Hey guys, just to revive this topic. I am a mathematics graduate and I have used Maple and Matlab as the university offered the license for both. I used to use Wolfram-Alpha and wasn't familiar with Mathematica, however, I got a copy of it in 2016 and started practising with linear algebra, complex analysis, number theory, several variable polynomials and general calculus. During my learning curve, I found it quicker to master and ended up doing none maths stuff like linguistics, animal data, country info, forex trading etc. I became hooked and have continued to use it even though I am not a researcher or physicist. I like how it is a blank sheet and hey presto you put the Mathematica syntax of anything properly, boom here is your answer. Comparing to Maple, I liked Maple but hated the fact you have to load a package e.g (with LinAlg) or (with differential geometry) whereas Mathematica you just type your wolfram syntax on the page and boom Bob's your uncle. With Matlab, you type in the editor sheet and then run the code..... I used it for numerical analysis and some linear algebra. Haven't bothered with it since my 2nd year and never used the symbolic toolbox.

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.

Yes, it was the cells and structures that drove me crazy in the probabilistic graphical models course.

Many! What about calculations with regions? How about GPS data and plotting them on maps?

How about the integrated knowledge? You need the viscosity of ethanol? Boom there it is! You need the wind direction in honolulu in christmas eve in 2004? here you go! You need the volume of dodecahedron? Done! largest building? check! Mountains? Yes! Bridges? jup! All the stuff you can imagine for any element or isotope? Sure thing! genomes, planets, volcanoes, countries, cities, calendars, aircrafts, airports, dictionary, ...... This is EXTREMELY useful. Not only do you have acces to it directly, it also is immediately in a format that you can work with, no need to import files and 'decode'....

Bianca - oh, I forget to thank you for the anecdotal evidence in favor of Mathematica in the context of physics research.

I wonder, is Mathematica the market leader in that field, would you guess? Is it a mix of the usual suspects? Or is there some dominant market player, like Solidworks in CAD?

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

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.)

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

You can produce Wolfram Language stand-alones applications that run without license via wolframscript. Apparentely very few people know it, and even less people know how to do it. I run my wolframscripts everywhere I can with no license.

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...

Szabolcs, yes I caught the distinction and blurred it, deliberately. Because I was trying to frame the question in a broader context - how widely in Mathematica (WL) used in physics research, generally? You said that your

impression as a physicist is that should be a significant percentage

Well, thats the point. My impression as a professional econometrician might be that Mathematica is widely used in econometric research. But that impression would be wrong. How do I know what? Because it is customary for researchers in that field to mention in their research papers the software used in the research (not always, admittedly). And, as I mentioned, I know quite a number of them.

Sander's experience mirrors my own in this regard, it appears.

So the question stands: can anyone (an academic researcher in physics) offer any anecdotal evidence about the usage of Mathematica in that field?

Eric,

Let's dispense with any continuing misunderstanding of the criteria I specified to qualify an application as "real-world". I did NOT say that the application had to be "re-sold" in order to qualify. What I said was that "money changed hands". This could involve re-selling (and I gave several specific examples of such applications in subsequent posts) or it could involve consulting fees. That deals with the straw-man objection that my criteria would disqualify Excel as a real-world application - because vast sums of money have been earned in consulting fees in relation to projects in which the deliverables included an Excel workbook and/or VBA code. As if that was not enough, I went on to make clear that "money changed hands" also included applications that were developed by paid researchers, because their salaries constituted money changing hands. Enormous sums are expended on the salaries of Wall Street quants, almost every one of whom, in my experience, makes extensive use of Excel. So - subject closed.

You asked what my perspective is. It is to find an answer to the simple question: what is Mathematica for?

I went on to make the specific point that, yes, of course, you can treat Mathematica as a Swiss Army knife, capable of duplicating what can be achieved in Excel, Powerpoint, Solidworks, or any number of other software programs. But if that is ALL Mathematica is, then frankly it's pretty unimpressive; because not only are there existing, often less expensive products that can do these things - but they can often do them more easily, or better than Mathematica. Sure, you can manipulate a spreadsheet and do Pivot Tables in Mathematica; but why on earth would you? Just because you can?

So the question I am really asking is: what are the core elements of Mathematica that make it unique, exceptional or which give the user a competitive advantage vis-a-vis other software tools? And I went on to ask the question, are there any such competencies, other than mathematics itself, specifically symbolic logic?

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.

True indeed! My previous university switched from Maple to Mathematica 1-2 years ago. So now students will 'grow up; with it (I guess). Though for the experimental physics I've seen very little usage of Mathematica, for theoretical, yes, lots of use!

