With support from the Sloan Foundation, the Wolfram Foundation proposes to create, collect and curate a new type of digital library and archive for mathematical data that will both ensure the preservation and promote the dissemination of mathematical knowledge for the public good.

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.

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.

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

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

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.

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.

Download and read the October 2013 report Mathematica notebook format PDF

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. http://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.

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