I challenge you to make the last graph of yours in Excel and in 10 'lines'! I think you just proved that it is really easy, all your examples are like 10 lines! I don't know any other software that can do that and still be reasonably readable and adjustable with such low amounts of lines.

Yes sometimes you have to wrap a Graphics around, and yes it is better to stay away from Epilog/Prolog if you combine some graphics, there is always room for improvement. But knowing that, i think it is very easy. I think your examples proof my point more than disproof it...

One thing they might do is to give users freer access for adding to the documentation, maybe like Wikipedia.

I would like to express my support to this idea. One example of another company doing this is the case of MySQL. Here you can see the official documentation for the SELECT statement and it is followed by user comments. Sometimes the comments end up being an essential to understanding the official documentation.

In regards to the original question of this thread, I work at an engineering company and I use Mathematica for:

• Fully automated reports generation and sending my email
• Development of tools for our internal use that run with the CDF Player (this requires the Enterprise license.)

And yes. I am sure that this could be done with different technologies, but I am also sure that it would take much longer to develop (if ever developed).

variability is a natural phenomenon. uncertainty is in the human mind. today it rains, tomorrow, it doesn't. that's variability. a forecast of 40% probability of rain illustrates uncertainty. Mathematica was used to "deconvolve" uncertainty from variability. http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.54746

2) Combining graphics is as easy as Show[{graphics1,graphics2,graphics3,..}] which is quite easy I would say ;) I've made many many Graphs in Mathematica, and never had a problem, and where necessary I made my own plot routine, which you can, really easily. I don't know any other products that supports such a customisable and wide variety of plotting routines! You can also write by default 'like a sheet of paper' right?

Graphics[{Blue,Rectangle[{0,0},{3,4}],Red,Point[xydata], Green, Line[xydata2]}]

I would say it is not 'extremely difficult' at all! very easy, just combine the primitives and plots you like using Show/Graphics/Graphics3D ! that's it!

3) I'm not sure what you are talking about, Lighting -> Neutral works as it should:

Graphics3D[Sphere[],Lighting->{{"Directional",Orange,{{0,0,4},{0,0,0}}}}]

and has always worked like this as far as I can recall. As far as extracting parts of graphic, I always remind myself this will be version specific, the primitives it creates might be different per implementation. So if you rely that it produces Rectangles, but now it gives rectangular Polygons (in another version), that should be easy to catch in subsequent version using a new rule. But I always try to stay away from these practices, it can be done, but that doesn't mean it should be done... You should customise directly using the plot routine and then combining with e.g. Show, or Epilog/Prolog.

4) Isn't the entire documentation available online?? http://reference.wolfram.com/language/ ?

I'm not an expert in Matlab. I've used it for a couple on-line courses, including convex programming and computational neuroscience.
I think that Mathematica's symbolic manipulation is a distinct advantage but I think there are other advantages. Mathematica supports procedural, rule based and functional programming. Matlab only has procedural programming. Also, in Matlab, the core data type is a 2nd rank matrix of real numbers whereas Mathematica is more general. I started an online course on probabilistic graphical models but dropped it because I got frustrated with trying to deal with higher than 2nd rank objects in Matlab.

Jonathan,

I hesitate to respond, because I'm not sure I understand your perspective. Your two criteria for "real world application" seem contrived on purpose to make it difficult to satisfy them. Your item (ii), for example, is self-contradictory. If there is no other application that does the job better than Mathematica, then why shouldn't Mathematica get credit? And item (i), is a very rigid, specific bias. Is Excel not useful in the real-world, because most users don't re-sell Excel "applications"?

Again, I'm not sure what your perspective is, but you seem to want to compare Mathematica (or Wolfram Language) to development languages/platforms that generate stand-alone applications. Perhaps that is a direction Wolfram is heading toward, but I've never viewed Mathematic in that light. Mathematica IS the product/application. There are myriad problems for which Mathematica offers a space for exploration, solution, invention, analysis, etc. At the end of all of that, if there is no stand-alone application to sell, then you dismiss it as not real-world and therefore (I infer) not particularly valuable. That's fine if that's your perspective, but why should I feel compelled to accept your perspective? Or, to put it bluntly, what's your point?