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

The reason to choose CDF over PDF would be a desire to include interactive functionality. But if you publish a paper as a PDF, you can still offer a link to additional material: A Youtube video, an app on your website, or maybe a publication on the Wolfram Demonstrations Project (hey, why not). And yet, with a traditional paper, you're on the safe side: People who think that the interactivity is too flashy and maybe not entirely super serious can just ignore the link (relax, it's just a footnote, the actual paper is totally super serious).

That aside, most researchers are just not free in how and where they publish: If it's not in the "usual suspects" group of journals (preferably with a high impact factor) and you can't find it through the field-relevant search portal, you might as well publish on the sidewalk. In chalk. Before the rain.

For more informal communication (e.g. direct exchange between coworkers), a Mathematica notebook will often do just fine, and generating a good-looking CDF is a bit of an unnecessary step. And if your coworker doesn't use Mathematica, you're better off finding a data and presentation format that both of you can actually edit.

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

Thanks for posting it here. I think the discussion it generates is interesting. StackExchange would not have given room for such a discussion. I wanted to make sure you understood that your post was not closed on SE because people object to it. It was closed because the format didn't fit.

I will not go directly to the application topic, since I think that some background is of interest. Also, I don't have one specific application, but I will actually be talking of the application I do of it. So, I'm on the category (from David Park answer):

There are many more who use Mathematica in their work but many of them say it is very difficult to get others in their company to use it.

I work at the engineering department of a big commercial company, on the area of water treatment (we design, build and operate water treatment plants). I'm not a programmer, and my formal training (and day to day work) is on sanitary engineering (a specialization of environmental engineering).

Our typical engineering tools are MS Office and CAD softwares (besides some other specialized commercial softwares for very specific tasks, plus an ERP, etc.)

On most of my use of Mathematica, I can't say that it would be the unique solution, but, for me, it is the most productive solution, both in time and cost (which is the same thing, but also not exactly).

I basically started to use it as a MS Excel substitute, or an Excel on steroids. Excel is probably the most used tool in the engineering environment. It is so ubiquitous that, when a client, partner or supplier asks for some particular calculation share, they are expecting a MS Excel spreadsheet, and nothing else; no need even to discuss on it. But, as soon as we want to evolve on our use of this calculation tool, it starts to become too much of software engineering (inventing strategies to accomplish things that it was not designed for) and not our own field engineering. I think of this limitation as equivalent to trying to build the ultimate slide ruler, linking lots of sliders, rotating disks, translation curves, etc., into a single cardboard..., when computers are available... (its a mental image I have..., that kind of graphically shows the absurd limitation). I have tried Matlab several times in the past, but never found it adequate for my needs (I guess it depends a lot on the details of what the person exactly does).

Introduced to Mathematica 5.2, I started using it more and more, and, at the same time, adventuring more and more on computation fields that I would not have dreamed of. And yet, I have been working on the same engineering field for the last 17 years.

While using Mathematica, I started to see my thinking process change, I would even go to the point of saying: radically change. I passed from one variable to full space exploration, and from (fictitious) exact engineering, to taking into consideration uncertainty and measuring the risk.

Here's a time sequence that, while being false/simplified, in someway explains the use I gave and give to Mathematica:

• prototyping tool for algorithms being programmed in VBA (simple programming)
• exploration of analytical solutions for some differential systems (true CAS)
• package development for some calculations, substituting Excel on the daily work, but not package selling (automation, more sophisticated programming work)
• Dynamic interfaces for client exploration of our design concepts (Dynamic, Manipulate, etc)
• CAD interfacing for direct calculation of 3D networks (graphs functionality, etc)
• analysis of temperature, humidity and wind direction at multiple sites. As a funny example, for instance, checking wind direction predominance, to determine floating debris accumulation points, on slow flowing water systems. (use of the online curated databases)
• image processing of 2D data acquisitions from laboratory experiments (use of the image processing capabilities)
• machine learning algorithms for multiple tasks, including on image data / film processing (use the machine learning new capabilities)

Obviously, this is a very short list, and does not exactly reveal all the uses I gave to it since version 5.2. But I think that one interesting thing it reveals is that, along the addition of functionality, I have added the new fields into my daily work AND NEED, while still being on the same job.

Would I have guessed that, one day, I would be applying machine learning and image processing to my daily work? Definitely not. It is not my core field, and very far from it. So, is it a real need or a need that I have invented? I think that there's no actually distinction of those two, but I can say that the use is real, and the cost (learning curve) / benefit has been extremely advantageous (when I say learning curve, I'm thinking on it being so short for the new fields that are added, that I can just apply them without actually thinking that I'm learning them). Do I really learn this new fields to the point that I can say that I master them? As with most other tools, in order to avoid mistakes, its application needs some intelligence. But, I think that the equilibrium I'm getting is of extreme benefit.

