Computational X for All X
Every field is becoming its computational version — build the notation that lets it.
- Difficulty
- Expert
- Time to result
- ~ongoing to results
- Steps
- 4
- Confidence
- 80%
Wolfram argues that just as mathematical notation (plus signs, equals signs) transformed how we describe the world 500 years ago and gave us algebra, calculus, and modern physics, computation is now the new substrate for making any field rigorous. He observes 'computational X' fields emerging across disciplines and frames his life mission as providing the language and notation that makes computational-X possible for all X. Crucially, math succeeded in physics but failed in biology and the social sciences; computation, with its 'simple rules, complex behavior' repertoire, reaches where equations couldn't. The result is not just clearer description but the ability to actually compute what will happen.
Origin
Beginning in the early 1980s, Wolfram set out to formalize thinking about the world beyond what calculus offered, which led to a 40-year effort to build Wolfram Language as a general notation for computation across every field.
Core principles
- 01For 300 years the way to make a field rigorous was to make it mathematical; the new way is to make it computational.
- 02A shared notation for computation unlocks whole new fields the way plus and equals signs unlocked algebra.
- 03Math worked in physics but failed in biology and social science; computation extends rigor to those domains.
- 04Providing the language for 'computational X' is a civilizational-scale tooling mission.
How to run it
- 1
Spot a field described only in words or partial math
Identify a domain — biology, a social science, an engineering niche — where informal description or classical math leaves gaps.
- 2
Find its underlying rules
Look for the definite rules that govern how the field's objects behave, expressed as structured transformations rather than only equations.
Pro tip Rules stated as 'this arrangement leads to that' can capture behavior integrals can't.
- 3
Encode in a shared computational language
Represent the domain's concepts and data in a precise computational notation so anyone can build on them.
Pro tip A common notation is what turns isolated results into a cumulative field.
- 4
Compute consequences, not just describe
Use the encoding to actually compute outcomes and build towers of consequences the field couldn't reach informally.
In the wild
Wolfram notes math explained physics well over 300 years and gave us modern engineering, but worked terribly in biology and the social sciences — people imagined a 'social physics' that never panned out.
→ The failure of equations in those domains is what motivates a computational rather than mathematical formalization.
Common mistakes
Assuming everything must be made mathematical
Forcing a field into multiplications and integrals ignores that many systems are better described by rules over discrete arrangements, which is why math stalled in biology and social science.
Is it for you?
Best for
Researchers and builders creating rigorous tools in a domain that words and classical math can't fully capture.
Not ideal for
Domains already well-served by continuous mathematics where no new formalization is needed.
From the transcript
“the sort of the new way to make science really work is to make it computational. And so you see all these different fields, you…”
“one of my big life missions has been to provide the sort of language and notation for making computational X for all X possible.”
From the episode
Stephen Wolfram: How AI Works and How to Use It to Stay Ahead
Stephen Wolfram