

a comparison of the number of recent posts to these forums might give us a 
clue. 
(Can anyone find a better way? Is this a totally flawed metric?).

As a test, I logged into Google groups about 10 days ago and quickly looked at 
both the sage-supp...@googlegroups.com and comp.soft-sys.math.mathematica 
lists. 
When you do this, Google set the time of "Last Visit" to zero and the number of 
"New Items" back to zero. Some time later, you can see when you last looked, 
and 
how many posts there have been since.

Here's a screen shot.

http://sage.math.washington.edu/home/kirkby/Mathematica-vs-Sage/mathematica-vs-sage-support-requests-19-11-2009.png

The number of new posts in this period, which was about 10 days, but I can't be 
sure exactly, are:

comp.soft-sys.math.mathematica 194
sage-supp...@googlegroups.com 113

That's a Mathematica/Sage ratio of 1.71

That's not a huge difference. If Mathematica has several million enthusiastic 
users, then Sage should have more than one million, which I very much doubt!

There are clearly problems with a direct comparison like this. It's clearly not 
a rigorous statistic.

* Mathematica users can email supp...@wolfram.com, but with a turnaround time 
of 
a few days, it is not very useful for quick questions/answers.

* Since comp.soft-sys.math.mathematica is moderated, some people do ask their 
questions in sci.math.symoblic too. But there are not that many Mathematica 
questions there, so I do not believe that distorts the number a lot.

* Perhaps Mathematica is so easy to use, few users need support. In contrast 
Sage is so hard to use, that a higher percentage of users need to ask for 
support. Personally I do not believe this to be so.

PS, you can't make similar assumptions about Solaris/HP-UX/AIX as all of them 
have other major public supports forums. But Sage and Mathematica do not, so a 
direct comparison of new posts, while not perfect, gives us at least a clue.

It will be interesting to see how that ratio changes over time. I might set up 
another google account, register both groups, but never read them. That will 
allow us see how these numbers changes over time.

Dave

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