Stephen Wolfram
Founder and CEO of Wolfram Research, creator of Mathematica and Wolfram|Alpha, and author of A New Kind of Science.
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What they believe
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Computational irreducibility is ubiquitous, affecting essentially any system whose behavior is not obviously simple.
computational irreducibility is not just something that's in principle possible; it's something that (according to the Principle of Computational Equivalence) is at some level ubiquitous-and affects essentially any system whose behavior is not obviously simple.
writings.stephenwolfram.comSaid 21 Jul 2026This on korrents
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AI-written code is fine when only the visual result matters, but insufficient in technical domains where understanding what is actually being computed is required.
But there are many situations, particularly in more technical areas, where "looking right" isn't good enough: you need to actually know what is being computed.
writings.stephenwolfram.comSaid 16 Jun 2026This on korrents
The bold line is korrents’ wording; the quote is theirs. These 2: what they wrote before what they said aloud, one per source, newest first.
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From one piece Towards a Theory of Bugs: The Ruliology of the Unexpected 3 beliefs · writings.stephenwolfram.com
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Their words
to make the program worth actually running, there have to be parts of its behavior you can't foresee. But then there's a piece of intuition from the Principle of Computational Equivalence: once there's anything you can't foresee, there tends to be a lot you can't foresee. In other words, the system will tend to be full of computational irreducibility.
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korrents.com
A program's simplicity of structure does not limit how sophisticated the computation it performs can be.Their words
even programs (or fragments of them) that are very simple in their structure can end up doing computation that is in a sense as sophisticated as anything.
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korrents.com
Computational irreducibility is ubiquitous, affecting essentially any system whose behavior is not obviously simple.Their words
computational irreducibility is not just something that's in principle possible; it's something that (according to the Principle of Computational Equivalence) is at some level ubiquitous-and affects essentially any system whose behavior is not obviously simple.
16 June
From one piece Launching Version 15 of Wolfram Language & Mathematica: Built-in (Useful) AI & Lots of New Core Functionality 2 beliefs · writings.stephenwolfram.com
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korrents.com
AI-generated code is not fully reliable and typically needs significant manual effort to keep it working correctly.Their words
Yes, it's not perfectly reliable, and typically requires quite sophisticated wrangling to keep it on track.
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Their words
But there are many situations, particularly in more technical areas, where "looking right" isn't good enough: you need to actually know what is being computed.
4 June
From one piece Games between Programs: The Ruliology of Competition 2 beliefs · writings.stephenwolfram.com
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Their words
It's notable that machine 22 (which corresponds to the famous "tit-for-tat" strategy) is quite far down in this ranking, even though it's often identified as the most successful in collections of human-suggested strategies.
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korrents.com
Adaptive evolution tends to achieve even a simple, fixed objective through complicated behavior.Their words
In other words, adaptive evolution will tend to make even a simple, fixed objective be achieved in a complicated way.
23 February
From one piece Making Wolfram Tech Available as a Foundation Tool for LLM Systems 2 beliefs · writings.stephenwolfram.com
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Their words
it's become much clearer that-at least for the modalities LLMs currently address-most of the growth in their practical value is going to have to do with how they are harnessed and connected.
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korrents.com
Large language models are broad and impressive but not precise, and are not fundamentally about deep computation.Their words
LLMs don't-and can't-do everything. What they do is very impressive-and useful. It's broad. And in many ways it's human-like. But it's not precise. And in the end it's not about deep computation.
4 February
From one piece What Ultimately Is There? Metaphysics and the Ruliad 3 beliefs · writings.stephenwolfram.com
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Their words
it's the fact that this is a single thread that seems to give us our sense of coherent existence, and in effect, of consciousness.
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Their words
what we see is that the Second Law is something that emerges because of us, and our characteristics as observers, and in particular our computational boundedness.
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Their words
space is not just a simple continuum. Instead, it's a complicated discrete structure that in fact represents every aspect of our universe-both what we normally think of as space, and everything in it.
30 January
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korrents.com
Even very simple, easily enumerated computer programs commonly produce extremely rich and complex behavior.Their words
But what I discovered in the early 1980s is that this is absolutely not the case-and that in fact it's very common for programs even small enough to be easily enumerated to show extremely rich and complex behavior.
