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After spending far too many late nights entering integration techniques as pattern-matching rules into Mathematica, I had the code at a reasonable state and I sent it to Wolfram Research for possible inclusion in Mathematica. Soon after, I was offered a job and ended up working for Wolfram for several years, predominantly on Wolfram|Alpha. My step-by-step integrator is still computing many integra
There’s a Computed Pokémon nearby! Here is a Poké Spikey. This will help you catch ’em all! In this blog post I will share with you several data insights about the viral social media phenomenon that is Pokémon GO. First I will get you familiarized with the original 151 Pokémon that have now invaded our real world, and then I’ll show you how to find the shortest tour to visit your nearby gyms. I fi
Note: There have been additional updates to Mathematica. Read about the updates in Version 11.1, Version 11.2 and Version 11.3 I’m thrilled today to announce the release of a major new version of Mathematica and the Wolfram Language: Version 11, available immediately for both desktop and cloud. Hundreds of us have been energetically working on building this for the past two years—and in fact I’ve
An idea, some initiative, and great resources allowed me to design and create the world’s first online syntax-free proof generator using induction, which recently went live on Wolfram|Alpha. Motivation It is no secret that Wolfram|Alpha is a well-used tool for math students, especially those taking first-year college and university math courses. In fact, one of the most common responses I receive
Announcing Wolfram Programming Lab January 19, 2016 I’m excited today to be able to announce the launch of Wolfram Programming Lab—an environment for anyone to learn programming and computational thinking through the Wolfram Language. You can run Wolfram Programming Lab through a web browser, as well as natively on desktop systems (Mac, Windows, Linux). I’ve long wanted to have a way to let anybod
Can computers learn to paint like Van Gogh? To some extent—definitely yes! For that, akin to human imitation artists, an algorithm should first be fed the original artists’ creations, and then it will be able to generate a machine take on them. How well? Please judge for yourself. Second prize in the ZEISS photography competition Recently the Department of Engineering at the University of Cambridg
In the Wolfram Language a little code can go a long way. And to use that fact to let everyone have some fun, today we’re introducing Tweet-a-Program. Compose a tweet-length Wolfram Language program, and tweet it to @WolframTaP. Our Twitter bot will run your program in the Wolfram Cloud and tweet back the result. One can do a lot with Wolfram Language programs that fit in a tweet. Like here’s a 78-
Launching Mathematica 10—with 700+ New Functions and a Crazy Amount of R&D July 9, 2014 We’ve got an incredible amount of new technology coming out this summer. Two weeks ago we launched Wolfram Programming Cloud. Today I’m pleased to announce the release of a major new version of Mathematica: Mathematica 10. We released Mathematica 1 just over 26 years ago—on June 23, 1988. And ever since we’ve b
Find out Etienne’s initial predictions by visiting last week’s World Cup blog post. The World Cup is half-way through: the group phase is over, and the knockout phase is beginning. Let’s update the winning probabilities for the remaining teams, and analyze how our classifier performed on the group-phase matches. From the 32 initial teams, 16 are qualified for the knockout phase: There have been so
Twenty-six years ago today we launched Mathematica 1.0. And I am excited that today we have what I think is another historic moment: the launch of Wolfram Programming Cloud—the first in a sequence of products based on the new Wolfram Language. My goal with the Wolfram Language in general—and Wolfram Programming Cloud in particular—is to redefine the process of programming, and to automate as much
Here at Wolfram Research and at Wolfram|Alpha we love mathematics and computations. Our favorite topics are algorithms, followed by formulas and equations. For instance, Mathematica can calculate millions of (more precisely, for all practical purposes, infinitely many) integrals, and Wolfram|Alpha knows hundreds of thousands of mathematical formulas (from Euler’s formula and BBP-type formulas for
Update: See our latest post on How the Wolfram Language Measures Up. I stumbled upon a nice project called Rosetta Code. Their stated aim is “to present solutions to the same task in as many different languages as possible, to demonstrate how languages are similar and different, and to aid a person with a grounding in one approach to a problem in learning another.” After amusing myself by contribu
When people tell me that Mathematica isn’t fast enough, I usually ask to see the offending code and often find that the problem isn’t a lack in Mathematica‘s performance, but sub-optimal use of Mathematica. I thought I would share the list of things that I look for first when trying to optimize Mathematica code. 1. Use floating-point numbers if you can, and use them early. Of the most common issue
When I first learned about π, I was told that a good approximation was 22/7. Even when I was 12 years old, I thought this was utterly pointless. 22/7 agrees with π to two decimal places (so three matching digits): Since there are three digits to remember in 22 and 7, what have you gained? You have just as much to remember, but have lost the notion that π is “just over 3”. Is there a better rationa
The Prize Is Won; The Simplest Universal Turing Machine Is Proved October 24, 2007 (Main prize page: The Wolfram 2,3 Turing Machine Research Prize) “And although it will no doubt be very difficult to prove, it seems likely that this Turing machine will in the end turn out to be universal.” So I wrote on page 709 of A New Kind of Science (NKS). I had searched the computational universe for the simp
The popularity of Twitter has really exploded in the past few months. The service poses a simple question: “What are you doing?” Users respond in 140 characters or less. The 140-character limit comes from the 160-character limit of SMS messages, minus a few characters for things like the user’s screen name. Twitter could probably best be described as “micro-blogging.” It’s kind of a cross between
The “Droste effect” is when images recursively include themselves. The name comes from Droste brand cocoa powder, which was sold in 1904 in a box that showed a nurse carrying the same box which, in turn, showed the nurse carrying the box, and so on. The simplest form is to use a scale and transform on an image to place an exact copy within it, and then repeat. Take a look at this Demonstration usi
Q: What do proteins, snowflakes, and these figures have in common? A: They’re all instances of “minimum inventory/maximum diversity” systems, a term coined by Peter Pearce in his book, Structure in Nature Is a Strategy for Design (MIT Press, 1978). A minimum inventory/maximum diversity system is a kit of modular parts and rules of assembly that gives you maximal design bang for your design-compone
Some might say that Mathematica and A New Kind of Science are ambitious projects. But in recent years I’ve been hard at work on a still more ambitious project—called Wolfram|Alpha. And I’m excited to say that in just two months it’s going to be going live: Mathematica has been a great success in very broadly handling all kinds of formal technical systems and knowledge. But what about everything el
On my way to becoming a graphics developer at Wolfram Research, I took detours through degrees in design and architecture. One of my enduring passions is exploring graphic design with programmatic and generative systems. While some aspects of design require the skilled hand of the designer, others can be formalized and explored by computer. For those tasks, Mathematica is an exceptional tool. As s
It’s been possible since Version 6 of Mathematica to embed images directly into lines of code, allowing such stupid code tricks as expanding a polynomial of plots. But is this really good for anything? As with many extremely nifty technologies, this feature of Mathematica had to wait a while before the killer app for it was discovered. And that killer app is image processing. Mathematica 7 adds a
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