WP7: Social Aspects
Lead Institution: University of Oxford
The processes by which mathematical knowledge and mathematical software are developed, validated and applied are quite distinctive. In other sciences, the universe provides “ground truth” and the scientific texts or theories can be validated against that by experiment. In mathematics the text itself is the ground truth. The traditional model of mathematical research is a mathematician, or a small group of mathematicians, standing around a blackboard, producing a proof they would “clean up”: remove all traces of the process that led to its discovery and then submit the “clean” text to their peers for review. Mathematicians have adopted new technology in a variety of ways: email and shared documents are used to collaborate on problem-solving and writing; larger “crowdsourcing” [33, 38], arrangements pull together diverse experts; symbolic computation tackles huge routine calculations; and computers check proofs that are too long and complicated for a human to comprehend. These technologies reveal (since email messages, version control systems and bulletin boards can be analysed) and alter the ways in which mathematicians collaborate. In an EPSRC funded project “The Social Machine of Mathematics” Martin and others are bringing together rigorous methods from the social sciences to study these collaborative processes. Combining this research with the algorithmic game theory expertise of Elkind and Pasechnik, in this work package we intend to pursue the following objectives: • incorporate the insights from this and similar projects into the design of OpenDreamKit VRE, ensuring that it supports the ways in which mathematicians really work, rather than the way software developers—or indeed mathematicians—think they do; • extend this work to study the collaborative processes of free open source (mathematical) software development so as to produce guidelines for best practice as well as to develop ideas for extending existing processes to a “system of systems”.
“Crowdsourcing”—fine-grained collaborative development of ideas, proofs or software—is a common theme to both objectives. The purpose of a VRE is to allow effective crowdsourcing of computationally supported mathematical results (theorems, proofs, etc.), while free software development is inherently a collaborative process, and we wish to study the best ways of allowing it to scale. In a sense, mathematics has been a crowdsourced endeavour, dating as far back as the foundation of the Royal Society (UK) in the seventeenth century. The first scientific journals were published collections of letters received, posing questions and observations and offering solutions. Although limited by the speed of physical post, this model had much in common with the public email lists that underpinned collaborative software development in the 1990s. In recent years, the internet and critical tools such as distributed version control have supported much more widespread and finer-grained forms of crowdsourcing, first in software development, and, more recently, in mathematics: examples are provided by online mathematics communities, such as Math-overflow  and Polymath Projects [33, 38]. Supporting and encouraging “Mutual crowdsourcing” is the main driving force for developing and maintaining any large-scale open-source virtual research environment. In this work package we will build on the work of Prof. Martin and her collaborators on the EPSRC project, and, in particular, their study of crowdsourcing, and integrate their findings with tools provided by the burgeoning field of algorithmic mechanism design in order to to optimise crowdsourcing workflows in open-source VREs.
See page 56 of the proposal for the full description.