12 January
From one piece What Is Ruliology? 2 beliefs · writings.stephenwolfram.com
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korrents.com
The behavior of the simplest computational rules is permanently foundational, not merely significant for the present.Their words
If one's dealing with the simplest rules of some type, they're going to be foundational not only now, but forever.
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korrents.com
Studying what arbitrary computational rules do is a distinct science, separate from computer science and mathematics.Their words
It's not computer science, because that would be about programs we construct for particular purposes, rather than ones that are just "out there in the wilds of the computational universe".
2 December 2025
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17 August 2010
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Lovedtheir ownrcmnd.app
MathematicaTheir words
By far my #1 tool is Mathematica. Which, of course, I built so I could have it to use!
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Usestheir ownrcmnd.app
Wolfram|AlphaTheir words
I use both the current Wolfram|Alpha, and versions running on our hierarchy of development and test systems.
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Usesrcmnd.app
FirefoxTheir words
These days I use Firefox as my primary browser, Adobe Connect for webconferencing, ShoreTel for telephony (I'm a stickler for audio quality), and a horrific calendar system that I've been trying to get us to replace for ages.
+ 3 more
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Usesrcmnd.app
MacBook ProTheir words
Around my house, I just switched to using a 15" MacBook Pro as my portable computer.
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Usesrcmnd.app
Lenovo ThinkPad X301Their words
Outside the house, I had been using a Lenovo ThinkPad X301 running Windows 7 with a cellular modem, but I'm now switching to a MacBook Air with a MiFi device.
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Usesrcmnd.app
iPhone 4Their words
I currently use an iPhone 4 as my main mobile phone, and I'm now carrying an iPad 3G around to use as my instant-on system.
7 September 2006
1 June 1986
1 April 1985
1 January 1985
1 May 1977
1 October 1975
Nothing matches.
Beliefs
Korrents What they believe 16 beliefs — each backed by an exact quote.
Each is a — compiled by korrents.com, not by them: the one-line wordings are korrents', the quotes are theirs.
Recent
Computational irreducibility is ubiquitous, affecting essentially any system whose behavior is not obviously simple.
computational irreducibility is not just something that's in principle possible; it's something that (according to the Principle of Computational Equivalence) is at some level ubiquitous-and affects essentially any system whose behavior is not obviously simple.
Towards a Theory of Bugs: The Ruliology of the Unexpected Said 21 Jul 2026
A program's simplicity of structure does not limit how sophisticated the computation it performs can be.
even programs (or fragments of them) that are very simple in their structure can end up doing computation that is in a sense as sophisticated as anything.
Towards a Theory of Bugs: The Ruliology of the Unexpected Said 21 Jul 2026
A program is only worth running if its behavior cannot be fully foreseen in advance.
to make the program worth actually running, there have to be parts of its behavior you can't foresee. But then there's a piece of intuition from the Principle of Computational Equivalence: once there's anything you can't foresee, there tends to be a lot you can't foresee. In other words, the system will tend to be full of computational irreducibility.
Towards a Theory of Bugs: The Ruliology of the Unexpected Said 21 Jul 2026
Show 13 more
AI-written code is fine when only the visual result matters, but insufficient in technical domains where understanding what is actually being computed is required.
But there are many situations, particularly in more technical areas, where "looking right" isn't good enough: you need to actually know what is being computed.
Launching Version 15 of Wolfram Language & Mathematica: Built-in (Useful) AI & Lots of New Core Functionality Said 16 Jun 2026
AI-generated code is not fully reliable and typically needs significant manual effort to keep it working correctly.
Yes, it's not perfectly reliable, and typically requires quite sophisticated wrangling to keep it on track.
Launching Version 15 of Wolfram Language & Mathematica: Built-in (Useful) AI & Lots of New Core Functionality Said 16 Jun 2026
Adaptive evolution tends to achieve even a simple, fixed objective through complicated behavior.
In other words, adaptive evolution will tend to make even a simple, fixed objective be achieved in a complicated way.
Games between Programs: The Ruliology of Competition Said 4 Jun 2026
The tit-for-tat strategy, despite its reputation as the most successful approach in game-theory strategy comparisons, ranks poorly when tested against the full space of possible strategies.
