Computational knowledge. Symbolic programming. Algorithm automation. Dynamic interactivity. Natural language. Computable documents. The cloud. Connected devices. Symbolic ontology. Algorithm discovery. These are all things we’ve been energetically working on—mostly for years—in the context of Wolfram|Alpha, Mathematica, CDF and so on.

But recently something amazing has happened. We’ve figured out how to take all these threads, and all the technology we’ve built, to create something at a whole different level. The power of what is emerging continues to surprise me. But already I think it’s clear that it’s going to be profoundly important in the technological world, and beyond.

At some level it’s a vast unified web of technology that builds on what we’ve created over the past quarter century. At some level it’s an intellectual structure that actualizes a new computational view of the world. And at some level it’s a practical system and framework that’s going to be a fount of incredibly useful new services and products.

I have to admit I didn’t entirely see it coming. For years I have gradually understood more and more about what the paradigms we’ve created make possible. But what snuck up on me is a breathtaking new level of unification—that lets one begin to see that all the things we’ve achieved in the past 25+ years are just steps on a path to something much bigger and more important.

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Today it’s exactly a quarter of a century since we launched Mathematica 1.0 on June 23, 1988. Much has come and gone in the world of computing since that time. But I’m pleased to say that through all of it Mathematica has just kept getting stronger and stronger. Continue reading

In a few weeks it’ll be 25 years ago: June 23, 1988—the day Mathematica was launched.

Late the night before we were still duplicating floppy disks and stuffing product boxes. But at noon on June 23 there I was at a conference center in Santa Clara starting up Mathematica in public for the first time:

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I’ve been curious about Gottfried Leibniz for years, not least because he seems to have wanted to build something like Mathematica and Wolfram|Alpha, and perhaps A New Kind of Science as well—though three centuries too early. So when I took a trip recently to Germany, I was excited to be able to visit his archive in Hanover.

Leafing through his yellowed (but still robust enough for me to touch) pages of notes, I felt a certain connection—as I tried to imagine what he was thinking when he wrote them, and tried to relate what I saw in them to what we now know after three more centuries:

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More than a million people have now used our Wolfram|Alpha Personal Analytics for Facebook. And as part of our latest update, in addition to collecting some anonymized statistics, we launched a Data Donor program that allows people to contribute detailed data to us for research purposes.

A few weeks ago we decided to start analyzing all this data. And I have to say that if nothing else it’s been a terrific example of the power of Mathematica and the Wolfram Language for doing data science.

We’d always planned to use the data we collect to enhance our Personal Analytics system. But I couldn’t resist also trying to do some basic science with it.

I’ve always been interested in people and the trajectories of their lives. But I’ve never been able to combine that with my interest in science. Until now. And it’s been quite a thrill over the past few weeks to see the results we’ve been able to get. Sometimes confirming impressions I’ve had; sometimes showing things I never would have guessed. And all along reminding me of phenomena I’ve studied scientifically in A New Kind of Science.

So what does the data look like? Here are the social networks of a few Data Donors—with clusters of friends given different colors. (Anyone can find their own network using Wolfram|Alpha—or the SocialMediaData function in Mathematica.)

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Last week I gave a talk at SXSW 2013 in Austin about some of the things I’m thinking about these days—including quite a few that I’ve never talked publicly about before. Here’s a video, and a slightly edited transcript:

Well, this is a pretty exciting time for me. Because it turns out that a whole bunch of things that I’ve been working on for more than 30 years are all finally converging, in a very nice way. And what I’d like to do here today is tell you a bit about that, and about some things I’ve figured out recently—and about what it all means for our future.

This is going to be a bit of a wild talk in some ways. It’s going to go from pretty intellectual stuff about basic science and so on, to some really practical technology developments, with a few sneak peeks at things I’ve never shown before.

Let’s start from some science. And you know, a lot of what I’ll say today connects back to what I thought at first was a small discovery that I made about 30 years ago. Let me tell you the story.

I started out at a pretty young age as a physicist. Diligently doing physics pretty much the way it had been done for 300 years. Starting from this-or-that equation, and then doing the math to figure out predictions from it. That worked pretty well in some cases. But there were too many cases where it just didn’t work. So I got to wondering whether there might be some alternative; a different approach. Continue reading

At the core of Mathematica is a language. A very powerful symbolic language. Built up with great care over a quarter of a century—and now incorporating a huge swath of knowledge and computation.

Millions and millions of lines of code have been written in this language, for all sorts of purposes. And today—particularly with new large-scale deployment options made possible through the web and the cloud—the language is poised to expand dramatically in usage.

But there’s a problem. And it’s a problem that—embarrassingly enough—I’ve been thinking about for more than 20 years. The problem is: what should the language be called?

Usually on this blog when I discuss our activities as a company, I talk about progress we’ve made, or problems we’ve solved. But today I’m going to make an exception, and talk instead about a problem we haven’t solved, but need to solve.

You might say, “How hard can it be to come up with one name?” In my experience, some names are easy to come up with. But others are really really hard. And this is an example of a really really hard one. (And perhaps the very length of this post communicates some of that difficulty…)

Let’s start by talking a little about names in general. There are names like, say, “quark”, that are in effect just random words. And that have to get all their meaning “externally”, by having it explicitly described. But there are others, like “website” for example, that already give a sense of their meaning just from the words or word roots they contain.

