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A bit of a loaded question, but in your opinion is Wolfram's team making good progress on improving their software?

I've used Mathematica for almost 10 years now, and honestly I'm personally surprised by how little things have changed since then. I personally see a lot of improvements that can be made to the system and wonder why they aren't done.

What is the community's opinion on the development team's progress as a whole? (Ideally only feedback from people who don't work there, for no conflict of interest).

Maybe there's not enough people using the software or there's not enough demand? I know there can be a lot of incentive problems within tech companies so I was curious what the communities thoughts are on it.

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    $\begingroup$ I feel like with anything complex, the answer is both yes and no. There have been lots of improvements in terms of getting cloud support to the point that people can (almost) host documentation in it. The FE now runs on a 64-bit platform on Mac. There's greater support for stuff like NumericArray and clear interest in improving on that. On the other hand, no matter what your field there are many things where you might want something to have been done, but it hasn't. My big thing is that packaging is still iffy, which dis-incentivizes the community to actually contribute to the system. $\endgroup$ – b3m2a1 May 12 at 1:36
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    $\begingroup$ I'm interested in what you want when you say: "I personally see a lot of improvements that can be made to the system and wonder why they aren't done.". We've all got things we want done, and I'm wondering which angle you're coming at this from. $\endgroup$ – b3m2a1 May 12 at 3:44
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    $\begingroup$ I think this question belongs on the main site. Meta is for questions about Mathematica Stack Exchange. $\endgroup$ – Simon Woods May 14 at 20:09
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    $\begingroup$ @StevenSagona At my institute (physics) people use it a fair bit for symbolic stuff. Actually, I would have said that the issue is that people tend to use it as a fancy symbolic calculator or plotter, and ignore the other abilities. It has always been my impression that physics has been a traditional stronghold of Mathematica. In other areas of physics (that they don't do at our institute) it is even more popular, see hepforge $\endgroup$ – Szabolcs May 16 at 8:11
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    $\begingroup$ @b3m2a1 "My big thing is that packaging is still iffy, which dis-incentivizes the community to actually contribute to the system." <-- This, 10 times. There are multiple projects that started out on Mathematica and moved fully to Python, e.g. xcellerator. I think this is the main reason. $\endgroup$ – Szabolcs May 16 at 8:16
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Mathematica is very large and complex software which covers many many different areas.

I can only comment myself on few areas. In the area of integration, this bar chart shows the progress made. This is for integration test using 14,944 integrals of many types

Integration

(Just updated to add 12.1 after it completed building). There are 2 integrals, out of 14,943 that 12.1 did not solve compared to 12.0, this explains why 12.1 got 94.42% and 12.0 got 94.43%. Still, the overall curve is upwards, but may be the curve is flattening now. But 94.4% is good score anyway, these are hard integrals. See these-indefinite-integrals-evaluate-in-12-0-but-not-in-12-1-what-can-be-done if interested to know more.

enter image description here

But the quality of the anti-derivatives has improved. This chart shows the percentage of A grade of anti-derivatives for same test over the years. A grade means optimal anti-derivative. (Higher is better)

enter image description here

There are 4 grades for each integral. A,B,C and F. Where A is best, and F for not able to integrate it.

The leaf size also improved. Lower leaf size is better. This is the size of the anti-derivative. This chart shows good progress in this area where the average size has decreased. (Lower is better)

enter image description here

So overall, I would say that Integrate has been improving over the years.

DSolve for PDE

For DSolve in the area of PDE's, using test suite of about 2,000 PDE's, here is the result

Mathematica graphics

This shows steady and good improvement in this area.

DSolve for ODE

In the area of DSolve and ODE's, using the famous Kamke's set of ODE's (1,940 differential equations from Kamke book), this is the result

Mathematica graphics

This also shows steady and good improvement in this area.

Some of the things that WRI needs to improve on is overall quality and performance of the FE and or the kernel, to make things more robust and less prone to hangs, crashes and sudden freezes, specially when using Dynamics.


Oh, and I forgot one thing we all need and been waiting for for many many years: an easy to use debugger !!

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    $\begingroup$ I think this is fair. One comment here is that I'm honestly not sure how many of these solutions are actually useful. While technically Mathematica can do a lot, we're at a point were even simple analytical problems can end up being obfuscated. You might get a solution to your differential equation but if its a nasty long expression that can't be written on the page, then it defeats the point. $\endgroup$ – Steven Sagona May 12 at 21:03
  • $\begingroup$ You often solve DEs with Maple that cannot be solved with Mathematica. In your judgment, which works better for symbolic solution of DEs? $\endgroup$ – bbgodfrey May 15 at 1:38
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    $\begingroup$ @bbgodfrey for analytical solutions of DE's, Maple still has small edge. For Murphy's collections of ODE (2,313 ODE's), Maple 2016 scored 95% and Mathematica 11 scored 85% (this needs to be updated to current version). On Kamke's collection, Maple 2020 scored 92% and Mathematica 12.1 scored 84%. But DSolve has been improving by few percentages over each release which is good. Also Maple's ODE solver still has more options and Misc. functions than DSolve has. $\endgroup$ – Nasser May 15 at 1:48
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    $\begingroup$ +1. Though if you used the same range [0, 100%] over the y axis of your histogram (en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics), someone could argue that indeed little progress has been made e.g. for integration :-) $\endgroup$ – chris May 16 at 7:21
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    $\begingroup$ @StevenSagona Maybe you're thinking of SageMath? As far as I'm aware, Maple is proprietary software, not open source. $\endgroup$ – MassDefect Jun 9 at 23:09
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I use Mathematica daily. I couldn't live without it. It's one of those things until you have it you don't know what you are missing and when you do you cant do calculus by hand anymore. I just wrote code in Mathematica that outputs Indian classical music pieces on its own. If that does not impress you, nothing will.

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    $\begingroup$ It would be really cool if you needed to self-answer a question you asked and had to share that code :O $\endgroup$ – CA Trevillian May 16 at 15:49
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    $\begingroup$ This doesn't address my question at all. I understand you use Mathematica daily, but the question is if you think Mathematica has adequately improved over the years. For example, are you using features that we added in the last 10 years? Have there been any new versions that you've been happy about? Have the new mathematica versions actually changed your mathematica experience at all? $\endgroup$ – Steven Sagona May 19 at 7:30
  • $\begingroup$ yes to all the questions. The latest version is the best. $\endgroup$ – Quasar Supernova May 22 at 3:35

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