Here at Wolfram Research and at Wolfram|Alpha we love mathematics and computations. Our favorite topics are algorithms, followed by formulas and equations. More »

Mathematics has many faces. It deals with diverse objects such as integers, points and lines, equations, graphs, categories, thousands of different spaces (from R³ to Hilbert, Banach, Fréchet, …), and so on. Mathematics can be constructive or just prove the existence of certain structures. Wolfram|Alpha has made a good fraction of computable constructive mathematics freely available to everyone: from line through (2,3) and (4, 5) to Fréchet derivative of (integrate exp(-f(x)^2) dx from -inf to inf) wrt f(y) to fractional derivative of ln(z). More »

A century ago, Srinivasa Ramanujan and G. H. Hardy started a famous correspondence about mathematics so amazing that Hardy described it as “scarcely possible to believe.” On May 1, 1913, Ramanujan was given a permanent position at the University of Cambridge. Five years and a day later, he became a Fellow of the Royal Society, then the most prestigious scientific group in the world. In 1919 Ramanujan was deathly ill while on a long ride back to India, from February 27 to March 13 on the steamship Nagoya. More »

Some common questions from the many student users of Wolfram|Alpha include “Isn’t cbrt(-8) = -2?” and “Why doesn’t the plot of the cube root include the negative part?” The answers are that -2 is just one of the three cube roots of -8, and that Mathematica, the computational engine of Wolfram|Alpha, has always chosen the principal root, which is complex valued. More generally, odd roots of negative numbers are typically assumed to be complex. You can see this in the output of (-8)^(1/3). More »

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. More »

I love dogs; they are the best. I find that they are suitable not only as companions, but as friends and confidants. That said, as much as I might anthropomorphize them, I do genuinely wish I could see the world in their eyes. Now, with Wolfram|Alpha, I can—and so can you. More »

My mother always loved gardening, and when I was growing up I enjoyed taking long strolls with her while she told me what all the different flowers were. She knew a lot about plants, but I remember sometimes asking her a question—like what was a plant’s taxonomic structure, or its optimal height compared to its average height—and she didn’t know what to say. Well, that’s why we’ve come up with the Wolfram Plants Reference App, available on iOS and PC. This app is for you, mom! More »

The 77th Masters Tournament begins today at Augusta National Golf Club. Many commentators think Tiger Woods is poised to score his fifth win (his last was in 2005), but strong challengers abound. More »

Now available on Android devices via the Google Play store, the Wolfram Algebra Course Assistant and Wolfram Calculus Course Assistant are part of the equation for academic success. More »

It’s tornado season in some parts of the United States, and while longtime users of Wolfram|Alpha are probably aware of our ability to analyze earthquake data, we weren’t able to say much about tornadoes. Now, utilizing data from from NOAA’s Storm Prediction Center, Wolfram|Alpha can answer questions about tornado activity in the US from 1950 to 2012. For good measure, we’ve also added data on worldwide volcanic eruptions to our knowledge base. More »

Today, we’re proud to unveil the Wolfram|Alpha Handwritten Knowledge Engine, a new, more personal way of delivering computed answers.

You might be wondering where this idea came from. Well, let me tell you a story.

We had a thought not long ago that it would be nice to get you (the internet) a gift. One of those “just because” things to spread a bit of happiness around the world.

Conventional wisdom holds that the best gifts are handmade. But making gifts by hand for over 2.2 billion people? It was a daunting challenge. Luckily, we had a head start: Wolfram|Alpha already computes its answers just for you. The answer to every query, question, and computation is custom-generated, drawing upon trillions of pieces of built-in knowledge.

We began to imagine ways to add that handmade, personal flair to Wolfram|Alpha results. Artisanal answers, if you will. We narrowed it down to “putting a bird on it” versus a handwritten interface, results pages and all. Handwriting won the coin toss.

You remember handwriting, right? The thing you used to do with a pen, to write letters and checks? Checks, well, they were these pieces of paper that represented… you know what, I should get back to the story.

We knew we’d need a goodly number of contributors, as well as some sort of training component—consistency is important, after all. Human Resources began recruiting in earnest (by the way, we’re hiring), as well as organizing a Corporate Penmanship Retreat.

That brings us to now. The retreat just wrapped, and the Wolfram|Alpha Handwritten Knowledge Engine is ready to go. Ask a question, and your machine-computed results will be transcribed and illustrated by a real live human being.

I recommend acting fast. A few of the physicists already have writer’s cramp, and the pop culture researchers might be next.

So what will you compute? I definitely cannot recommend running your homework through Wolfram|Alpha, printing out the handwritten results, and trying to pass them as your own. Definitely not. But here are some other ideas to get you going.

Go meta, and get handwritten knowledge about the word handwriting:

Find derivatives… with style:

Put your mind at ease with a handwritten verification of some important information:

Why not Zoidberg?

We hope you enjoy the Wolfram|Alpha Handwritten Knowledge Engine. Please share your favorites in the comments.

April 2, 2013 Update: We hope you enjoyed the handwritten Wolfram|Alpha results on April Fools’ Day. While some staff are recovering from carpal tunnel, we have returned to the normal styling for all results.

If you want to see the handwritten results, begin any query with “handwritten style” (without quotes), and our staff will get back to work!

