The Semantic Representation of Pure Mathematics
December 22, 2016
Eric Weisstein, Senior Researcher, Wolfram|Alpha Scientific Content
Ian Ford, Pure Math Developer, Wolfram|Alpha Scientific Content
Introduction
Building on thirty years of research, development and use throughout the world, Mathematica and the Wolfram Language continue to be both designed for the long term and extremely successful in doing computational mathematics. The nearly 6,000 symbols built into the Wolfram Language as of 2016 allow a huge variety of computational objects to be represented and manipulated—from special functions to graphics to geometric regions. In addition, the Wolfram Knowledgebase and its associated entity framework allow hundreds of concrete “things” (e.g. people, cities, foods and planets) to be expressed, manipulated and computed with.
Despite a rapidly and ever-increasing number of domains known to the Wolfram Language, many knowledge domains still await computational representation. In his blog “Computational Knowledge and the Future of Pure Mathematics,” Stephen Wolfram presented a grand vision for the representation of abstract mathematics, known variously as the Computable Archive of Mathematics or Mathematics Heritage Project (MHP). The eventual goal of this project is no less than to render all of the approximately 100 million pages of peer-reviewed research mathematics published over the last several centuries into a computer-readable form.
In today’s blog, we give a glimpse into the future of that vision based on two projects involving the semantic representation of abstract mathematics. By way of further background and motivation for this work, we first briefly discuss an international workshop dedicated to the semantic representation of mathematical knowledge, which took place earlier this year. Next, we present our work on representing the abstract mathematical concepts of function spaces and topological spaces. Finally, we showcase some experimental work on representing the concepts and theorems of general topology in the Wolfram Language.
Protecting NHS Patients with the Wolfram Language
December 16, 2016 — Robert Cook, Senior Consultant, Wolfram Technical Services
The UK’s National Health Service (NHS) is in crisis. With a current budget of just over £100 billion, the NHS predicts a £30 billion funding gap by 2020 or 2021 unless there is radical action. A key part of this is addressing how the NHS can predict and prevent harm well in advance and deliver a “digital healthcare transformation” to their frontline services, utilizing vast quantities of data to make informed and insightful decisions.
This is where Wolfram comes in. Our UK-based Technical Services Team worked with the British NHS to help solve a specific problem facing the NHS—one many organizations will recognize: data sitting in siloed databases, with limited analysis algorithms on offer. They wanted to see if it was possible to pull together multiple data sources, combining off-the-shelf clinical databases with the hospital trusts’ bespoke offerings and mine them for signals. We set out to help them answer questions like “Can the number of slips, trips and falls in hospitals be reduced?”
Launching Wolfram|Alpha Open Code
December 12, 2016 — Stephen Wolfram
Code for Everyone
Computational thinking needs to be an integral part of modern education—and today I’m excited to be able to launch another contribution to this goal: Wolfram|Alpha Open Code.
Every day, millions of students around the world use Wolfram|Alpha to compute answers. With Wolfram|Alpha Open Code they’ll now not just be able to get answers, but also be able to get code that lets them explore further and immediately apply computational thinking.
Edit Your NaNoWriMo Novel with the Wolfram Language
December 9, 2016
Zach Littrell, Technical Content Writer, Technical Communications and Strategy Group
John Moore, Wolfram Blog Team
If you’re like many of us at Wolfram, you probably know that November was National Novel Writing Month (NaNoWriMo). Maybe you even spent the past few weeks feverishly writing, pounding out that coming-of-age story about a lonely space dragon that you’ve been talking about for years.
Congratulations! Now what? Revisions, of course! And we, the kindly Wolfram Blog Team, are here to get you through your revisions with a little help from the Wolfram Language.
Computational Thinking beyond Computer Science Education Week
December 5, 2016 — Alyson Gamble, Wolfram Blog Team
Whatever their future fields, students need to learn computational thinking, a method of problem solving in which questions are framed in a way that can be communicated to a computer.
New in the Wolfram Language: FeatureExtraction
December 2, 2016 — Etienne Bernard, Lead Architect, Advanced Research Group
Two years ago, we introduced the first high-level machine learning functions of the Wolfram Language, Classify and Predict. Since then, we have been creating a set of automatic machine learning functionalities (ClusterClassify, DimensionReduction, etc.). Today, I am happy to present a new function called FeatureExtraction that deals with another important machine learning task: extracting features from data. Unlike Classify and Predict, which follow the supervised learning paradigm, FeatureExtraction belongs to the unsupervised learning paradigm, meaning that the data to learn from is given as a set of unlabeled examples (i.e. without an input -> output relation). The main goal of FeatureExtraction is to transform these examples into numeric vectors (often called feature vectors). For example, let’s apply FeatureExtraction to a simple dataset:
![fe = FeatureExtraction[{{1.4, "A"}, {1.5, "A"}, {2.3, "B"}, {5.4, "B"}}]](http://blog.wolfram.com/data/uploads/2016/12/FeatureExtraction_InOut1.png "fe = FeatureExtraction[{{1.4, \"A\"}, {1.5, \"A\"}, {2.3, \"B\"}, {5.4, \"B\"}}]")
Making Wikipedia Knowledge Visible
November 23, 2016 — John Moore, Wolfram Blog Team
Over the past few months, Wolfram Community members have been exploring ways of visualizing the known universe of Wikipedia knowledge. From Bob Dylan’s networks to the persistence of “philosophy” as a category, Wolfram Community has been asking: “What does knowledge actually look like in the digital age?”
Launching Wolfram Player for iOS
November 16, 2016 — John Fultz, Director of User Interface Technology
It’s been a long road.
To some degree, we’ve been working on a Wolfram notebook front end for iOS for about six years now. And in the process, we’ve learned a lot about notebook front ends, a thing we already knew a lot about. Let’s rewind the tape a bit and review.
Celebrating Gottfried Leibniz on the 300th Anniversary of His Death
November 14, 2016 — Kathryn Cramer, Technical Communications and Strategy Group
Today is the 300th anniversary of the death of Gottfried Leibniz, a man whose work has had a deep influence on what we do here at Wolfram Research. He was born July 1, 1646, in Leipzig, and died November 14, 1716, in Hanover, which was, at the time, part of the Holy Roman Empire. I associate his name most strongly with my time learning calculus, which he invented in parallel with Isaac Newton. But Leibniz was a polymath, and his ideas and influence were much broader than that. He invented binary numbers, the integral sign and an early form of mechanical calculator.
The 2016 Wolfram One-Liner Competition Winners
November 9, 2016 — Christopher Carlson, Senior User Interface Developer, User Interfaces
Could you fit the code for a fully functional game of Pong into a single tweet? One that gives you more points the more you take your chances in letting the “ball” escape? Philip Maymin did, and took first prize with that submission in the One-Liner Competition held at this year’s Wolfram Technology Conference.
Participants in the competition submit 128 or fewer tweetable characters of Wolfram Language code to perform the most impressive computation they can dream up. We had a bumper crop of entries this year that showed the surprising power of the Wolfram Language. You might think that after decades of experience creating and developing with the Wolfram Language, we at Wolfram Research would have seen and thought of it all. But every year our conference attendees surprise us. Read on to see the amazing effects you can achieve with a tweet of Wolfram Language code.
Honorable Mention
Amy Friedman: “The Song Titles” (110 characters)
