Social processes and proofs of theorems and programs
Communications of the ACM
Mechanizing proof: computing, risk, and trust
Mechanizing proof: computing, risk, and trust
Weaving the Web: The Original Design and Ultimate Destiny of the World Wide Web by Its Inventor
Weaving the Web: The Original Design and Ultimate Destiny of the World Wide Web by Its Inventor
Automated Theory Formation in Pure Mathematics
Automated Theory Formation in Pure Mathematics
The Early Search for Tractable Ways of Reasoning about Programs
IEEE Annals of the History of Computing
Mathematical applications of inductive logic programming
Machine Learning
MATHsAiD: A Mathematical Theorem Discovery Tool
SYNASC '06 Proceedings of the Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Communications of the ACM - Organic user interfaces
Software Design for Empowering Scientists
IEEE Software
Handbook of Practical Logic and Automated Reasoning
Handbook of Practical Logic and Automated Reasoning
A Review of Mathematical Knowledge Management
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Automated theory formation in mathematics
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 2
Journal of Automated Reasoning
The polymath project: lessons from a successful online collaboration in mathematics
Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
Predicting the perceived quality of online mathematics contributions from users' reputations
Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
Automated theorem provers: a practical tool for the working mathematician?
Annals of Mathematics and Artificial Intelligence
Conjecture Synthesis for Inductive Theories
Journal of Automated Reasoning
Scheme-based theorem discovery and concept invention
Expert Systems with Applications: An International Journal
Reinventing Discovery: The New Era of Networked Science
Reinventing Discovery: The New Era of Networked Science
Provenance as dependency analysis
Mathematical Structures in Computer Science - Programming Language Interference and Dependence
Participation in an online mathematics community: differentiating motivations to add
Proceedings of the ACM 2012 conference on Computer Supported Cooperative Work
Editorial: Reasoning with Context in the Semantic Web
Web Semantics: Science, Services and Agents on the World Wide Web
Engineering mathematics: the odd order theorem proof
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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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 check proofs too long and complicated for humans to comprehend. The Study of Mathematical Practice is an emerging interdisciplinary field which draws on philosophy and social science 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 deduction and proof, in the production of mathematics, and have given us new ways to think about the 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.