It's notable that machine 22 (which corresponds to the famous "tit-for-tat" strategy) is quite far down in this ranking, even though it's often identified as the most successful in collections of human-suggested strategies.
Games between Programs: The Ruliology of Competition Said 4 Jun 2026
Large language models are broad and impressive but not precise, and are not fundamentally about deep computation.
LLMs don't-and can't-do everything. What they do is very impressive-and useful. It's broad. And in many ways it's human-like. But it's not precise. And in the end it's not about deep computation.
Making Wolfram Tech Available as a Foundation Tool for LLM Systems Said 23 Feb 2026
Most future growth in large language models' practical value will come from how they are harnessed and connected to other tools, not from the core models alone.
it's become much clearer that-at least for the modalities LLMs currently address-most of the growth in their practical value is going to have to do with how they are harnessed and connected.
Making Wolfram Tech Available as a Foundation Tool for LLM Systems Said 23 Feb 2026
Space is fundamentally a discrete structure rather than a continuum.
space is not just a simple continuum. Instead, it's a complicated discrete structure that in fact represents every aspect of our universe-both what we normally think of as space, and everything in it.
What Ultimately Is There? Metaphysics and the Ruliad Said 4 Feb 2026
The Second Law of thermodynamics is not an intrinsic law of nature but emerges from the computational boundedness of observers.
what we see is that the Second Law is something that emerges because of us, and our characteristics as observers, and in particular our computational boundedness.
What Ultimately Is There? Metaphysics and the Ruliad Said 4 Feb 2026
A sense of coherent consciousness arises from experience being compressed into a single thread rather than from the brain's full underlying activity.
it's the fact that this is a single thread that seems to give us our sense of coherent existence, and in effect, of consciousness.
What Ultimately Is There? Metaphysics and the Ruliad Said 4 Feb 2026
Even very simple, easily enumerated computer programs commonly produce extremely rich and complex behavior.
But what I discovered in the early 1980s is that this is absolutely not the case-and that in fact it's very common for programs even small enough to be easily enumerated to show extremely rich and complex behavior.
P vs. NP and the Difficulty of Computation: A Ruliological Approach Said 30 Jan 2026
Studying what arbitrary computational rules do is a distinct science, separate from computer science and mathematics.
It's not computer science, because that would be about programs we construct for particular purposes, rather than ones that are just "out there in the wilds of the computational universe".
What Is Ruliology? Said 12 Jan 2026
The behavior of the simplest computational rules is permanently foundational, not merely significant for the present.
If one's dealing with the simplest rules of some type, they're going to be foundational not only now, but forever.
What Is Ruliology? Said 12 Jan 2026
The behavior of very simple computational rules can require large amounts of obscure mathematics to fully capture.
But it's remarkable how quickly the mathematics tends to get out of hand, with even a very simple rule having behavior that can only be captured by large amounts of obscure mathematics.
What Is Ruliology? Said 12 Jan 2026
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Recommends rcmnd
rcmnd What they recommend 6 things — each backed by an exact quote.
Compiled by rcmnd.app, not by them: the quotes are theirs, and each links to the post it was copied from.
Recent
Uses iPhone 4
I currently use an iPhone 4 as my main mobile phone, and I'm now carrying an iPad 3G around to use as my instant-on system.
usesthis.com 17 Aug 2010
Uses Lenovo ThinkPad X301
Outside the house, I had been using a Lenovo ThinkPad X301 running Windows 7 with a cellular modem, but I'm now switching to a MacBook Air with a MiFi device.
usesthis.com 17 Aug 2010
Uses MacBook Pro
Around my house, I just switched to using a 15" MacBook Pro as my portable computer.
usesthis.com 17 Aug 2010
Show 3 more
Uses Firefox
These days I use Firefox as my primary browser, Adobe Connect for webconferencing, ShoreTel for telephony (I'm a stickler for audio quality), and a horrific calendar system that I've been trying to get us to replace for ages.
usesthis.com 17 Aug 2010
Uses Wolfram|Alpha
I use both the current Wolfram|Alpha, and versions running on our hierarchy of development and test systems.
usesthis.com 17 Aug 2010
their own
Loved Mathematica
By far my #1 tool is Mathematica. Which, of course, I built so I could have it to use!
usesthis.com 17 Aug 2010
their own
Where they publish
Site stephenwolfram.com His personal site: books, projects and biography.