I’ve named all sorts of things in my time. Science concepts. Technologies. Products. Mathematica functions. I’ve used different approaches in different cases. In a few cases, I’ve used “random words” (and have long had a Mathematica-based generator of ones that sound good). But much more often I’ve tried to start with a familiar word or words that capture the essence of what I’m naming. Continue reading

Richard Crandall liked to call himself a “computationalist”. For though he was trained in physics (and served for many years as a physics professor at Reed College), computation was at the center of his life. He used it in physics, in engineering, in mathematics, in biology… and in technology. He was a pioneer in experimental mathematics, and was associated for many years with Apple and with Steve Jobs, and was proud of having invented “at least 5 algorithms used in the iPhone”. He was also an extremely early adopter of Mathematica, and a well-known figure in the Mathematica community. And when he died just before Christmas at the age of 64 he was hard at work on his latest, rather different, project: an “intellectual biography” of Steve Jobs that I had suggested he call “Scientist to Mr. Jobs”.

I first met Richard Crandall in 1987, when I was developing Mathematica, and he was Chief Scientist at Steve Jobs’s company NeXT. Richard had pioneered using Pascal on Macintoshes to teach scientific computing. But as soon as he saw Mathematica, he immediately adopted it, and for a quarter of a century used it to produce a wonderful range of discoveries and inventions.

He also contributed greatly to Mathematica and its usage. Indeed, even before Mathematica 1.0 in 1988, he insisted on visiting our company to contribute his expertise in numerical evaluation of special functions (his favorites were polylogarithms and zeta-like functions). And then, after the NeXT computer was released, he wrote what may have been the first-ever Mathematica-based app: a “supercalculator” named Gourmet that he said “eats other calculators for breakfast”. A couple of years later he wrote a book entitled Mathematica for the Sciences, that pioneered the use of Mathematica programs as a form of exposition.

Over the years, I interacted with Richard about a great many things. Usually it would start with a “call me” message. And I would get on the phone, never knowing what to expect. And Richard would be talking about his latest result in number theory. Or the latest Apple GPU. Or his models of flu epidemiology. Or the importance of running Mathematica on iOS. Or a new way to multiply very long integers. Or his latest achievements in image processing. Or a way to reconstruct fractal brain geometries.
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I was just in New York City for the grand opening of the National Museum of Mathematics. Yes, there is now a National Museum of Mathematics, right in downtown Manhattan. And it’s really good—a unique and wonderful place. Which I’m pleased to say I’ve been able to help in various ways in bringing into existence over the past 3 years.

Of all companies, ours is probably the one that has been most involved in bringing math to the world (Mathematica, Wolfram|Alpha, Wolfram Demonstrations Project, MathWorld, Computer-Based Math, Wolfram Foundation, …). And for a long time I’ve thought how nice it would be if there were a substantial, physical, “museum of mathematics” somewhere. But until recently I’d sort of assumed that if such a thing were going to exist, I’d have to be the one to make it happen.

A little more than 3 years ago, though, my older daughter picked out of my mail a curious folding geometrical object—which turned out to be an invitation to an event about the creation of a museum of mathematics. At first, it wasn’t clear what kind of museum this was supposed to be. But as soon as we arrived at the event, it started to be much clearer: this was “math as physical experience”. With the centerpiece of the event, for example, being a square-wheeled tricycle that one could ride on a cycloidal “road”—a mathematical possibility that, as it happens, was the subject of some early Mathematica demonstrations. Continue reading

There aren’t very many qualitatively different types of computer interfaces in use in the world today. But with the release of Mathematica 9 I think we have the first truly practical example of a new kind—the computed predictive interface.

If one’s dealing with a system that has a small fixed set of possible actions or inputs, one can typically build an interface out of elements like menus or forms. But if one has a more open-ended system, one typically has to define some kind of language. Usually this will be basically textual (as it is for the most part for Mathematica); sometimes it may be visual (as for Wolfram SystemModeler).

The challenge is then to make the language broad and powerful, while keeping it as easy as possible for humans to write and understand. And as a committed computer language designer for the past 30+ years, I have devoted an immense amount of effort to this.

But with Wolfram|Alpha I had a different idea. Don’t try to define the best possible artificial computer language, that humans then have to learn. Instead, use natural language, just like humans do among themselves, and then have the computer do its best to understand this. At first, it was not at all clear that such an approach was going to work. But one of the big things we’ve learned from Wolfram|Alpha is with enough effort (and enough built-in knowledge), it can. And indeed two years ago in Mathematica 8 we used what we’d done with Wolfram|Alpha to add to Mathematica the capability of taking free-form natural language input, and automatically generating from it precise Mathematica language code.

But let’s say one’s just got some output from Mathematica. What should one do next? One may know the appropriate Mathematica language input to give. Or at least one may be able to express what one wants to do in free-form natural language. But in both cases there’s a kind of creative act required: starting from nothing one has figure out what to say.

So can we make this easier? The answer, I think, is yes. And that’s what we’ve now done with the Predictive Interface in Mathematica 9.

The concept of the Predictive Interface is to take what you’ve done so far, and from it predict a few possibilities for what you’re likely to want to do next.

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