Jonathan, the answer is very simple:

"Mathematica is for Stephen Wolfram to do his NKS-stuff on."

Other features are put in from time-to-time and as is deemed necessary to make Mathematica sufficiently saleable to support Stephen so he doesn't have to get some other less enjoyable occupation while he pursues NKS.

;-)

B

I always enjoy using Mathematica for serious and less serious work. Don't want to spend all time on finding the right python libraries and check there vitality etc when most absolutely necessary. I think Mathematica is fantastic and thoroughly enjoy listening to Stephen wolfram's discussions with his outstanding team. I mean I don't know any other cto doing that. I also believe that Wolfram is really looking for "stuff" that is actually useful for his customers. Other languages have also great features and sometimes better syntax but that doesn't matter. The flexibility is incredible. I also enjoy the documentation and all the crosslink to other fields that might be useful. You always learn from it. No other languages has given me more pleasure programming than this Wolfram language. I once played with low code software mendix in combination with sap software. I didn't really like it. Low code for sure but many many many clicks and different windows.. Not for me.

I think Mathematica is far behind Python. Since I have used Python, I seldom use Mathematica. Python is much more powerful than Mathematica in data processing.

Philipp,

Thanks for your thoughtful input. One can only hope that someone at WR is paying attention...

Perhaps the single biggest shortcoming in Mathematica, compared to, say, Matlab or Python is in regard to deployment in production. I have developed a couple of production systems IN WL, but my sense in each case was that I was pushing the envelope in terms of Mathematica's core capabilities. I always had to be ready to handle bug fixes and crash-recovery scenarios. Unlike other languages, which also had their fair share of bugs and crashes along the route to deployment, there never really seemed to come a time when Mathematica could be expected to work seamlessly - there always seemed to be another problem waiting in the wings. Similar systems developed in C#, C++, Python or Matlab would always (eventually) get to a point where they were reliable enough to deploy in a production setting, with a reasonable expectation of reliable performance. But I can't say the same for systems I have developed in Mathematica.
Now, it could be that this is just my lack of experience/expertise in developing production ready systems in WL. But I also think that it is perhaps one of the key limitations of the language. It's not to do with the language being interpreted - so are Matlab and Python - but some other aspect of the language architecture (e.g. memory management) that renders it unsuitable for deployment in production. I wish it were otherwise; but I can live with that limitation, providing I know it exists.

In any case, while the title of the post is about what Mathematica is For, it is perhaps also useful to produce a list of things that Mathematica is NOT suitable for, which from my perspective would include:

1) Anything that can be done more easily in Excel

2) Anything requiring deployment in production

What about other users' experience? Can anyone else offer an alternative view of Mathematica's capabilities in relation to development and deployment in a production setting?

Are there any other limitations you see Mathematica as having?

My use of Raspberry Pi? Mainly for having the alternative mobile access to Mathematica (for mobile coding, or as calculator) and to my personal locally saved Mathematica notebook files. The web browser access and the Android app access are convenient and very good to have but they are not full versions of a Mathematica installation. So through the VNC access (does everyone here know what a VNC access is, oh please?) you're on the road and have access to a full local Mathematica installation, namely the one on your Raspberry Pi sitting at home near the Wi-Fi router. Seriously, this is reason enough and reason alone to buy and setup a Raspberry Pi, and shame on whomever that there is no youtube video showcasing how Mathematica can be used this way on a phone while you're on the road, apart from browser access and Android app access! Shame. The youtube title should be "How To Use Mathematica On Your Phone Through VNC Access" and it should demo both the VNC Wi-Fi access and the VNC Cloud access. No, i am not gonna do such a video, not my job. It's Wolfram marketing department's job :P

I also used the Raspberry Pi for logging electronic devices, like a logging multimeter, a logging charger/discharger, or other similar eletronic devices which offer a USB connection (or serial connection) for logging purposes. You can let the Pi do the logging for days and weeks, non-stop! There's logging software for Linux/Raspbian, wonderful stuff.

And i don't mind letting the Pi stream music non-stop from a streaming music subscription website, looping an online playlist infinitely. I only need to turn on the speakers and there's music!

