Networked Mathematics

Organizing mathematics into a coherent, searchable whole.

Information overload affects mathematics too. A striking example comes from an episode reported by Quanta Magazine in November 2019. A group of physicists discovered a useful mathematical identity, and did not know if it was novel. To check, they emailed a number of mathematicians, including Fields Medallist Terence Tao. Despite believing the result was “so short and simple – it should have been in textbooks already”, Tao had not previously heard of it. This led to a paper submitted for publication and, soon after, the article in Quanta. In the weeks after the story emerged, more than three dozen previously published instances of the result were reported, dating back to 1934. 

How can it be so hard for even experts to find widely published, basic results?

The ramifications of this are significant: wasted search time, duplication of research, and missed connections between researchers. Scientists spend 23% of their time searching the literature; the figure is likely similar for mathematicians. Very often, this search does not bear fruit. For example, a recent paper in the Applied Category Theory 2020 conference counts nine different introductions of the concept of a cartesian monoid, most in well-established literature. The result is that many ideas have to be rediscovered over and over, and opportunities for collaboration between different researchers and subfields are missed.

To solve this problem, we build MathFoldr, a search tool for mathematics. MathFoldr leverages both statistical, similarity-based methods from natural language processing and logical, semantic methods from proof assistants to integrate mathematical knowledge into a coherent, searchable whole.

Research Lead: Valeria de Paiva