# LFCS Lab Lunch by Ursula Martin

How I started thinking about computer proof a completely different way (and fell into social machines along the way)

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers, using programs designed to verify hardware, check proofs that are just too long and complicated for any human to comprehend.

Mathematical practice is an emerging interdisciplinary field which draws on philosophy, social science and ethnography, to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question answering system *mathoverflow* contains around 40,000 mathematical conversations, and *polymath* collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of "soft" aspects such as analogy and creativity, alongside formal deduction, in the production of mathematics, and have given us new ways to think about the possible complementary roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal.

Crowdsourced mathematical activity is an example of a "social machine", a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.