Many of us are familiar with motion in a straight line: you speed up and move faster, you travel forward and end up someplace new. But there is another type of motion: angular motion, or the motion in a circular path. These are the kinematics of a merry-go-round, a spinning top, or the orbit and rotation of the Earth. More »

It’s that time of year again! Time to apply for the Mathematica Summer Camp 2013! The camp is being held at Bentley University in Waltham, Massachusetts, July 7–19. Students will have the opportunity to learn Mathematica’s computing language, work with Wolfram mentors, and interact with other students with similar interests. By the end of camp, each student will have created his or her very own Mathematica program! More »

I’m not a doctor, but for the purpose of this blog post, please imagine that I am wearing a lab coat and a stethoscope—maybe even two stethoscopes, just to be extra professional. Wolfram|Alpha now has an understanding of sig codes, which are the marks on your drug prescriptions that tell the pharmacist what it is you’re getting, what it does, and when precisely it should be taken. Patients aren’t often exposed to sig codes these days, but pharmacy techs learn them, since they receive these abbreviated instructions from the doctor. More »

Throughout the history of physics, scientists have postulated laws and theories about the nature of the world around them. Some were proven false, while others have grown to be the basis of entire fields of study. One such field is classical mechanics, which describes the area of physics most familiar to us, that of the motion of macroscopic objects, from baseballs to planets and traveling along hills to falling from space. As one of the oldest subjects in science, the work here serves as a basis for less familiar areas such as relativity and quantum mechanics. More »

Today is National Tooth Fairy Day, a day where we can be reminded to take good care of our teeth, and in the event we’re young and some fall out, to put them under our pillows for magic money. I once heard that the source of this magic money is from some sort of self-described guardian, but I’ve never actually met him or her. More »

Superlatives, like hyperbole, are my favorite thing. So it is with the greatest excitement that I am devoting this blog post to superlatives and range searching, as Wolfram|Alpha has again expanded its functionality in these areas.

I once heard from an actor pretending to be a scientist that the denser an element is, the better that element is for fighting terrible monsters. I cannot speak on the accuracy of that statement, as I am not an actor pretending to be a scientist, but if you wanted to apply superlatives to chemistry, Wolfram|Alpha can do that. More »

Years ago when I was young,
there was something I wanted to know:
“Could math ever be super popular,
or has it begun to plateau?”

Although being “smart” and quite “witty,”
I never could figure math out.
Its numbers were letters, its letters were prime,
I wanted to stand up and shout. More »

In our previous post about expanding step-by-step solutions, we introduced a revamped equation solver. I’m proud to say that it has now been extended to solve systems of linear equations. In addition, you have four different methods to choose from when looking for a solution! These methods are elimination, substitution, Gaussian elimination, and Cramer’s rule. Let’s look at x + y = 5, x – y = 1 to see all four methods in action. More »

I just got a flat tire and I need to replace it with a new one. What size tire do I need to get? This can be a tricky question, and many of us would just take our cars into a dealership or repair shop and let them deal with it. But it’s not as hard as you might think, and now Wolfram|Alpha provides tools to help you understand tire sizes. More »

This Sunday, the Baltimore Ravens and the San Francisco 49ers are going to play against each other in Super Bowl XLVII, which takes place in New Orleans. So what do we know about the teams and their histories, and what can we determine from their statistics this season? More »

Tools are a natural extension of our mastery of physics. By putting our knowledge to use, we are able to manipulate the world around us on a much larger scale. Tools and machines have allowed us to build great monuments, to settle otherwise inhospitable locations, and to launch ourselves into space. More »

As a continuation of our new math content blog series, I’d like to talk about an exciting new step-by-step feature. Previously I talked about differential equations, but today I’d like to look toward the other end of the spectrum: basic arithmetic. Wolfram|Alpha can now help you work out long addition, subtraction, multiplication, and division with hints and steps! Let’s go ahead and look at some examples. More »

Football, basketball, and baseball have two common elements. The first, each sport is the “best” depending on which one I’m watching at a given moment. The second, each sport’s raw data can now be computed and juxtaposed in Wolfram|Alpha, which means arguments over statistics, histories, and comparisons will be better than ever before. More »

Today we’re excited to announce the first upgrade to Wolfram|Alpha’s Personal Analytics for Facebook. There’s much more to analyze, see, and do—here’s a quick look! More »

Wolfram|Alpha has released a suite of apps that cover all of your financial needs. The apps are profoundly powerful tools, allowing you to stay informed about your business’s finances and the marketplace at large while in the office or on the go. More »

The Wolfram|Alpha math team adds new and exciting content to Wolfram|Alpha on a daily basis! In fact, over the past few months we’ve added a wide range of features and we will be introducing them in a blog series here. Lately, we’ve made an effort to make Wolfram|Alpha a powerful learning tool for those learning arithmetic! If you are either teaching or learning addition, multiplication, or basic math word problems, Wolfram|Alpha can help you. More »

When I was younger, I held the naive and incorrect view that mathematics was divorced from the arts. As I’ve gotten older, I’ve become more aware of not only how mathematics is the foundation for any of the hard sciences, but also how it is intrinsically linked to essentially any form of creativity. Certainly users of our Wolfram Music Theory Course Assistant could have told me that, but I’m not just referring to music. In truth, I’m not even trying to make some highbrow appeal to abstract art, either, although I happen to rather like that sort of thing. What I’m trying to say is that mathematical equations can make pretty pictures.

More »