Not industry, but it's pretty popular among theoretical physics researchers.

I had it in an engineering inner sanctum of Apple. had used it since it came out in 1988 on campus in Illinois, and folks in Apple definitely knew it. Not sure who all was doing what with it.

Steve Jobs and Stephen Wolfram were friends for years. Mathematica shipped preinstalled on early NeXT systems.

SJ recommended some of the UI bits of the notebook. Particularly the separators between cells.

How could I forget this! He also recommended the name.

Wolfram had come up with some normal techie names "computron", "math-o-matic" or whatever. SJ said No those suck, use something simple like Mathematica.

I used Mathematica on a NeXT computer back in 1991. It was a beautiful machine to work on. I did a student project where I simulated the flow of the boundary of a plane region over time (like how the shape of a drop of oil in water changes over time) and it was very, very easy to write in Mathematica with cool graphics.

Still nowadays? My impression is that in (pure) math it's lost most of its market share in the last few years. But maybe that's only in my circles.

what do you or others use instead?

Probably the most general-purpose one is SageMath, which is open-source and basically Python with a ton of sophisticated math stuff built into it. Everything I used to do in Mathematica I now do in sage, and I don't think I'm the only one. Probably field-dependent though.

Of course there is a whole constellation of more specialized things in certain fields, that has come a long way in the last 15 years. So people needing things like that no longer kludge things together in Mathematica.

Does SageMath use Sympy, or is there some other integrator built in? Last I heard Sympy was one of the worst performers, even among other open source CASs.

https://www.12000.org/my_notes/CAS_integration_tests/reports...

It used Maxima many years ago.

Maple would be the main proprietary alternative but yes, there's also SageMath.