Stephen Wolfram Q&A
Submit a questionSome collected questions and answers by Stephen Wolfram
Questions may be edited for brevity; see links for full questions.
Wolfram Language
(51)January 1, 1993
From: Interview by Michael Swaine, Dr. Dobb's Journal
If you were writing Mathematica today, what would you leave out?
I’ll give you an example of something that I put into Mathematica that I thought was a good idea but that turned out not to be. It was this function called Short. It just has to do with printing our expressions…
It goes through the expression [as] a tree and it has a certain amount of energy that starts off at the top of the tree, Read more
January 1, 1993
From: Interview by Michael Swaine, Dr. Dobb's Journal
You’ve spent a significant amount of time doing language design. What does a language designer really spend the bulk of the time doing?
Almost all the time is spent trying to simplify the construct one comes up with. You start off with this idea about what capability you want it to have. Then the trick is, find the simplest, most transparent way to represent that.
January 1, 1993
From: Interview by Michael Swaine, Dr. Dobb's Journal
With Mathematica, did you set out to create an application program or a programming language? You sell it as an application.
I viewed the intellectually most significant [part] of the enterprise as being the creation of the elements of a programming language.
[Selling it as an application] has to do with the practical problem of introducing programming languages. Programming languages are a surprisingly slow-moving field. Fortran was invented before I was born and C is more than 20 years old now. Read more
January 1, 1993
From: Interview by Michael Swaine, Dr. Dobb's Journal
You’ve considered “making a thing that will probably be called M, that is essentially Mathematica without the mathematics”. But how seriously?
We’ve built little Ms. There is no doubt that Mathematica without the mathematics will exist one day. The main issue for us is to figure out how it makes sense to distribute the thing. Right now there are particular application areas where people have written programs in Mathematica that don’t use the mathematical side of Mathematica, Read more
January 1, 1993
From: Interview by Michael Swaine, Dr. Dobb's Journal
What are the virtues of symbolic languages like Mathematica vs. procedurally based languages like Basic?
When you’re working with a procedurally based numerical language, there’s a lot of mysterious hidden state associated with what’s happening. For example, you have a standard program written in C, and you have various data structures, and you have subroutines that call each other and pass pointers to these data structures. Read more
January 1, 1993
From: Interview by Michael Swaine, Dr. Dobb's Journal
What were the intellectual roots of Mathematica?
I got to do a test run of some of the ideas in Mathematica in a system called SMP that I built in the late ’70s or early ’80s. It was more oriented toward computer algebra; it wasn’t as ambitious a system as Mathematica. What I did there was a very educational experience. Read more
January 1, 1993
From: Interview by Michael Swaine, Dr. Dobb's Journal
When you were first testing your ideas for Mathematica in SMP, it would have been about the time Clocksin and Mellish were bringing Prolog to a wider audience with their book. Were you influenced by Prolog at that time?
No, actually I wasn’t. I had never written a program in Prolog. I’d read the manual. The main thing that I was trying to do was to imitate what seemed to be what happens when you do mathematical calculations; that is, that you are continually applying rules of mathematics. The transformation-rule model has not been widely adopted. Read more
January 1, 1993
From: Interview by Michael Swaine, Dr. Dobb's Journal
How did SMP influence Mathematica?
One of the ideas I had in SMP was, “Figure out a good programming paradigm and just stick to it”. This was a mistake. I think it’s not a trivial mistake. You might think, “If there is a natural way to specify how programs should work, that maybe hooks into some way that has to do with how the brain processes ideas about things, Read more
January 1, 1993
From: Interview by Michael Swaine, Dr. Dobb's Journal
What kinds of design ideas went into the writing of Mathematica?
One way I tried to design Mathematica was the following: Think about computations that one wants to do, and think about well-defined chunks of those computations that one could give a definite name to and do lots of times. A very simple one might be Nest, a function in Mathematica that is sort of an iteration construct. Read more
January 1, 1993
From: Interview by Michael Swaine, Dr. Dobb's Journal
Is there anything you’d do differently if you were writing Mathematica today?
Were I to build Mathematica again I would probably have 5 percent less stuff in it.
March 1, 1993
From: Interview by Paul Wellin, Mathematica in Education
What is the breakdown of educational vs. research users of Mathematica?
