What Is the Wolfram Language?

The Wolfram Language is the programming language of Mathematica, created by Stephen Wolfram and first released (as Mathematica) in 1988. It also powers Wolfram|Alpha, the computational knowledge engine.

Integrate[x Sin[x], x]
Select[Range[30], PrimeQ]

-x Cos[x] + Sin[x]
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

One line found an integral symbolically — the exact formula, not a number — and the next listed the primes up to 30. That mix of symbolic math and general programming is the language's signature.

Its defining traits:

• Symbolic — x doesn't need a value. Formulas, equations, graphics, and even programs are all data you can compute with.
• Everything is an expression — x + y, {1, 2, 3}, and a plot are all written as head[arguments], so one set of tools works on everything.
• Huge built-in library — more than 6,000 built-in functions, from algebra and statistics to image processing, graph theory, and machine learning, all designed to work together.
• Built-in knowledge — curated data about countries, chemicals, movies, units, and much more.
• Notebooks — interactive documents mixing code, results, text, and graphics.
• Functional and rule-based — pure functions, Map, and pattern rules are the everyday style; loops are available but rarely needed.

This course teaches Wolfram Language 15 (the current version); almost everything also works in versions 13 and 14.

How the examples were checked: the Wolfram Engine needs an online license activation, so the examples in this course were written and reviewed carefully against the official documentation rather than run. Results are shown as plain text; the Output section of the first-program lesson explains how they relate to what a notebook displays.