Of course, the Pi is not a replacement of a full PC. One can watch a youtube or a HD video with VLC media player but you can't do both at the same time. In summary, my personal main uses are: 1) having access to a full local Mathematica installation (granted the Wi-Fi or mobile internet is working), 2) logging electronic devices, 3) 24/7 streaming of music. There is so much more, purposeful things, one could do with a Pi, but as you can see, I keep it simple, basic, boring.

Yes, it would include standalone applications designed for general use and not requiring user familiarity with Mathematica (or possibly even a Mathematica runtime module). In Matlab, for example, applications developed in Matlab can be compiled as standalone C++ applications - a capability that Mathworks has worked long and hard on to produce.

But I also mean WL applications that are designed for use in the WL by Mathematica users (e.g. in package form, in a Mathematica notebook). Even here, as I said, it is challenging to produce an application for use in production, where application errors and bugs are very infrequent and remedied relatively easily. In most other languages bugs tends to get ironed out eventually, whereas my experience is that a Mathematica application is much harder to stabilize and often continues to surface problems. This is not always the case: for example my MATH-TWS application (which connects Mathematica to IB TWS) has proved very reliable. However, the great majority of that application is written in C++ and interfaces to the IB TWS api. So it doesn't really count as a true Mathematica application in the sense I mean here.

@Wenguang Wang, maybe it is because you did not have a chance to get to the Mathematica's full potential. I heard a different story. My friend uses Mathematica extensively, data science, analytics, general coding, etc. Then she had to use python for some of her new work tasks. She got very frustrated with how not-smooth the experience was with some workflows and the front end in python. To me hybrid numeric-symbolics and fundamental symbolic nature of Mathematica and its functional style coding architecture seems far superior than python. Some similar user opinions here: https://mathematica.stackexchange.com/questions/86058

Hi Philipp,

Wolfram Application Server was announced today. Perhaps it will address some of the issues we face with deploying and supporting WL-based applications in production environments. There is no mention of pricing / licensing but I suspect it will likely be out of reach for most startups / small companies.

Hi Kay, yes indeed it might that the premise is wrong (and in my original post I gave one possible explanation for the downtrend that is innocuous). In this case, however, I think that perhaps the chart for Facebook accurately reflects the slowdown in usage growth of the platform:

Source: Statista

So, while it certainly doesn't mean Facebook is dying yet, it tells us that growth is slowing, which may ultimately mean the same thing.

In term of your other points, I think we are saying the same thing: Mathematica has come so far as to be considered excellent in many fields, but seems to lack the last x% of functionality to render it truly outstanding (like design of experiments in statistics, in your example). Perhaps that is by design. A rational argument might be presented along the following lines:

Usage growth Mathematica is slowing. We (i.e WR) can't reverse that trend by providing more functionality to existing users who are already committed to our product. We have to find new users and bring them on board. To do that we have to provide new functionality that will appeal to potential users who haven't tried Mathematica before. That argues in favor of adding more breadth to the product scope, rather than more depth, beyond a certain level.

If this argument were to be accepted, it would mean that WR would be constantly developing functionality in a field up to a certain level - typically below what is required by a professional at the forefront of the field - before abandoning it to focus on developing new functionality in other areas.

It seems to me that WR needs a "finish the job" Tzar, whose function would be to identify the critical functionalities missing from key subject matter areas and with the authority to prioritize them for development.

In many cases the gaps in necessary functionality could be filled with a handful of new functions. But for some fields (e.g. machine learning) the list would be very long indeed.

Hi Rohit,

Thank you for the information. I will take a look at it as soon as there is a trial version available. There was also a presentation about WAS at WWDC 2020. Hopefully it will be easy accessible => pricing information available online without contacting sales, trial license for download, …

My thoughts on this topic, besides that it should recieve more public discussion, are twofold.

First, I am not sure whether I will buy Mathematica once I exit academia. As long as I have a 'free' license though, I'm hooked. I think both mathematics and computer science students have a hard time approaching MMA even though it has tremendous potential to benefit both kinds of people†. I like to tell them that MMA is the worlds best software rapid prototyping tool; or when I'm being cynical, that MMA is both good for nothing and good at literally everything††. Frivolous yet powerful things are often the most compelling and fun...