I've seen Mathematic in contexts that I consider real-world: Public school education, Private professional training, Generating assets for book publishing, Engineering problem solving, Alternative to Excel, Alternative to PowerPoint, Data analysis, Prototyping.

These observed real-world usages are mostly "accidental", in that I'm not really in a position to hunt for Mathematica in the real-world, and so I suspect that others could expand this list greatly. I don't think anyone is making a claim that Mathematica is a silver bullet that solves all real-world problems, nor that Mathematica's breadth of functionality is such that no other applications will ever be needed. So, again, I'm curious about the point you're trying to make, what actual relevant question you're trying to ask, or what methodology suggests your specific criteria.

There are some terrific replies here, which I want to spend time thinking about before responding. However, I did want to answer Sander's point about my "weird" definition of real-world, because it has come up elsewhere.

The definition is somewhat strained, I agree, but deliberately so - one of the concerns I expressed about Mathematica is that it may encourage a kind of "intellectual dilettantism". One way to distinguish between genuinely useful endeavor (whether commercial or research-oriented) and dilettantism is that the former creates value (hence worth paying money for), while the latter typically does not. I would argue that genuine academic research falls within the ambit of my definition, since academics are paid researchers (albeit paid quite poorly, in many cases). While I agree that the end-goal of academic research is publication rather than financial reward, the former is generally regarded as part of the job-description ("publish or perish").

That said, even if we allow that academic research falls within the scope of the definition, I can allow that the wording is deliberately skewed towards commercial applications. This, too, was deliberate, because Wolfram's success depends no less (and perhaps more) on its penetration of commercial markets than its adoption in the academic world. (The reason is probably self-evident: commercial organizations tend to pay full-freight; academic institutions do not). Wolfram itself recognizes this. As evidence, I would point to the fact that most, if not all, of Wolfram's "customer stories" involve commercial applications.

To sum up: it may be that one ultimately draws the conclusion that the real benefit of a product like Mathematica is to be found in its applications in academic research. But I would suggest that is not a view that would likely be acceptable to Wolfram, even if it were true.

I would just like to comment on this one:

I would say, it seems there is a lot to be done to UNDERSTAND the behavioural patterns of new (potential) users, especially in corporate (!!!)

Actually, if the corporate world was such a relevant target market, Excel Link would not be an add-in, let alone sold as an extra (now that it is managed/owned? by WRI).

Have Player Pro, or Enterprise signed CDF, communicate with Excel (or a CAD system, or a ...). Have a message appear, near the clock / notification bar, each time the kernel is launched, saying "your computations are now being powered by the Wolfram Language" (or every x minutes on a non pro, non Enterprise signed scenario). And all that large amount of several hundred/thousand employees companies that just have one single Mathematica license, will, at the very least, see a considerable growth on the amount of potential users that have heard of the Wolfram Language.

Afraid of someone duplicating all functions of Mathematica, by just "re-branding" them into an Excel add-in? As for the CDF restrictions, if it is illegal, wouldn't that be enough? Or, actually, wouldn't it be a complete marketing success if it happened? Is the Wolfram Language potential paying market really the type of market that will put itself into illegal scenarios? Before CDF, we had to have our dynamic content distributions signed directly by WRI. Would that reduce the fear factor? (although, not sure how many corporates would be accepting that...)

The Private Wolfram Programming Cloud is another technology that seems to have been packaged to enter into the corporate world by the front door, while we, in the corporate world, know that the most successful entry is made by the insiders... Make a free version and sell tokens (similar to the public cloud, but with the price reflecting the fact that processing hardware and maintenance is by the client). This makes it by-pass all sorts of budget check-points, while it is gaining momentum. A lot of software is more and more based on tokens (from the very small vendor to the several times "bigger" than WRI offering vendor). The current starting cost not only needs to get approved by two hierarchical levels (on the companies I know), but also needs to be on the year budget from the start... This makes its entry extremely difficult. Make it accessible by the passionate (that will just put $25, from his own wallet, to give it a try), and make it grow, with time, to the full time no token product.

Just my 2 cents... (the amount of times I discussed, in the past, the above corporate related topics, have probably already accumulated to a Dollar...)