You mentioned CAD capability. Does it make sense or not that Mathematica goes in that direction. I can say that I'm eagerly waiting for a more complete regions framework (mesh and non mesh being mixed by boolean operations, etc.), and for it to be faster, for a very specific need I have on the CAD world; and I can say that I'm pretty much at ease with CAD software, working, on average, at least one hour per day, and having programmed some add-ins for some CAD packages). Of course that Mathematica is (currently?) extremely far away from covering the functionalities of CAD tools. And also that CAD tools are currently very far away from covering computational environments' functionalities. And, although connection seems the obvious solution, some particular applications (like mine), work better if the integration is absolute. I'm even thinking on candidating to the next Wolfram Innovation Summer School, to help me on one of my less standard projects.

So, although I haven't mentioned on my list: Regions, FEM, and other of the new stuff, I know that for a lot of them it is just a matter of a few more months for me to start to need them... Some I haven't used because they are still not well fine tuned. Others, like FEM, are a little away from my preference, which would have been FVM, but still a good addition, for which I have practical uses in mind.

But, for instance, why don't I just use a specific image processing tool from the market? I think that the answer is integration. If it is integrated on a well known environment, I can just start using it, with a very favorable learning curve, and mixing up with other fields, without being a programming specialist.

To answer directly to your post:

applications in mathematics (symbolic logic)

Not my case

Mathematica's primary usefulness is in encouraging a kind of intellectual dilettantism

I don't think that this is my case. I apply it to real life cases, from which I take monetary benefit, on a very competitive environment.

of the hype around Mathematica

I have always found it interesting that one can use superlatives for a lot of products, including a lot of software products used on the engineering field (of any kind and any cost), and yet, for some other products, its use is judged abusive and offensive. I guess this comes from the duality and the distance, on many aspects, between the commercial and the academic world.

Mathematica somehow fails to live up to its apparently unlimited potential for encapsulating creative thought-product across an almost unlimited span of human intellectual endeavor

I think that all tools are doomed to fail on such a big phrase. But, I give credit for trying, and also, for not being so far away from the target (in relative terms). Considering that I make real use of some functionalities that I never thought I would be using, I think that the tool has achieved something. Do I see shortcomings? Yes. A lot. And yet, I just keep using it.

(i) money changed hands (e.g. a commercial product was sold, or consulting fee earned) ; and

Working in a commercial environment, on the modern world, while producing something that doesn't bring money back, is currently impossible. So, my work with Mathematica is being consciously paid for.

(ii) an alternative solution was considered and Mathematica preferred for specific reasons ("it was the only software we could afford or that was available to tackle the job", is not a valid reason to qualify the application as real-world, according to this definition)

Alternative solutions are constantly being used by my peers. I have used alternative solutions, and I'm forced to go back to them from time to time. And I can't emphasize more the "forced" word.

And, from David Park's answer:

1) Mathematica and the Wolfram Language are difficult to learn.

I think that difficulty is relative. I think that it has to be seen as an effort / benefit ratio. What happens is that the effort is not always possible. But passing away from the benefit is less and less affordable.

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

I agree. Like two sections: WRI and Community section

3) Mathematica is not as stable over versions as they nonchalantly claim.

Probably true. I, myself, prefer a good design to a backwards compatible design. I think that this depends on how you use it. If we make a lot of development on it, having to review it every single time there's a new version, can indeed be annoying. It's not my case, and I actually wish they were more actively correcting not so well design features.

6) Diffuse effort. Instead of perfecting the "Application" model for building capability over time, Wolfram Research has been drawn into many other endeavors.

Indeed. Although, its clear that what is currently presented is a product that can cover many more user applications, and that, because of it, starts to get more known. Eventually new users bring money, and money brings development resources. I think that adding new entire fields, from one version to the other, is great. It is probably the balance between the maintenance of the existing ones and the development of new ones that is not fine tuned. On my personal case, what borders me is the fact that many bug reports (the ones that are really bugs), take so many versions to get fixed (and I'm talking of bugs that do have a fix, and not bugs that are on the edge of human knowledge). I have hope on the new momentum the fast release track has brought, and I'm just hoping for that equilibrium to be found.

So, some conclusions:

• I use it on a commercial environment.
• It allows me to do things that I couldn't do before using it.
• It has been fun to follow Mathematica development, and to belong to its community of users.
• Some fine tuning (including less bugs, etc), is in need...
• ... and yet, there's still a lot of functionality and entire fields that I'm missing.

And, as Conficius said:

Choose a job you love, and you will never have to work a day in your life.

Mathematica helps a lot on that direction.

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 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...

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.

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).