Second, can MMA ever have a practical use†††? I think besides small niches, there is exactly one possibility. I haven't played with it's C code generation very much, but it seems like it's mainly limited to producing 'zombie routines' that must hook into a kernel. The symbolic nature of WL admits, for instance, a search over all possible algorithms to achieve a task. I think a richer library of code generation tools/examples plus an expanded code generation interface (i.e. x11 calls, various windows dlls; think of existing gpu and ffmpeg functionality) could start to make WL useful for 'actual code development'.

†In many lower division math classes, the entirety of homework can be automated in MMA. Document scanning, equation parsing, equation solving with steps, typesetting and printing. Literally the whole process: it's a thing of beauty. Applied computer science students, once relieved of worrying about the nontrivial trivialities of modern software, can appreciate the beauty of theory.

††Good for nothing in that it's useless for producing anything dynamic (i.e. production software), and good for everything in that it's capabilities are wiiiidespread and richly interconnected and as a result can produce amazing static visualizations, sounds, videos etc. Most academic publications are entirely static--most of scholarship is just prototyping ideas--such that MMA is the perfect scholarly workbench.

†††Again, practical in the sense of providing a directly valuable service--there's some economics word I'm looking for. One might say I'm asking for the well crafted code that goes into the kernel to be freely given up. Instead, I'm suggesting that the symbolic power of WL could be suited for automatedly writing lots of code--I would only be able to give examples if I were to embark on this as a project.

Adam,

I think my view is quite well aligned with yours: Mathematica is unparalleled in its facility for doing mathematics and its interactive nature makes it an outstanding choice for doing research, experimentation and prototyping. Which thereby also makes it an excellent pedagogical tool.

If we were to draw a line here and say: "this is what Mathematica is for", would that be so bad? Does its current inadequacy as a platform for developing production systems render it useless? No of course not, not at all. Why should it? After all, I have never heard anyone complain about R's shortcomings in the same area - why should Mathematica be held to a higher standard?

Well, I think there may be a couple of reasons (in addition to cost, of course):

Firstly, if we dispense with the notion that Mathematica can ever become a platform for doing series development work in a production environment, it means that you have to become highly proficient in at least one other language. And given the scope and complexity of WL, and of the other language one may be obliged to learn (e.g. Python, Java, C# or C++ ), a developer can be forgiven for thinking that they may as well save some time and effort and just focus on the second language, which can do everything (although perhaps not as elegantly as WL, in some areas).

Second, Stephen Wolfram's boundless enthusiasm and ambition for the WL leads one to hope that perhaps, eventually, a way will be found to remedy the WL's deficiencies and make it suitable for development of production systems. This is, after all, what Mathworks appears to have achieved with Matlab/Simulink, enabling Matlab code to be translated into production-suitable C++.

However, I suspect this is just a pipe dream: there are all kinds of structural reasons why a similar translations capability would be next to impossible to achieve in WL (beyond the very limited extant ability to compile simple functions).

Perhaps as you say the solution to the challenge facing WR is not to try to "fix" MMA to enable it to do production work, but to focus on the Wolfram engine instead...

Exactly. Of course, the Wolfram engine, as I understand it, is mostly the Kernel, plus some bits that ended up in the front end for historical reasons. So, it really isn't focusing on the Wolfram Engine as a separate project, but making sure that there is functional parity -- as well as full support for native hardware.

An interesting test case will be whether, as part of the port of the Wolfram Engine to Apple Silicon, it will also be available for iPadOS. If this turns out to be the case, then I can see a lot of apps that use the Wolfram Engine, but which use a custom UI. One of the issues (among many others) with porting Mathematica to iPad is the need to make the UI for the iPad version as close to the desktop as possible, a formidable task given two fundamentally different design principles at work.

I want to re-iterate that Mathematica and its notebook interface is perfect for a wide range of applications and probably is the best in class for the vast majority of Mathematica users. But it should not try to be all things to all people: the best hammer in the world is not much use if you need a wrench.

The only difference is that a 2.0W RPi is constantly powered on, in its booted state. A 400W PC usually is turned off for the night or when you're travelling. Other than that, there is no difference between VNC access to RPi or VNC access to home PC, you're right. A full-fledged PC is more powerful than a small RPi, of course. Do you have your PC (or Mac) turned on for 24 7 365, see? With a RPi, one does so, for the sake of nonstop remote access to Wolfram L full installation, at slow performance.

