mathematica is built by a company that seems to take a lot of pride in quality. they are also clearly incentivized by keeping the company afloat and thus by addressing major issues.
i hear people barking incessantly about open source software in mathematics and science, but i just don't see what would actually be successful. in most people's daily jobs in engineering and even in large science projects, proprietary code is used everywhere. it's the only way to get things done in many cases. in my experience, getting a bug acknowledged, prioritized, and then fixed in open source software is like pulling teeth. what are you going to do with open source mathematics or scientific software where only like a person or two understand the bug? your story could easily have replaced mathematica with sage, and the story wouldn't be changed at all. okay fine, sage is open source. but what's more likely to be successful: (1) you are going to look through the likely millions of lines of code that makes up sage and find what's happening, or (2) you call up wolfram and ask what's going on since you have support for a product that you paid for?
how is open source software supposedly inherently better for math and science research?
(As a funny story, even Wolfram-the-company can’t run SMP, the predecessor of Mathematica. Why? They can’t decrypt it or unlock it, and can’t figure out how to work around it.)
Every major tech company on earth uses open source software at the heart of their business. So we know something sustainable is possible.
Open source, one-size-fits-all math software is a tough nut to crack. I think most people could get most of their algebra and calculus done with existing open packages like wxMaxima or Sage. Specialized computations, such as those in group theory, already have open source implementations that exceed any closed competitor.
As for the construction of a competing CAS, some organization would have to employ a team. That costs money, and so far no company (that I know!) sees it as either a worthwhile investment or charitable cause. If folks do know of a company, I’d love to know.
why? why is proprietary software less reproducible? aside from cost, i might even argue that proprietary software is more reproducible. open source software often has dependency hell. how are you sure that the dependencies and software installation is the same between two computers?
how are results not able to be reconstructed with proprietary software, aside from cost (which is not your argument)? if someone has a result found in mathematica, then couldn't that same method be reconstructed in other software to compare results? if it can't, then mathematica provides some feature not found in other software.
and plenty of science operates by not being fully reproducible by independent parties due to cost and available equipment. that's often mitigated by people reproducing the experiments or results with different equipment and even methods. and even then, every regular joe still can't reproduce the results due to massive costs.
Proprietary software is less reproducible because the software artifacts literally cannot be reproduced in different environments. That's why I mentioned SMP as an example; even the vendors of the software can't reproduce their own artifact. Moreover, vendors rarely provide access to previously released versions, because "newer is always better". And nobody, except the vendor, is allowed to host or publish old/different versions. The availability of the source code does not also somehow prohibit binaries from being published.
> how are results not able to be reconstructed with proprietary software [...]?
Cost, legal viability, availability, shareability, etc. Cost is just one aspect. I also can't provide my copy of Mathematica along with my code that produces my results to you; I'm contractually obliged to not copy the software, and so even if I wanted to allow you to reproduce my results, I have no power to do so.
> and plenty of science operates by not being fully reproducible [...]
This doesn't mean we should be driving away from reproducibility just because it's lacking in some areas of science.
here's a quote from the NSF: "reproducibility refers to the ability of a researcher to duplicate the results of a prior study using the same materials as were used by the original investigator. That is, a second researcher might use the same raw data to build the same analysis files and implement the same statistical analysis in an attempt to yield the same results…. Reproducibility is a minimum necessary condition for a finding to be believable and informative".
https://stm.sciencemag.org/content/8/341/341ps12.full
let's say someone has some data and a method to process that data. if they implement it in mathematica, then someone else can do the same implementation in mathematica and attempt to reproduce the results. so what if they had to pay for it? that doesn't affect the reproducibility. it's a barrier maybe, and a small one, but it doesn't make it inherently less reproducible. someone else could take the data and method and implement it in something else, say matlab, sage, octave, or whatever, and attempt to reproduce the results. i know of a researcher who does this very thing. he likes mathematica, but his graduate students use a range of software to do their own work and produce results. he takes their methods and investigates and implements them in mathematica to see if they are reproducible. this is good mathematics and good science. just because mathematica is involved doesn't all of the sudden make everything un-reproducible and bad science.
if you're thinking, but oh, if it's open source, i could crawl through and understand everything the code is doing. but nobody does that. it isn't even feasible in anything but the simplest of simple cases.
> This doesn't mean we should be driving away from reproducibility just because it's lacking in some areas of science.
i didn't say we should. but in all the comments sections of big physics announcements, we don't see people whining about reproducibility. i can't go and reproduce the LIGO experiment in my backyard because it takes huge amounts of money, equipment, and engineering expertise. that's why many things don't compete that well with mathematica. it takes a lot of time, money, and expertise to develop such a software package. the opposing model (open source software) just barely drags along and could disappear at any time as maintainers come and go.
With regards to conditioning the result, it should be as such, but no researcher would ever smear their result like that. Research is cutthroat.
As a tiny anecdote, a colleague of mine recently published a paper in quantum computation and computed a representation of some mathematical object, specifically the exact value of an angle which modulates a particular quantum gate. In the paper was this bizarre continued fraction along with arctans and pi’s that no experimental physicist in their right mind would have derived themselves.
“Where in the world did this come from?” I asked, while reviewing the paper.
“Oh, it’s just what Mathematica gives,” he responded. “I don’t even fully understand it. But I do use it as proof that the angle is an irrational number and thus breaks its inclusion in some known finite group.”
You might call out this otherwise accomplished physicist for what appears to be misusing the tool—taking results at face value without understanding them—but I guarantee scientists and engineers are doing this stuff daily, in more consequential places than abstract quantum physics papers.
Wolfram and his team have built something amazing, and built an incredibly successful business, but I hope he uses his business acumen to find a way to contribute to the “greater good” while he continues to enjoy running a company and making money.