David Keith's post is illuminating in terms of describing his successful application of Mathematica in his work. Several of his points chime with my own experience, where I have found Mathematica to be a great prototyping tool. I think the key to Mathematica's usefulness lies in its core capabilities, so aptly described by David in his post, as follows:

One very important reason for that is that, at its heart, it is a symbolic math tool. For me, the first step in looking at most problems is to look at the mathematical dependencies. This means looking at equations and relationships in symbolic form. After that, even more intuition can be gained by trying real numbers and viewing these relationships graphically. Mathematica excels at both these tasks.

Likewise, Bianca Eifert also pointed out the usefulness of Mathematica's graphical capabilities for the preparation of figures for publication.

To define Mathematica's core capabilities only in terms of symbolic logic and symbolic manipulation, as I have done above, appears to be too narrow. David and Bianca are quite right to highlight Mathematica's graphical capabilities also, which are indeed exceptional.

I am tempted also to add Mathematica's facility for creating dynamic user interfaces. These capabilities, too, are outstanding. Where this falls down, however, is with the difficulties presented in getting such content in front of a non-Mathematica user. CDF is a great attempt at a solution to this problem, but too often fails in practice (and anyway requires the user to download and install additional software). Web and cloud-based solutions may be a better attempt, but entail further investment and development effort.

In summary, while no doubt WR would argue strongly in favor of Mathematica's capabilities across a much broader spectrum of applications, the product appears most effective in providing solutions for problems that entail:

• Rapid prototyping
• Manipulating mathematical symbols and equations
• Graphing the results

I am somewhat uncomfortable with the limitation imposed by the first of these points, because it plays down Mathematica's capability to produce extremely polished, industrial strength solutions (see several of the Applications described on the WR web site for examples). However, I suspect that for the great majority of Mathematica users, the main benefit lies in prototyping rather than producing the kind of large-scale application more usually developed in languages like C++, or Java. Very happy to hear opposing views on this point, however.

As far as Matlab vs Mathematica, it should be noted that there are free online courses that teach Matlab and others which use Matlab. In many of these courses, a temporary license is provided. I've suggested to the sales team that Wolfram Research do something similar but have been told that the videos provided on the web site are just as useful. I don't agree with that statement.

Yeah it is different, but if one is totally fixated on Matlab, one will not publish it in Mathematica CDF files....

David Park's post contained a lot of interesting points. But one comment in particular caught my attention, because I found it rather shocking:

I haven't done a thorough search but I suspect that you won't find a single Mathematica notebook or CDF document on physics archives.

Can this really be correct, does anyone know? Can it really be true that Mathematica's penetration of the market for physics research is so limited?

I would find it quite remarkable that Mathematica has enjoyed so little success in a field so closely tied to its core competencies. But perhaps I shouldn't be surprised; no less shocking to me is how few professional econometricians and statisticians make regular use of Mathematica. I am not claiming for one moment that no professional researchers use Mathematica to do econometric or statistical analysis - just that I don't know any amongst my quite wide circle of contacts in those fields. They all use something else: Matlab, Gauss, RATS, Stata, etc. This is despite the fact that Mathematica has all the necessary capabilities (and more) to carry out this kind of research.

So there may be something interesting going on here, which I suspect has less to do with the technical challenges of the product (which of us has not struggled with the idiom, from time to time?) and more to do with WR's business model. There is a lot more to say on that topic, but first I would be very interested to get some qualitative feedback from subject matter experts about their experience of the usage of Mathematica in their own field of expertise.

David, just some thoughts:

(1) Difficult to learn. Mathematica was, for me, one of the easiest programming languages to learn. The sheer size of it, as you say, makes it time-consuming to become familiar with all of its functionality, but that is a completely different issue, in my opinion, than learnability.

(2) Difficult graphics. I'd really like to know which graphics-oriented applications you use that are easier than Mathematica. Granted, in specific contexts, like CAD-CAM, there are very powerful niche applications that outshine Mathematica in one sliver of functionality, but I've never worked with an application whose general graphics capabilities are broader or easier than Mathematica. And there is a great deal of what you call correlation. Mathematica's graphics functions all follow very strong patterns and conventions. There is a real disconnect here, because I don't recognize Mathematica at all in your criticism. Frankly, I don't know how it could be more like "drawing on paper"--that's almost literally how it feels to me.

Jack, ditto:

Are you able to give some specific example of how Wolfram script enables you to deploy stand-alone applications? I'd like to dig into it a little more, as it may be that I (and others) are missing a trick...

