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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I’m excited to be able to announce that today we’re releasing Mathematica 9—and it’s big! A whole array of new ideas and new application areas… and major advances along a great many algorithmic frontiers.

Next year Mathematica will be 25 years old (and all sorts of festivities are planned!). And in that quarter century we’ve just been building and building. The core principles that we began with have been validated over and over again. And with them we’ve created a larger and larger stack of technology, that allows us to do more and more, and reach further and further.

From the beginning, our goal has been an ambitious one: to cover and automate every area of computational and algorithmic work. Having built the foundations of the Mathematica language, we started a quarter century ago attacking core areas of mathematics. And over the years since then, we have been expanding outward at an ever-increasing pace, conquering one area after another.

As with Wolfram|Alpha, we’ll never be finished. But as the years go by, the scope of what we’ve done becomes more and more immense. And with Mathematica 9 today we are taking yet another huge step.

So what’s new in Mathematica 9? Lots and lots of important things. An amazing range—something for almost everyone. And actually just the very size of it already represents an important challenge. Because as Mathematica grows bigger and bigger, it becomes more and more difficult for one to grasp everything that’s in it. Continue reading

This is an edited version of a short talk I gave last weekend at The Nantucket Project—a fascinatingly eclectic event held on an island that I happen to have been visiting every summer for the past dozen years.

Lots of things have happened in the world in the past 100 years. But I think in the long view of history one thing will end up standing out among all others: this has been the century when the idea of computation emerged.

We’ve seen all sorts of things “get computerized” over the last few decades—and by now a large fraction of people in the world have at least some form of computational device. But I think we’re still only at the very beginning of absorbing the implications of the idea of computation. And what I want to do here today is to talk about some things that are happening, and that I think are going to happen, as a result of the idea of computation.

I’ve been working on this stuff since I was teenager—which is now about a third of a century. And I think I’ve been steadily understanding more and more.

Our computational knowledge engine, Wolfram|Alpha, which was launched on the web about three years ago now, is one of the latest fruits of this understanding. Continue reading

I have four children, all with very different interests. My second-youngest, Christopher, age 13, has always liked technology. And last weekend he and I went to see the wild, wacky and creative technology (and other things) on display at the Maker Faire in New York.

I had told the organizers I could give a talk. But a week or so before the event, Christopher told me he thought what I planned to talk about wasn’t as interesting as it could be. And that actually he could give some demos that would be a lot more interesting and relevant.

Christopher has been an avid Mathematica user for years now. And he likes hooking Mathematica up to interesting devices—with two recent favorites being Arduino boards and quadricopter drones.

And so it was that last Sunday I walked onto a stage with him in front of a standing-room-only crowd of a little over 300 people, carrying a quadricopter. (I wasn’t trusted with the Arduino board.)

Christopher had told me that I shouldn’t talk too long—and that then I should hand over to him. He’d been working on his demo the night before, and earlier that morning. I suggested he should practice what he was going to say, but he’d have none of that. Instead, up to the last minute, he spent his time cleaning up code for the demo.

I must have given thousands of talks in my life, but the whole situation made me quite nervous. Would the Arduino board work? Would the quadricopter fly? What would Christopher do if it didn’t?

I don’t think my talk was particularly good. But then Christopher bounced onto the stage, and soon was typing raw Mathematica code in front of everyone—with me now safely off on the side (where I snapped this picture):

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