MathSoMac: the social machine of mathematics

数学是一项深刻的智力成就，对商业和社会的各个方面都有影响。几个世纪以来，数学的最高水平一直被视为一种孤立的创造性活动，以产生供研究同行审查和接受的证明。数学现在正处于一个非凡的转折点，新技术从根本上扩展了个人的力量和极限。“众包”将不同的专家聚集在一起解决问题;符号计算处理大量的日常计算;而计算机则使用专门设计用于验证硬件的程序来检查证明，这些证明太长太复杂，任何人都无法理解。然而，这些技术目前都是以独立的方式使用的，缺乏相互整合，也缺乏与人类创造力或易出错性的整合。社会机器是伯纳斯-李（Berners-Lee）提出的新范式，将人和计算机的组合视为一个解决问题的实体。我们的长期愿景是改变数学，通过创建一个数学社会机器来改变数学研究的范围，速度和影响：一个人，计算机和档案的组合来创建和应用数学。因此，例如，想要设计具有特定属性的网络的行业研究人员可以快速获得各种研究技能和研究;探索假设;讨论可能的解决方案;获得所需水平的正确性，并创造新的数学，个人的努力可能永远无法想象或验证。在“引擎盖之下”的无缝集成可能是不同的人和机器、正式和非正式的方法、旧的和新的数学、实验和证明的混合体。实现这一愿景的障碍是：（i）我们对人和机器的数学生产没有高水平的理解，（二）不同的研究方法之间没有共同的观点，搜索和用户社区是什么，可能是可能的或可行的奖学金的结果将是一个数学社会机器的新愿景，改变数学的范围，速度和影响。它将提供：分析和实验，以了解数学作为社会机器的当前和未来生产;设计和原型;学术和行业利益相关者的所有权;交付下一代社会机器的路线图;以及准备将其变为现实的国际团队。

Mathematics is a profound intellectual achievement with impact on all aspects of business and society.For centuries, the highest level of mathematics has been seen as an isolated creative activity, 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 that are just too long and complicated for any human to comprehend, using programs designed to verify hardware.Yet these techniques are currently used in stand-alone fashion, lacking integration with each other or with human creativity or fallibility.Social machines are new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity. Our long-term vision is to change mathematics, transforming the reach, pace, and impact of mathematics research, through creating a mathematics social machine: a combination of people, computers, and archives to create and apply mathematics.Thus, for example, an industry researcher wanting to design a network with specific properties could quickly access diverse research skills and research; explore hypotheses; discuss possible solutions; obtain surety of correctness to a desired level; and create new mathematics that individual effort might never imagine or verify. Seamlessly integrated "under the hood" might be a mixture of diverse people and machines, formal and informal approaches, old and new mathematics, experiment and proof.The obstacles to realising the vision are that(i) We do not have a high level understanding of the production of mathematics by people and machines, integrating the current diverse research approaches (ii) There is no shared view among the diverse re- search and user communities of what is and might be possible or desirableThe outcome of the fellowship will be a new vision of a mathematics social machine, transforming the reach, pace and impact of mathematics. It will deliver: analysis and experiment to understand current and future production of mathematics as a social machine; designs and prototypes; ownership among academic and industry stakeholders; a roadmap for delivery of the next generation of social machines; and an international team ready to make it a reality.