I have found Mathematica essential in production settings for at least 20 years. Most of those were before the Wolfram Engine (and the more recent cloud offereings). I have re-analyzed some of the applications I mention below, and we could have cost-effectively used the Wolfram Engine if it had been available. Stability of the kernel has also dramatically improved.

I have used Mathematica in at least three different companies. In a consulting environment, we did all our in-house analyses using Mathematica. Notebooks would call large databases, issue SQL commands, and bring in the data for further processing and visualizations. Most algorithms we needed had to be developed from scratch, and Mathematica made it quick to go from reading a paper or a pencil and paper calculation, to something tested and working on data. The graphics would usually get some tweaking in Illustrator, but would often be close to camera ready. We also used Mathematica to create reference algorithms to be implemented in C++ or Java. Many of these where not numerical algorithms.

At my next company we used Mathematica directly as a compute engine. We had developed a very performant cyber security system that identified executing malicious code by observing the stream of system calls. All the machine learning steps were done in Mathematica (this was before the free Wolfram Engine). It allowed us to have version 1 of our system up way faster than if we had implemented them directly. We experienced memory leaks and random hangs that forced us to periodically kill and restart the compute engine, but we were able to engineer it so that those issues remained invisible to the user. Over time, because of costs, we replaced the Mathematica subsystem with Java code.

In my current work we still develop most of the algorithms in Mathematica. We are building a system that use Mathematica for some core data generation; reference algorithms are still in Mathematica. We also use it as a thinking tool (see my blog post). Having all that curated data at one's fingertips is great.

I feel costs have prevented a wider adoption. Wolfram Research now offers low cost versions for non-commercial applications, which should encourage wider adoption, but I sometimes worry that its market may be shrinking.

I think one thing that Mathematica does well is solving differential equations including differential-algebraic equations with DSolve.

Yes, I completely agree. I used MMA to help solve a very challenging problem in stochastic calculus many years ago and find it invaluable for scratch-pad type quant work, or more complex research in mathematical finance.

Indeed.

Much has been said here that I understand and agree with. Especially the uselessness for real production systems. I myself have discovered WL only as about the 20th programming language since I am a pensioner. Before that it was always about large systems in FORTRAN, PL/1, C, C++, Java as a system architect and developer.

Today I program just for fun, and for that WL is great. For me especially because of the symbolic and mathematical capabilities and graphics. And I love notebooks that contain code and its documentation at the same time. Now I do everything simple with EXCEL VBA and everything else with WL.

I would like to add two important points that I think hinder the success of WL:

• The impenetrable jumble of products and licenses, i.e. the marketing.
• The price. For people who just want to get to know the product, especially students, a license is way too expensive (the cloud is not a way out, in my opinion you really need a desktop version with local files).

The second point is existential. Students can do all their tasks for free with things like Microsoft Visual Studio, Eclipse, C#, C++, Java, R, Python and the like, but nothing with WL because they can't afford a license.

Do you have any references for that? I'm curious.

There is a video of the making of Pirates of the Caribbean, although it's been years since I watched it. As for references to specific sites: that is a matter of intellectual property.

I'm aware of research units in university social sciences and liberal arts with Mathematica installations.

A couple of recent comments led me to review the original post and some of the replies from community members which, I have to say, I find rather interesting (although I suspect Stephen Wolfram would perhaps beg to differ). A thought on this subject that I have been entertaining for some time is the concept of Mathematica as a kind of computational Wikipedia. Perhaps, if it has any relevance at all, the comparison could be better made between Wikipedia and Wolfram Alpha, rather than Mathematica.

In any event, what I find interesting is that for a long time Wikipedia looked like a hopeless quest: in the early days many subjects were barely covered and the quality of the articles was often very poor. But then, amazingly, the whole idea took off and Wikipedia became the kind of indispensable reference that Jimmy Wales imagined it could become.

I think something similar may be happening with Mathematica (or, rather, Wolfram Alpha) as its scope has enlarged over time (and the quality of the reference material has always been excellent). My sense is that it is close to some kind of tipping point, on the verge of becoming the kind of indispensable computational resource that Stephen Wolfram had in mind from the outset.

Do others agree? Or take an altogether different view?

I think the complaints about cost are misplaced. Wolfram products are in high demand and so I don't believe the price is going to come down.

I am a Wikipedia editor and I think Wikipedia is a good reference.