That’s a bit of a difficult question to answer. Because when you have a class that uses Mathematica, how do you count the individual students that are going through there? I think that about 40% of the number of copies of Mathematica that are out there are in the educational sector. Read more
March 1, 1993
From: Interview by Paul Wellin, Mathematica in Education
I noticed a rather long debate on the nets recently about the current “role” of Mathematica. Some people were arguing that presentation features should not be focused on—that all work should go into algorithm improvement. I am sure that a similar argument could be put forth about the Mathematica language itself as well. What is your view of its present role?
In terms of algorithm development, I am really very satisfied with the point we’re at and the rate at which things are progressing. My big test for these things in terms of, for example, algebraic algorithms is to be able to clearly say that if there is an integral you can think about doing, Read more
March 1, 1993
From: Interview by Paul Wellin, Mathematica in Education
From an educational point of view, would you put the Mathematica language on a par with Fortran or Pascal?
People might attack me for immodesty, but I think in the present day and age, if you’re teaching general people about programming computers, Mathematica is far and away the best programming language to use—and I’ll tell you why. There are a certain set of people, who when they are grown up, Read more
June 1, 1996
From: Interview by Stephen Collart, Euromath Bulletin
The reception of the Mathematica system in the mathematical community has on occasion raised unexpectedly high feelings, and has sometimes appeared to take on the dimensions of a zealot’s war of disparagement against hype. Do you have an explanation for this fairly unique occurrence? What is your view of the matter?
I’m not quite sure what you mean. Any successful enterprise will have its detractors—that’s just the way the world works. I guess mathematicians can sometimes get a little more righteously out of control than other folk—witness the Unabomber. But I think that considering the level of success we’ve had, there have been surprisingly few detractors—even in mathematics.
June 1, 1996
From: Interview by Stephen Collart, Euromath Bulletin
What is your most important long-term plan for Mathematica?
Well, I’m not sure how long term you mean. I’m sure Mathematica will still be being developed when I’m an old man. The core will be the same, but there’ll be lots of new stuff made possible by new computer technology, new mathematics and so on. My plan with our company is to keep doing what we’ve been doing for 10 years already—trying to push the state of the art, Read more
June 1, 1996
From: Interview by Stephen Collart, Euromath Bulletin
What has been in your view the most important effect of Mathematica since its release?
Basically that we’ve defined a whole new way for people to use computers—and that more than a million people have found out that it’s a good idea. For your audience, I’d say the most important thing is that lots and lots of people from all sorts of fields have now been exposed through Mathematica to issues about computers and mathematics—and have started to care about them. Read more
June 1, 1996
From: Interview by Stephen Collart, Euromath Bulletin
Where has Mathematica not met your expectations?
Technically I think Mathematica is great. I’m always thinking of more things to make it do, but I’m very happy with what’s there. One thing I guess I’m slightly disappointed about is that we don’t seem to have managed to communicate some of the intellectual advances in Mathematica as thoroughly as I’d like to people in areas like computer science and mathematics. Read more
June 1, 1996
From: Interview by Stephen Collart, Euromath Bulletin
With the benefit of hindsight, is there anything you would have developed differently in Mathematica?
Surprisingly little, actually. Of course it’s very scary when one makes a system that lots of people use: one has to get things right the first time—one can’t go back later and make incompatible changes. But eight years on I’m actually very pleased with how few things I would have done differently. Read more
June 1, 1996
From: Interview by Stephen Collart, Euromath Bulletin
Some observers see a research crisis in mathematical computation—a dearth of both fundamental and practical advances; others are concerned about a looming funding crisis. How do you see the situation?
Well, I think Wolfram Research has one of the largest—if not the largest—R&D efforts in mathematical computation anywhere. And certainly I’m pretty happy with the stuff we’re getting done—which ends up being both practical and fundamental. I don’t know so much about the academic mathematical computation scene. But I’m a bit surprised you ask about funding. Read more
June 1, 1996
From: Interview by Stephen Collart, Euromath Bulletin
Lisp was built on the tradition of the lambda calculus. When Prolog became popular a good dozen years ago, it also spawned a flurry of research into the semantics of logic programming. The evaluation model of Mathematica as a programming language is at least as complex and interesting: why has there been no comparable interest?
I’ve wondered that myself. There has been some work, but there could certainly be much more. Perhaps it’s another sign of the decay of academic computer science. After all, thinking about evaluation models is intellectually quite difficult, especially when there’s a real system out there to stop people being able to hide in pure formalism. Read more
September 30, 1996
From: Interview by Robers Lee Hotz, Los Angeles Times
What is more important to you—the technical elegance of the Mathematica program or the financial rewards it brings?
