Semantic Representation of Mathematical Knowledge Workshop: Capturing Knowledge from the Literature of Mathematics for Today's and Tomorrow's Mathematicians and Designing a Human- and Computer-Readable Language for Representing Pure and Applied Mathematics

The Semantic Representation of Mathematical Knowledge Workshop was held at the Fields Institute in Toronto on February 3–5, 2016. This invitation-only workshop was designed to lay out principles for a semantic capture language of mathematics and was funded through a grant from the Sloan Foundation.

Objectives

In particular, the workshop aimed to pool the knowledge and experience of a group of experts in order to produce agreement on design principles to lead the way toward an implementation of a semantic capture language applicable to all of mathematics. Such an encoding would allow the realization of the "Math Heritage Project," a uniform, expandable mathematical knowledge base that will preserve and disseminate the entire literature of mathematics for the benefit of today's and tomorrow's mathematicians.

White paper

PDF

Videos

• Interviews and Highlights from the Workshop
• Excerpts from the Documentary "Towards a Semantic Language of Mathematics"

Project Materials

Some documents of interest and possible discussion at the workshop have been extracted from the original Sloan proposal and are available for download below:

• Appendix E: Some challenges of a human- and computer-readable semantic representation of mathematics
• Appendix F: Examples of existing semantic representations of mathematics
• Appendix G: Some questions concerning the representation of theorems
• Appendix H: Developments relevant for building a semantic collection of mathematical theorems
• Appendix K: Bibliography

Additional collected theorems from the literature illustrating the breadth and diversity (but at the same time, unity in style) of published mathematical results across many fields:

• Theorem Examples: Additional theorem examples from the literature

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eCF: Encoding Continued Fraction Knowledge in Computational Form

The eCF project created a novel type of digital mathematics library by semantically encoding known results about continued fractions and marking up these results to make them easy to find, retrieve and use. Building on the infrastructure developed for Wolfram|Alpha, the eCF project encoded results and identities involving continued fractions using an entity-property framework, and exposed them using a powerful natural language interface.

Objectives

The overall goal of the eCF project was to prototype potential features of a mathematical digital library, with the additional goal of increasing the accessibility of a chosen segment of mathematical knowledge: the theory of continued fractions.

This project was carried out from March 2012 to September 2013.

Project Materials

The project materials linked above were developed with the support of a grant from the Sloan Foundation. As such, the data they contain may be used without restriction for the public good. Please inform us of any reuse of this material (so we may be made aware of any further applications) and use the citation described below:

Continued fraction data/citations/results/etc. from: The Wolfram Foundation. "eCF: Encoding Continued Fraction Knowledge in Computational Form." 2012–2013. https://www.wolframfoundation.org/programs/computable-archive-of-mathematics.html

Links to individual results as presented on Wolfram|Alpha are also welcome, with recommended citation practices as discussed on https://www.wolframalpha.com/faqs6.html.

Related Coverage

• Computational Knowledge of Continued Fractions, by M. Trott, E. W. Weisstein
• After 100 Years, Ramanujan Gap Filled, by O. Marichev, M. Trott

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