Every language is an algebra.

Given the prices of textbooks, I believe that is very reasonable.

We should leave Wolfram Alpha out of this discussion about programming languages. This is not a programming language at all, but a search or - if you like - answer engine. You can't do anything in it that could be called "programming".

I think a technically educated person should be writing with a word processor, doing reports with a spreadsheet, and thinking with a technical computing language as an extension of their thought process.

I observe that people don’t think about things much. If they do, they use a spreadsheet. And that may be too complicated for some. The market for technical computing language may be limited to what I think of as “practicing PhD’s”. Mathematica makes it practical to think about a problem in terms of differential equations, for example, but one first needs some understanding of calculus and not everyone does.

I have recommended Mathematica to others but so far none have been able to use it well enough for it to be an extension of their thought process. It’s a steep learning curve. I have been using Mathematica since version 1.

A technical computing language is not the right tool for producing commercial computer applications. They are two very different things. This is not good or bad, just two different things. And tools for commercial computer applications are well developed. I had an application where I was writing c-code for a microcomputer. It needed a digital filter. I used Mathematica to simulate the data and to design a digital filter. Expressing the filter as c-code was trivial.

My typical Mathematica notebook often starts with some simple notes on a topic. It extends to some “proof of concept” analysis. Then expands from there. This was the development pattern in a recent activity where I extracted telemetry data from a GoPro MP4 file and used it to analyze sailing performance.

My answer: “it’s an extension of one’s though process.”

Years ago, we may have understood that an analysis might be theoretically doable, but we did not have tools to do it. Now with a technical computer language as an extension of one’s thought process we can. The possibilities for expanding understanding become endless. Perhaps we should put more emphasis on teaching a technical computing language. It might enable people to use, for example, calculus in a meaningful way.

Hi Tom,

I think a technically educated person should be writing with a word processor, doing reports with a spreadsheet, and thinking with a technical computing language as an extension of their thought process.

This strikes me as too prescriptive. Fifty years ago you would have had to write, perhaps: "a technically educated person should be writing with a fountain pen, doing reports using a pocket calculator and hardly thinking at all about technical computing languages, unless they are computer scientists".

The point is: time moves on. If you work at Wolfram Research I imagine you (try to) do everything in WL, whether it be writing text, producing some analysis, or programming an application. Certainly that's my understanding of Stephen Wolfram's expectation, anyway. For myself I do a large proportion of my work in WL, including carrying out analysis, creating presentations, and programming applications. It's very convenient to use a common UI and tech stack for all these varied tasks: it save shifting from one application to another, having to be concerned about file format compatibility, etc.

A technical computing language is not the right tool for producing commercial computer applications.

I understand your point, but I expect that there are legions of Fortran programmers, to say nothing of the good people at WR and Mathworks who would heartily disagree with you. And indeed on the pages of this post several examples are given of commercial applications developed in WL (including one or two of my own).

To your point, however, it's obviously a significant challenge to develop a commercial application in WL, even though it can be and has been done. I certainly wouldn't regard the development of commercial applications as a forte of Mathematica, in they way that, for instance, symbolic programming clearly is. Which goes to the topic of this post - i.e. what is Mathematica for? And I would have to concur that the development of commercial applications is not one of those things - although I am quite sure that Stephen Wolfram and others at WR would strongly disagree.

My answer: “it’s an extension of one’s thought process.”

This is a bold claim for any programming language/technology platform, including Mathematica. Could one not make a similar claim about C++, Java, or Julia? I suspect that, unless you are a professional developer, probably not. Mathematica has certain unique features that make it a natural fit for the rapid exploration of ideas, in a way that certainly isn't true of most other computer languages that I am aware of.

I think that your description encapsulates what Stephen Wolfram may be aiming for: a kind of cognitive sand-pit offering a plethora of computational tools that provide a unique way to explore ideas, whether experimentally, graphically, or analytically, that will assist the process of developing them into functional algorithms.

You may want to revise your 'way-back' time. Lotus did not come out until 1983. The HP-35 debuted in 1972, but the programmable HP-65 came out in 1974 -- at a whopping $795 -- equivalent to $4k in today's dollars. HP portables no earlier than 1987.