Link verified 5 Sept 2026.
Blog Stephen Wolfram Writings Long-form essays on science, computation and the history of ideas.
Open writings.stephenwolfram.com
Recent
- What’s the Future for Pure Math Research in the Age of AI? 28 Sept 2026 Headlines and History The headlines keep coming: such and such an AI system has solved such and such a math problem. And more and more I’m hearing people saying: maybe we don’t need people doing math research anymore; m…
- In Memory of My Wife, Elise Cawley (1961–2026), with Thanks for 36 Wonderful Years 4 Aug 2026 Something terrible just happened. My wife, Elise Cawley, was recovering from heart surgery and had just attended virtually a celebration for one of our children when she had a freak, vast cardiovascular event—and died i…
- Towards a Theory of Bugs: The Ruliology of the Unexpected 21 Jul 2026 “My Program Did the Wrong Thing!” Bugs are a ubiquitous phenomenon in the software world. And—essentially by definition—each one of them is somehow unique and unexpected. But—particularly given their ubiquity—one might…
Show 9 more
- Launching Version 15 of Wolfram Language & Mathematica: Built-in (Useful) AI & Lots of New Core Functionality 16 Jun 2026 June 23, 1988 is when we launched Version 1.0 of Mathematica. Today—almost 38 years later—we’re launching Version 15 of what—in recognition of how far it’s expanded beyond “math”—we now call Wolfram Language. It’s an im…
- Games between Programs: The Ruliology of Competition 4 Jun 2026 The Basic Setup Whether one’s dealing with biology, economics, politics or a host of other fields, it’s common to encounter situations that can be modeled as involving two agents that repeatedly compete with each other.…
- Making Wolfram Tech Available as a Foundation Tool for LLM Systems 23 Feb 2026 Foundation Models Need a Foundation Tool LLMs don’t—and can’t—do everything. What they do is very impressive—and useful. It’s broad. And in many ways it’s human-like. But it’s not precise. And in the end it’s not about…
- What Ultimately Is There? Metaphysics and the Ruliad 4 Feb 2026 The Wolfram Institute recently received a grant from the Templeton World Charity Foundation for “Computational Metaphysics”. I wrote this piece in part as a launching point for discussions with experts in traditional ph…
- P vs. NP and the Difficulty of Computation: A Ruliological Approach 30 Jan 2026 Empirical Theoretical Computer Science “Could there be a faster program for that?” It’s a fundamental type of question in theoretical computer science. But except in special cases, such a question has proved fiendishly…
- What Is Ruliology? 12 Jan 2026 Ruliology is taking off! And more and more people are talking about it. But what is ruliology? Since I invented the term, I decided I should write something to explain it. But then I realized: I actually already wrote s…
- Instant Supercompute: Launching Wolfram Compute Services 2 Dec 2025 To immediately enable Wolfram Compute Services in Version 14.3 Wolfram Desktop systems, run RemoteBatchSubmissionEnvironment["WolframBatch"]. (The functionality is automatically available in the Wolfram Cloud.) Scaling…
- What’s Special about Life? Bulk Orchestration and the Rulial Ensemble in Biology and Beyond 11 Nov 2025 Towards a Theory of Bulk Orchestration It’s a key feature of living systems, perhaps even in some ways the key feature: that even right down to a molecular scale, things are orchestrated. Molecules (or at least large on…
- The Ruliology of Lambdas 15 Sept 2025 Click any diagram to get Wolfram Language code to reproduce it. What Are Lambdas? It’s a story of pure, abstract computation. In fact, historically, one of the very first. But even though it’s something I for one have u…
Link verified 5 Sept 2026. Recent items update automatically from the channel.
