It's not unique in that there literally exist other computer algebra systems (CAS), sure. But it is unique in two meaningful ways:

1. It is arguably the most sophisticated CAS available. Open source tooling has crept up in performance and completeness in recent years, but Mathematica still dwarfs every open source system in performance and feature availability. Competing proprietary systems like Maple are capable of beating Mathematica in certain specific domains (like PDEs), but that leads me to my second point.

2. Mathematica isn't just a CAS. It also supports sophisticated data analysis and ingestion, visualization, (some) machine learning, natural language processing, speech recognition, signal processing, climatology, meteorology, geography, financial analysis, and limited forms of convex optimization.

Some things that Wolfram Language does that maxima doesn't: machine learning, image processing, audio processing, time series analysis, user interface construction, build-in data, geo computation, natural language processing....

Maxima is just a computer algebra system- one small part of what Wolfram does.

Are Maxima's CAS algorithms comparable to Mathematica's? I have tried to used Sage and other systems in the past, but Mathematica has always been better at finding solutions for what I tried to do. But I have never used Maxima for real.

Maxima is a serious CAS and can do serious work, but it’s a few decades behind the latest R&D. It can do algebra and calculus usefully.

Can you explain which features are similar? I am not an expert, but I suspect you are discounting some significant features of Wolfram.

Computing symbolic derivatives and integrals, simplifying algebraic expressions, arithmetic with arbitrary length integers, solving simple ODE, computing limits and series, things like that.

Maxima is a fine piece of software, and I’m a huge proponent of its development, but doesn’t compete in the breadth or depth of Mathematica (or Maple) at all.

It certainly competes due to the fact of being free software, which is a strong requirement of my workflow. I can try Mathematica and Maple (and love them), but ultimately I have to end using a free software solution.

>>It certainly competes due to the fact of being free software, which is a strong requirement of my workflow.

The parent said it doesn't compete "in the breadth or depth of Mathematica" and you responded with "it does compete because it's free!"

Your response does not refute the parent's argument.

Indeed, being open source is a major advantage!

> Maxima… doesn’t compete in the breadth or depth of Mathematica (or Maple) at all.