I started coding in 1972, and it was on a timesharing PDP-5. No personal computers at all -- Altair 8800 debuted in 1974. I got an HP-35 shortly after it came out, which meant that I could ditch my slide rule and log/trig tables. Most of us who learned to code in those days didn't take CS, because most schools didn't offer them. (I was a maths major, so I did have numerical analysis.)

So, 50 years ago (1972), I was writing on a typewriter (an IBM Selectric if I did so at work), doing calculations with my slide rule or walking to the Medical School computer facility -- or by hand, and when I did learn to code, used Assembly and BASIC. C came out in 1972, but I did not have access to a computer the compiler (etc.) would run on until the late 1980s.

SO, no need to make the 1970s 'better' than it was. It was the wild frontier.

Mathematica started as a computational algebra system; a product with its own proprietary language and unique notebook system to integrate computational code with text and graphics.

It works very well as a sandbox computational environment for e.g. research, analyze, document and develop new models and computational methods (algorithms). It’s strengths are:

• Symbolic computation combined with numerical methods
• Functional and rule-based programming (and procedural)
• Large library of functions so you can write concise code
• Well-written documentation
• A notebook environment.

Mathematica is a fun system to work with and it delivers results quickly, even though its learning curve is steep (maybe because some of us came from procedural languages and there are many ways to achieve the same result).

I don’t agree with Jonathan on the use of Excel versus Mathematica. Mathematica is my go-to system to analyze data and models and yes it replaced Excel for me in most cases.

I used Excel for large datasets, with pivot tables, VBA and many worksheets. However, my code to analyze data became opaque or hidden in many worksheet formulas. As such, Excel became unworkable. Now I may use Excel to create a well-formed CSV file, which I import to create a Dataset and analyze it in a Mathematica notebook. I spent a lot of time to master Datasets and associations and now it pays off.

Mathematica's language i.e. the Wolfram Language, has transcended its original product: it has become the vehicle for all things computable. So Jonathan’s question “what is Mathematica for” is relevant.

I think Mathematica should serve a niche market, comprising of mostly researchers, analysts and maybe some system designers. It should become a vehicle of state-of-the-art computational functions and methods. I agree with Jonathan: WR should focus on finishing and polishing e.g. statistics and time series analysis, machine learning and a number of other application areas, so it becomes the go-to tool for research. If you have Mathematica, you shouldn’t need any other specialized application to do your research.

I think the WL should focus on a computational ecosystem with capabilities to develop, test and deploy code, create APIs and GUIs for different OS or distributed computing environments. Its symbolic computational capabilities and extensive library of functions make the WL an ideal language for education or data analysts.

Having said this, I see a number of improvement areas to facilitate the WL/Mathematica adoption:

Transparency of outstanding issues. If Mathematica becomes the indispensable tool for researchers, then more transparency about stability, reliability and accuracy becomes paramount. We need to be able to rely on the tool and hence we need insight in outstanding issues, bugs and workarounds. I hope access to redmine is a first step into more transparency.

Reduction of the number of functions to a select number of unique ones. Mathematica prides itself of its 5000-odd number of functions. However, I see a lot of redundancies i.e. new functions that do things slightly different from similar functions. I like to see a reduction of redundant functions. For example take the ListPlot function: we have ListLinePlot, DateListPlot, StepListPlot, DateStepPlot etc. they are all of the class “ListPlot” and with the new axis capabilities, they can all be integrated into one function. This saves us the effort to remember the name of each specialized function, it makes code maintenance and documentation easier for WR too.

Document implemented methods. I would like to see WR open up the black box of some functions in the documentation i.e. explanation of methods used or references to methods implemented.

Conclusion

I think the purpose of Mathematica should be the go-to tool for researchers and analysts. I agree with Jonathan that WR should focus on delivering a complete set state-of-the-art tools.

I think the Wolfram Language could become the computational ecosystem to develop, test and deploy code for all things computable. We have some miles to go there.

At last, the adoption of Mathematica and WL could be facilitated if:

• We have more transparency of outstanding issues and bugs.
• The number of "redundant" functions has been reduced to a number of unique ones.
• We see more documentation to help us look inside the black box of some functions.

This is a very well thought-out reply with several interesting points.

Now I may use Excel to create a well-formed CSV file, which I import to create a Dataset and analyze it in an Mathematica notebook. I spent a lot of time to master Datasets and associations and now it pays off.

