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.