x.com @stephen_wolfram
Recent
- I love the art of language design ... and 9 years ago decided to start showing the world what's involved---live and unscripted. Today I'm about to start my 1000th livestreamed Wolfram Language design meeting. It's a level of openness I'm not sure anyone else---even after all these years---quite has the nerve for.... 14 Oct 2026
- Science & Technology Q&A for Kids (and others) [Part 169] 9 Oct 2026
- Searching in my archives for a person I was about to visit ... I found a hit from 40 years ago... and was reminded of lots of interesting (and surprising) history about ruliology, neural nets and more... (oh, and a "lost" abstract) 8 Oct 2026
Show 17 more
- Future of Science and Technology Q&A (October 2, 2026) 2 Oct 2026
- What’s the Future for Pure Math Research in the Age of AI? 30 Sept 2026
- Since all sorts of people have asked me, I decided to write down my current thoughts on "What's the Future for Pure Math Research in the Age of AI?" 28 Sept 2026
- History of Science and Technology Q&A (September 23, 2026) 23 Sept 2026
- Personal Update & AMA [September 18, 2026] 18 Sept 2026
- After a hiatus brought on by tragedy, I'm planning to return to livestreaming tomorrow (Friday) ... and will start with a personal update and AMA. What would people like to ask about? 17 Sept 2026
- 67 (or should it be 6 7?) 29 Aug 2026
- Sharing a great personal tragedy 4 Aug 2026
- At #ICM2026 something we're starting to talk about is the new Wolfram Institute Pure Math Project... 24 Jul 2026
- We also just finished our 2026 Wolfram Summer Research Institute (formerly Wolfram Summer School): 50 original projects, now including many that align with Wolfram Institute research that I'm excited about... 22 Jul 2026
- Remember busy beavers? Now meet wily weasels: Turing machines that hide their bugs for as long as possible. (The wily weasel function WW says how wily a Turing machine of a given size can be.) 22 Jul 2026
- "What could possibly go wrong?" Exploring the ruliology of the unexpected ... to develop a theory of bugs ... 21 Jul 2026
- Just finished the very energizing experience of working with 84 talented high-school students at our 2026 Wolfram Summer Research Program (and coming up with projects that suit them). It's so impressive and encouraging to see what they were able to do in under two weeks with Wolfram Language! 16 Jul 2026 education.wolfram.com
- Mourning the loss of my friend @JoshuaBaer (1975-2026) and his passion for life and the future. Whether it was about his business, his mentoring, his family, his latest personal productivity hack---or his planned science fiction book---Josh exuded a rare and generous enthusiasm that lifted those around him. All cut short by a freak plane accident on Tuesday evening. 18 Jun 2026
- History of Science and Technology Q&A (June 17, 2026) 17 Jun 2026
- Another new thing delivered with Version 15: click a button to give Wolfram superpowers to your AI system! Immediately connect Claude, Codex, etc. to your local Wolfram|One, Mathematica, etc. via MCP... 17 Jun 2026
- Exploring Wolfram Language V15 16 Jun 2026
Link verified 5 Sept 2026. Recent items update automatically from the channel.
Papers ORCID Their ORCID record: peer-reviewed papers, newest first.
Academic papers, most recent first, restricted to open-access articles published in an identified journal. Fetched live from OpenAlex, keyed by this ORCID.
Recent
- The Future of Computation 7 Sept 2006 Edited transcript of a videoconference keynote address given at IMS 2005.
- Random sequence generation by cellular automata 1 Jun 1986
- Symbolic mathematical computation 1 Apr 1985 Standard programming languages are inadequate for the kind of symbolic mathematical computations that theoretical physicists need to perform. Higher mathematics systems like SMP address this problem.
Show 3 more
- Twenty Problems in the Theory of Cellular Automata 1 Jan 1985 Cellular automata are simple mathematical systems that exhibit very complicated behaviour. They can be considered as discrete dynamical systems or as computational systems. Progress has recently been made in studying se…
- Lepton energy spectra in e+e− annihilation and other processes 1 May 1977
- Hadronic Electrons? 1 Oct 1975 A new form of high energy electron-hadron coupling is examined with reference to the experimental data. The electron is taken to have a neutral vector gluon cloud with a radius ~ 10-18 m. This is shown to be consistent…
Link verified 9 Sept 2026. Recent items update automatically from the channel.
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Some people here publish in a language other than English. Where they do, this site shows a machine translation beneath the post, in this typeface — the site's own, not theirs.
The post itself is never changed, moved or hidden: what is set in the serif above is exactly what the person published, and it is what to quote them on. A translation can be wrong in ways that matter, especially about tone.
Only the post's own words are translated. A quoted post, a linked article and a belief on korrents.com are left in their original language.