Dave may well be right that the trade-off between using Excel vs Mathematica for pivot-table type analysis comes down to a question of familiarity and dexterity with the WL functionality. Mathematica has a steeper learning curve than Excel, but once you have mastered tools such as datasets and associations you can do much more in MMA than Excel, of course. And there is a bonus in being able to do everything in one application rather than switching between two.

I believe this is what WR is aiming for:

If you have Mathematica, you shouldn’t need any other specialized application to do your research.

which leads logically to Dave's conclusion that:

WR should focus on finishing and polishing e.g. statistics and time series analysis, machine learning and a number of other application areas, so it becomes the go-to tool for research.

I agree in principle that:

If Mathematica becomes the indispensable tool for researchers, then more transparency about stability, reliability and accuracy becomes paramount.

However, that is always going to be something of a challenge for a development platform built with proprietary software. Similar issues may arise w.r.t. Dave's other appeal for more documentation of implemented methods.

I, too,

see a lot of redundancies i.e. new functions that do things slightly different from similar functions.

But I am less convinced than Dave that this may be cluttering up the language unnecessarily - the jury's still out on that question, I think.

I find myself in complete agreement with Dave's final conclusion that:

the Wolfram Language could become the computational ecosystem to develop, test and deploy code for all things computable. We have to some miles to go there.

There are two additional items I should have considered in my earlier presentation of what I considered to be the key features of Mathematica/the Wolfram tech stack, but which I neglected to discuss properly.

The first is such an integral part of Mathematica that it is easy to overlook - and yet it is one of its core features and a cornerstone of the technology, i.e., the Notebook. This concept has been copied by others (e.g., Python), but no one has ever surpassed Wolfram in the functionality and flexibility of its notebook technology.

The second feature that is gradually becoming more and more important is computational data. This is something that I believe Stephen has, from the outset, regarded as being integral to the Mathematica product, as demonstrated by the integration of Wolfram Alpha and the development of the Entity Store concept.

My sense is that, at the beginning, when computational data is limited, this feature looks rather unimportant, and only over time does its real significance become apparent to the end user. An analogy might be made with Wikipedia. At the beginning, when articles were scarce and of questionable quality, the enterprise looked doomed to failure. But gradually, over time, more users discovered the site and perceived how useful a universal online encyclopedia might become. This drove the creation of more, higher-quality articles, which attracted more users, and so on. There is a concept in Systems Dynamics that describes this phenomenon, known as the "success to the successful" paradigm. This is what I believe is now beginning to happen with Mathematica/Wolfram Alpha, although the rate of development and user acceptance is slower than for Wikipedia as the technology is proprietary.

The functionalities you've listed only scratch the surface. For example, consider the interconnectivity to devices. Mathematica is used as a controller for laboratory apparatus, as a receiver for remote sensing applications, and so on. Take a stroll through the main Language Documentation webpage and you'll find more capabilities you missed.

With regard to LaTeX, it's remarkable that Wolfram provides any support at all to something that is not a product but rather an ever-growing collection of TeX macros. As Peter points out, there is serious support for TeX. You can also use the Mathematica "Copy As" (select, right click) to paste Mathematica output as TeX and paste it into your TeX document. If you need something fancier, then use your programming skills to generate TeX within Mathematica and write it to a TXT file.

Those "specialist alternatives" often contain modules pieced together by graduate students with no background in numerical analysis, and consequently led to a proliferation of errors spanning decades. Then by demand of specialists, some of the erroneous approaches have found their way into commercial software. Ecology has its share of this, including fantasies such as Bayesian Clustering.

http://wireilla.com/papers/ijcsa/V12N4/12422ijcsa01.pdf

Most users of phylogenetic software do not understand what it is actually doing, nor therefore the potential for inferential errors, let alone actual algorithmic or coding mistakes. Which is part of a larger discussion that goes well beyond phylogenetics. But how to solve the problem?

Much of biology has become mathematically inclined over the past 40 years. Early on, Biology departments started teaching their own mathematical analysis courses - in part because math departments refused to add pair-joining and pseudo-metrics to their course curricula. This has not been the case with other math-oriented majors - they require their undergraduates to take the junior level numerical analysis course, and their graduate students to take applied math analysis + numerical analysis II.

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