In the world of high-tech industry, the money becomes the main point for a lot of people. Take your company, puff it up a bit, take it public, cash out, retire. And then what? I have kept my company private and intend to continue doing that because what I am really interested in is the long-term intellectual achievement that our product represents. Read more
September 30, 1996
From: Interview by Robers Lee Hotz, Los Angeles Times
You started your design of Mathematica where most software developers end theirs—by writing a 1,395-page users’ manual. Why?
If you can’t explain it honestly in the manual, then you are probably making a mistake in the way it is designed and people will never be able to understand how it is ever going to work.
One of the things I found to be the most intellectually demanding in building big systems like Mathematica is this whole thing of starting from nothing and then having to build some kind of language and some kind of structure that a lot of people are going to live inside. Read more
September 30, 1996
From: Interview by Robers Lee Hotz, Los Angeles Times
What would you consider your most serious mistake running Wolfram Research?
Part of our market is selling to universities—maybe 25% of our revenues. When Mathematica first came out, academics were used to the idea that any software they cared about was free—at least to them.
I thought there was a serious market for Mathematica in the academic market. We had to dig in our heels and say this is going to cost you real money. Read more
May 29, 2009
From: Interview by Monica Attard, ABC Local
Is Wolfram|Alpha another Google, a simple search engine? Or is it like a vast encyclopedia of sorts?
When you look up a term in the encyclopedia, you still have to go and read the paragraph about that term and you have to make sort of your own conclusions from the narrative text that’s written there.
The idea of Wolfram|Alpha is you have a specific question, you know: where will the Sun be at, Read more
May 29, 2009
From: Interview by Monica Attard, ABC Local
How important is it to you to identify sources on Wolfram|Alpha?
Well, I think our approach as you’re alluding to, it’s rather different from a search engine. A search engine is just saying, look we as the search engine, we’re not making any judgments about any of this information—we’re just giving you… you know, here are 10 links that you can go read and make your own judgment about them. Read more
May 29, 2009
From: Interview by Monica Attard, ABC Local
How do you access all those repositories of knowledge that you use in Wolfram|Alpha?
It’s been lots of work. I mean we had a foundation which was, in terms of the algorithmic side of things, had a system called Mathematica which we’ve been building and selling out there in the world for 23 years now. And that’s the platform from which Wolfram|Alpha is built.
In terms of the actual raw data about the real world, Read more
May 29, 2009
From: Interview by Monica Attard, ABC Local
Google is planning to launch a similar service to Wolfram|Alpha called Google Squared. Do you see it as similar?
I don’t really know enough about it. I mean, I think that what we’ve been doing here is a much more insanely ambitious project than I think anybody else really could seriously imagine at this point. I don’t really know about the details, but the general search engine concept tends to be you’re foraging information from the web and kind of using some purely automated algorithm to present that foraged information in some useful way. Read more
August 31, 2009
From: Interview by Kaustubh Katdare, CrazyEngineers
Could you give a brief overview of the algorithms that make Wolfram|Alpha work and produce great results?
It’s a big system! These days about 6 million lines of Mathematica code. It relies on a very large number of different algorithms and methods, a large fraction of which we’ve had to invent. In a sense it’s NKS that makes it possible: the paradigmatic idea that there can be fairly simple underlying programs that produce the rich and complex behavior we need. Read more
August 31, 2009
From: Interview by Kaustubh Katdare, CrazyEngineers
Where does Wolfram|Alpha get all its data? Does it crawl the Internet like web search engines?
We try to get data from the most definitive, authoritative, sources. Often the web is a good place to start in helping us identify those sources. But then we tend to go to them directly. Identifying the best sources is just the first step, though. Then we have to curate the data, Read more
August 31, 2009
From: Interview by Kaustubh Katdare, CrazyEngineers
What kind of problems can we attempt to solve in the future using Mathematica?
Anything that can be made computational! There’s a huge knowledgebase of algorithms and data now in Mathematica. And the symbolic programming paradigm that underlies Mathematica has turned out to be incredibly general and powerful. It’s really fun for me to see how incredibly productive people who know Mathematica well can be. Read more
August 31, 2009
From: Interview by Kaustubh Katdare, CrazyEngineers
How did you go about building Wolfram|Alpha? What were the design challenges and architecture of Wolfram|Alpha?
