I work on geometric computation and graphics in Mathematica, and for Mathematica 6 I was responsible for our new surface-drawing capabilities. When I talk about my work at university mathematics departments, I am often told that I just have to see what the department has tucked away in some corner of its building: plaster casts of intriguing mathematical surfaces, created in the early part of the twentieth century to illustrate the achievements of the field of differential geometry.

It’s been very difficult even to reproduce those plaster casts, let alone to go beyond them—each one represents a sophisticated combination of symbolic mathematics, numerics, and geometry. But with Mathematica, we now have just the combination of capabilities that are needed. And I always find it fun to reproduce those plaster-cast surfaces—often with single lines of Mathematica code, usually centered on the function ParametricPlot3D. With 3D printing, I’ve even been able to make my own physical versions of lots of these surfaces.

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A year ago, we highlighted some of our work for the CBS-Paramount TV series NUMB3RS. In September 2007, we wrote about our enhanced involvement and our launch of The Math behind NUMB3RS. The site presents math highlights and activities for every episode, starting with Season 4.

Tonight on CBS, Season 4 reaches a conclusion with the 78th episode—When Worlds Collide—and we’ve got our write-up for it available for your perusal. What happens when the worlds of science and government disagree? History provides numerous examples of this timeless subject. Italy, 212 BC: Archimedes wouldn’t leave his diagrams fast enough for a soldier’s liking and was killed. Spain, 1808: Arago was imprisoned as a spy while measuring the shape of the Earth. Poland, 1939: Kuratowski taught math at an illegal underground university. Tonight’s episode gives a modern version of the clash between state and science.

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The Wolfram Functions Site—which just tripled in size—has a rich story. I have spent most of my career deriving integrals and formulas about mathematical functions. When I lived in the Soviet Union, I co-wrote some of the largest books of formulas ever, which contained altogether about 5000 pages and a total of about 30,000 formulas, and have been reprinted in several languages.
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You’ve probably seen examples of photo mosaics where each “tile” in the mosaic is a tiny photograph, selected so the overall brightness and color of the tiny photo averages out to the brightness and color needed for its position in the overall mosaic.

Following a suggestion by Ed Pegg, I suddenly found it impossible to imagine life without a photo mosaic of Dmitri Mendeleev, the principal inventor of the periodic table, made out of photographs of the elements.

It was convenient in this regard that I possess the world’s largest stock library of photographs of the chemical elements—about 2000 photographs of roughly 1550 different physical samples of the pure and applied elements—along with a photograph of Mendeleev and a bit of software called Mathematica. (You can see this library at periodictable.com; don’t forget to order a copy of my photo periodic table poster.)

You might think that creating photo mosaics is a standard task for which software, probably even free software, is available. And for all I know it is. But upon brief reflection I decided it would probably be faster and easier for me to write code to do this from scratch in Mathematica than it would be to find something to download and then figure out how to use it.

It turns out you can do a first pass at it with three lines of input.
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In Mathematica, a core principle is that everything should be scalable. So in my job of creating algorithms for Mathematica I have to make sure that everything I produce is scalable.

Last week I decided to test this on one particular example. The problem I chose happens to be a classic. In fact, the very first nontrivial computer program ever written—by Ada Lovelace in 1842—was solving the same problem.

The problem is to compute Bernoulli numbers.

Bernoulli numbers have a long history, dating back at least to Jakob Bernoulli’s 1713 Ars Conjectandi.
Bernoulli’s specific problem was to find formulas for sums like .
Before Bernoulli, people had just made tables of results for specific n and m. But in a Mathematica-like way, Bernoulli pointed out that there was an algorithm that could automate this.
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A few days ago we built the millionth version of our software products. For the outside world, we recently shipped Mathematica 6.0.2. But internally we’ve now built a million versions of Mathematica and our other products.

I’ve been at Wolfram Research for 17 years, and for the past 13 years I’ve been responsible for our automated product build systems. Every night (and sometimes during the day) a large cluster of computers builds new versions of every product we make.

Building a single Mathematica is a complex process, involving a host of different computer languages and systems, and a final Mathematica contains more than 10,000 separate files.
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On Sunday, April 13, 2008, John Wheeler passed away at the age of 96.

He was a central figure in twentieth-century physics, in the middle of it all, working on the H-bomb and studying black holes. His legacy in physics is continued in his influence on a vast number of students, and their students in turn.

His contributions were many. Some have found their way into Demonstrations:

Gravitation versus Curved Spacetime

Zonohedron Turned Inside Out

Particle Moving around Two Extreme Black Holes

Schwarzschild Space-Time Embedding Diagram

But I want to mention his role in the history of computation in science. In a sense, he is a spiritual grandfather of NKS and of Mathematica.
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Have you ever created a Mathematica notebook (a .nb file) and sent it to a colleague who doesn’t yet have Mathematica? In the past, you’d have to explain about downloading Mathematica Player. This isn’t difficult, but it is an extra step. Wouldn’t it be better if it “just worked”?

Well now, on Windows, it does.

Thanks to our longstanding relationship with Microsoft, the .nb file format is now officially part of the automatic Windows File Association system. So, whenever any Windows computer with no Wolfram software gets a Mathematica notebook, the operating system automatically takes you to a download link for Mathematica Player. This is also the case for the published notebook files (.nbp) that have been prepared specifically for interactive use in Player.

Only the most widespread and useful formats are included in the Windows File Association system, and we’re happy that Microsoft has now extended the system to include the .nb and .nbp formats. It’s a nice reflection of the growing acceptance of these formats as the standard for interactive documents.

On The Wolfram Demonstrations Project we automatically point people to Mathematica Player if they need to download it. But if you post a notebook to a site outside of our domain or if you send a notebook in email, we can’t provide automatic, convenient access to Player for others to be able to view it. With .nb and .nbp included in the Windows File Search system, we don’t have to.

Now, anyone can use .nb and .nbp files and have confidence that anyone else will be able to read them. It’s another small step in making Mathematica notebooks—and Mathematica—more ubiquitous.

I would like to point to a recent member of The Wolfram Demonstrations Project: Numerical Methods for Differential Equations.

It was submitted a few weeks ago, and I rather liked it because it illustrated several basic numerical approaches to solving a first-order differential equation. Without much fuss this quickly brings one into numerical analysis, approximation methods, and other polysyllabic topics important to engineering, math, and related fields.

As it was making the rounds through our review process, I received one of those phone calls that parents know all too well: the college student emergency homework appeal. I picked up the phone.
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Reading Theo’s blog post about his website reminded me that our excitement about the grand projects that get done in Mathematica often make us forget to talk about all the exciting little things that Mathematica makes possible too.

It would be easy to think that Mathematica is only suitable for website production if you have something on the grand scale and high traffic of periodictable.com. So I wanted to write about using Mathematica to make a website that is anything but grand and far from popular… my own.

My pages are just an attempt to put my footprint on Google so that I can be found. It mostly consists of a few basic pages about me and my work with Mathematica.

So what advantage did I get out of doing it in Mathematica?

Well the first was pretty basic personal practicality—why learn new tools if you don’t have to? I know Mathematica, and I knew it would be faster for me to create it in Mathematica than to find and learn how to use other content management and authoring tools.

Once I had coded up a page template in the symbolic XML features of Mathematica, I could create any new page by applying that function to the page content text. The whole lot is automatically written out as HTML and uploaded to the server by Mathematica.

But the one unusual part of the content is ONLY practical with Mathematica. My work with Mathematica takes me to a lot of places—giving talks about it, meeting business and technology partners and all kinds of users. I also travel for fun. I wanted to make a definitive list of places that I have been to and to present that visually.

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