I also recently discovered this great way to deploy!

I totally agree with this post and it seems to me that I share same (positively inclined, by the way) concerns with Jonathan. There is 90% of the concern on the part of business model and communication strategy. I would say, it seems there is a lot to be done to UNDERSTAND the behavioural patterns of new (potential) users, especially in corporate (!!!) sector. I'm not quite sure that target users are well-defined at all - there is a nice mixture of cure-it-all and niche ad-hocery. Self-reference criterion is almost always a poor adviser, but I remember a lot of caveats on my road to Mathematica (absolute independent on any background or tutors advices). I believe that I've passed the starting 'death valley' of the road, but looking back, I feel surprised that I passed them. And these are not only technical issues. So "sleeping potential" of MMA is a great task for research, as marketing so academic. (I'm not saying here about simple QWERTY effects and network externalities that are obvious form many posts).

What about the annoyance of having cells, structures, and arrays (matrices?) which are just 'list' in Mathematica.

You're absolutely right, my points above won't give us new insight when comparing Mathematica to Matlab. You know, it's really very telling that we instinctively consider Matlab to be the direct competitor (and I'm sure it's true if you do some market research). Because if we actually considered the Wolfram Language "another programming language", then we'd compare it to Python, Ruby, R... Maybe not to C or Java, but any of the highly abstracted interpreted languages would seem like a natural point of reference.

I do believe that Wolfram Research wants to go in a direction of establishing the Wolfram Language as a language, I think that's quite obvious. Let's see what becomes of that. It's a great tool by any name.

Personally, I can't give you any thoughts on Matlab because I've never used it - quite simply because my university has no site license, and it doesn't seem sufficiently different from Mathematica to make me want to buy a personal license. (Certainly not when there are so many languages out there that I can learn for free.)

Frank, I would certainly argue that symbolic manipulation is a core competency of Mathematica and an area in which it enjoys a distinct competitive advantage. Question is, is there anything else?

In Mathematica, symbolic manipulation is part of the core functionality. In Matlab, it is an add-on.

I suppose the free cloud plans may be useful for someone who just wants to try out the language...

I've read this thread with great interest, and just wanted to say that I feel @Eric Rimbey has touched upon a very important point. We can't really compare the Wolfram Language to other programming languages in a context of commercial software development.

With other languages, you can create a stand-alone application that your customer buys and uses. Emphasis on stand-alone. There may be all sorts of challenges on the developer's end of things: Packaging interpreters or libraries with the final product, or buying additional tools to do something-or-other. But the customer shouldn't worry about any of this. (Shouldn't even notice it, ideally.)

With the Wolfram Language, the user basically needs a Mathematica license. Is your application amazing enough to push that additional cost and hassle on the customer? No? Well, then you can only sell to existing Mathematica users. That means that the developer is confined to producing add-ons to an existing software suite. There's nothing wrong with that at all, but it's a completely different market compared to software development done in other languages.

In some fields, this may not matter because Mathematica is wide-spread already. In other fields, CDFs or a web service doing some computation on the seller's servers may suffice, and a stand-alone program isn't even the target. Those are the fields where you will find successful Wolfram Language applications.

By the way, this is what people usually mean when they say that the Wolfram Language isn't really a programming language.

Edit: I would like to emphasize that for all the other cases of "money changing hands", this is not particularly relevant. I just wanted to comment on the "programming language" aspect of Mathematica.

It is quite limited indeed; I, myself, have used it throughout my bachelor, master, PhD and now postdoc. But I was already using before in high school too. But I'm one of the few who uses Mathematica, 'everyone' is obsessed with Matlab! And also books tend towards Matlab... I think it is because a lot of people think Mathematica is only for equation solving, and have no idea it can do (almost) everything Matlab can do.

I find your definition of "real world" kind of weird:

"money changed hands" surely does not equal real-world. Because now you exclude basically all academics! A HUGE number of academics do there analysis using Mathematica/Matlab/...... without getting money for it! It is to publish something. But not directly getting money.

I'm one of the very few in the group that I'm working in that uses Mathematica, but if I compare speed of building software to do analysis, Mathematica trumps any Matlab implementation. Nearly all the code is shorter, more legible, and much faster to implement. I generally have little programs done while the others are still struggling to import some data or so.... Of course that varies a lot on what you do exactly!