It’s a complicated project. Certainly it has many more “moving parts” than anything I’ve ever tried to do before. There’s the data side of it: building a pipeline to organize and expertly curate data from all different domains. Then there’s implementing all the methods and models that we know from science and other fields. Read more
August 31, 2009
From: Interview by Kaustubh Katdare, CrazyEngineers
What kind of infrastructure do you have to process all the data in Wolfram|Alpha?
We have several supercomputer-class clusters running Wolfram|Alpha. All of the code of Wolfram|Alpha is written in Mathematica. When you give an input, it gets handled by webMathematica, then parallelized through a version of gridMathematica.
January 5, 2010
From: Interview by Gregory T. Huang, Xconomy
From a technology standpoint, what’s next for Wolfram|Alpha?
In Wolfram|Alpha, a lot of what it works out is “old science” based. There is an existing model for such and such economic process [for example]. These models are based on equations and mathematical kinds of things. But can we not only compute on the fly, can we also invent and create on the fly? Read more
January 5, 2010
From: Interview by Gregory T. Huang, Xconomy
How mainstream will Wolfram|Alpha become, compared with search engines like Google or Bing?
These are complementary kinds of things. It’s like asking, how successful is science going to be in the world? It’s saying, what can you compute in the world? How could search engines become so important? When it becomes sufficiently easy to be a reference librarian hundreds of times a day.
I think the set of people for whom Wolfram|Alpha is useful is very broad. Read more
January 5, 2010
From: Interview by Gregory T. Huang, Xconomy
Are physicists at the Large Hadron Collider (LHC) using your computational techniques?
There’s a lot of Mathematica usage. I’d expect LHC people would use [NKS] on their laptops for searching the space of models. It’s for the future of NKS to figure out if something bizarre is seen at LHC.
November 3, 2011
From: Interview by Mark Jannot, Popular Science
Is it fair to say that the fundamental aim of Wolfram|Alpha is to foster and democratize computational knowledge?
That’s what we’re trying to do. That’s the big effort. That’s the thing: Absent these various realizations, one might have thought that with computational knowledge, we’ll really not be able to get very far; it’s very specialized and won’t be able to be generally useful. And for me, that’s the big metadiscovery of the past two years: that at this time in history, Read more
November 3, 2011
From: Interview by Mark Jannot, Popular Science
The notion that all of our exponential growth curves in data gathering, storage and processing ability have delivered us to a real paradigm-shift moment in terms of how data can both help us to understand our world and to change it. Do you agree with that? And how does that dovetail with your own work with data and computation?
There are several different branches here. Let’s start with, when you say data, what are the sources of data in the world today? One source of data is people compiling data—census data, data on properties of chemicals. This is largely human-compiled data. What has happened today is that there are very large data repositories in lots of different areas. Read more
May 14, 2012
From: Reddit AMA
Mathematica, NKS, Wolfram|Alpha, what comes next? How are they all related and what is your criteria for choosing a project?
First, lots of combinations of those. There are some really interesting things emerging there.
I’m hoping one day to make a serious assault on finding the fundamental theory of physics. Perhaps that will be my next “very different” project.
How are all my projects connected? Well they all have in common that they involve taking some big hairy area and trying to break it down to find what’s essential, Read more
February 23, 2016
From: Reddit AMA
What ages are appropriate to learn Wolfram Language? Do you see Wolfram Language in third world countries like an Open Source platform in the future?
My theory has been that age 12 is where Wolfram Language starts to be the right thing to learn. But I’ve now seen a good number of 9-, 10- and 11-year-olds who seem to be having a great time with it, so at least for some kids I have to revise my estimate down. Read more
February 23, 2016
From: Reddit AMA
What do you think of the current “deep learning” methods? Will that fit into Wolfram software?
Yes, we’ve done a lot with these things, and will be doing a lot more. See e.g. https://www.imageidentify.com that we released a year ago. We’ve also got a lot of machine learning built directly into the Wolfram Language (and we use machine learning to automate it, so you don’t need machine-learning experts to use it). Read more
July 20, 2016
From: Reddit AMA
You have an uncommon experience of being (and being around) many prominent figures in the scientific community. How has this influenced the development of the Wolfram Language?
