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The Semantic Representation of Pure Mathematics

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.
Eric Weisstein, Senior Researcher, Wolfram|Alpha Scientific Content Ian Ford, Pure Math Developer, Wolfram|Alpha Scientific Content
Computation & Analysis

Protecting NHS Patients with the Wolfram Language

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?"
Robert Cook, European Sales
Computation & Analysis

Edit Your NaNoWriMo Novel with the Wolfram Language

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.
Zach Littrell, Technical Content Writer, Technical Communications and Strategy Group John Moore, Marketing and Technical Content Team Lead, Technical Communications & Strategy Group
Computation & Analysis

New in the Wolfram Language: FeatureExtraction

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:
Etienne Bernard, Lead Architect, Machine Learning
Announcements & Events

Launching Wolfram Player for iOS

UPDATE:

Wolfram Player for iOS is out of beta! You can download it from the App Store today. Learn more in this blog post. 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.
John Fultz, Director of User Interface Technology
Announcements & Events

Announcing Wolfram Enterprise Private Cloud

Today I'm pleased to announce Wolfram Enterprise Private Cloud (EPC), which takes the unique benefits of the Wolfram technology stack---ultimate computation, integrated language and deployment---and makes them available in a centralized, private, secure enterprise solution. In essence, EPC enables you to put computation at the heart of your infrastructure and in turn deliver a complete enterprise computation solution for your organization.
Conrad Wolfram
Education & Academic

How to Teach Computational Thinking

The Computational Future Computational thinking is going to be a defining feature of the future—and it’s an incredibly important thing to be teaching to kids today. There’s always lots of discussion (and concern) about how to teach traditional mathematical thinking to kids. But looking to the future, this pales in comparison to the importance of […]

Stephen Wolfram
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