In 2011, when I applied to my current position as Swiss National Science Foundation Assistant Professor, I included an Annex to the proposal, titled Making data useful for mathematical collaboratories and the example of the LMFDB project.
A collaboratory  is an organizational entity that spans distance, supports rich and recurring human interaction oriented to a common research area, and fosters contact between researchers who are both known and unknown to each other, and provides access to data sources, artifacts, and tools required to accomplish research tasks.
—Science of Collaboratories, SNF survey 2007
Already then, I highlighted a significant evolution in mentalities since a reference SNF survey of 2007. This trend was explained by Michael Nielsen in a TED talk at around the same time, also taking mathematics as basis for many of his examples.
In the Annex, I make a distinction between horizontal and vertical projects. Horizontal projects are more infrastructure-like, with a wider mathematical audience, essentially the whole pure mathematical community.
I would expect this difficulty in integrating new data to be the main cause of the lack of mathematical collaboratories. As such, it should be solved as a horizontal rather than vertical problem. From now on, I only discuss this problem, i.e. the creation of a flexible and coherent mathematical database starting from heterogenous data.
Pushed to the extreme, one could see this problem as integrating all compiled knowledge in mathematics, echoing a description by Voevodsky.
This was based around my experience for a few years with the LMFDB project, which is aimed at integrating lots of mathematical data in the general area of L-functions (two of the Clay Millenium problems are in this area, the Riemann Hypothesis and the Birch and Swinnerton-Dyer conjecture).
One interesting aspect of this annex is that it was, well, an annex. I knew including this as part of my main project could actually be hurtful and judged distracting to my main research proposal, since many of the ideas of Science 2.0 had not taken hold yet. Indeed, the Annex comes with a big disclaimer:
I have also described my more personal project, which is concerned with the integration of mathematical data for collaboratories. While I do not consider this project a mathematical project, I think it could be of great value to research in mathematics in general. I intend on pursuing it on the side as a service to the community, just as paper refereeing, outreach, CAS development, etc. I am only mentioning it here because of its (presumed) originality and wide audience.
One year later, I coorganised a workshop at Edinburgh. The topic was Online databases: from L-functions to combinatorics, and it was meant to start unifying two separate areas in this horizontal problem.
|||A portmanteau of collaboration and laboratory.|