Designing a language that’s supposed to “know about everything” means one has to know about a lot of things oneself! It’s been absolutely crucial that I’ve been exposed to lots of different areas, and gotten to know the originators of lots of fields. At a practical level, it’s very common that I’ll want to get some judgement call on some detailed thing in some particular area. Read more
July 20, 2016
From: Reddit AMA
Are there problems that were difficult to solve (historically) but can now be solved trivially using the Wolfram Language? If so, which are your favorites?
About problems that become easy to solve with the Wolfram Language: yes, lots and lots and lots. People mostly just go and use Mathematica—or now the Wolfram Language—to solve problems, and I don’t hear about what they do. But it’s amazing how often I’ll be at some science or technology event and some prominent person will say “oh, Read more
November 7, 2016
From: Interview by Dingyu Chen, Eton Magazine
Your products so far have been wildly successful and crucial in the lives of many. Do you have any plans for future releases?
Of course! In early December you’ll see Wolfram|Alpha start letting you “open up the code” so you can take the Wolfram Language code it uses, and do your own computations with it. That will be important to lots of students, but it’s just a corner of our R&D efforts. We’ve been at this for 30 years now, Read more
March 8, 2017
From: Interview by John Horgan, Scientific American
What’s the ultimate purpose of the Wolfram Language? Can it fulfill Leibniz’s dream of a language that can help us resolve all questions, moral as well as scientific? Can it provide a means of unambiguous communication between all intelligent entities, whether biological or artificial?
My goal with the Wolfram Language is to have a language in which computations can conveniently be expressed for both humans and machines—and in which we’ve integrated as much knowledge about computation and about the world as possible. In a way, the Wolfram Language is aimed at finally achieving some of the goals Leibniz had 300 years ago. Read more
March 4, 2019
From: Reddit AMA
Do you use software to keep track of all or some of the projects happening in your company? Is it really just email threads? Do you use a slack-like application? Do you use something to schedule your day and/or keep track of what you want to be doing?
We have a good project management team and system at our company. I think probably the project management culture is the most important part. Different project teams end up using different specific software systems (some use Jira, some use RT, some use homegrown solutions, etc.) We have pretty active RocketChat going on around our company. Read more
March 4, 2019
From: Reddit AMA
You gather data on your daily activities using Mathematica. As more biofeedback tech (smart watches, neuro tech, etc.) comes along what will Mathematica’s role be in helping make use of this data in a meaningful way? Also if I want to make use of a Muse device’s data (EEG data) what would be the best approach for doing so in Mathematica?
Mathematica/WL have been able to import EDF for a long time. EEG is really complicated, though I have to believe that modern machine learning should finally be able to unscramble it better.
As far as decoding biofeedback data: ultimately one needs a model for the human to know what it means. Read more
July 24, 2019
From: Interview by Will Carey, Creative Chair
Could the Wolfram code be used to assign meaning to the Arrival logograms effectively be used to assign meanings to any shapes?
No—because there can’t be a general way to do this. Think about the shapes we see in the natural world. What “meaning” do they have? Or think about shapes we see in archaeology. We often don’t know when they were “ornamental”, and when they were “functional”. There is no abstract way to associate meaning with a shape. Read more
November 4, 2019
From: Interview by Margaret Harris, Physics World
What’s the rationale behind developing the Wolfram Language?
The concept of Wolfram Language (which is a direct extension of my original vision for Mathematica) is to have a computational language that can describe things in the world—things people want to talk about—in computational terms. It’s common to take small pieces of natural language (like “density of tungsten”) and have our natural language understanding system turn them into symbolic representations from which we can do computation. Read more
November 4, 2019
From: Interview by Margaret Harris, Physics World
Why did you create Mathematica?
Because I wanted to use it myself. I was interested in physics from a young age, and I started doing physics research when I was in my early teens, in the mid-1970s. I didn’t like doing all the mathematical calculations that were needed, and I thought it should be possible to automate them. Read more
November 4, 2019
From: Interview by Margaret Harris, Physics World
How has Mathematica changed over the past 30 years?
Ninety-five percent of what’s in it now wasn’t there 30 years ago. The core principles of the system have stood the test of time extremely well, and I’m pleased to say that almost any Version 1 program from 1988 will still run in Version 12 today (something that is very rare in the computing world). Read more
November 4, 2019
From: Interview by Margaret Harris, Physics World
How is computing different from programming?
The key to computational language is to find a way to express whatever one wants to talk about in a form that a computer can understand. Programming languages are about starting from the underlying operations in a computer and working out how to tell the computer which operations to perform. A programming language has concepts like arrays or pointers. Read more