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Extension: MathSoMac: the social machine of mathematics

扩展：MathSoMac：数学社交机器

基本信息

批准号：
EP/R03169X/1
负责人：
Ursula Martin
金额：
$ 116.16万
依托单位：
University of Edinburgh
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2018
资助国家：
英国
起止时间：
2018 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FR03169X%2F1
关键词：
Extension MathSoMac social machine mathematics

项目摘要

This is an extension of the Fellowship: 'MathSoMac: the social machine of mathematics', which is an Established Career Fellowship, 2014-2018, EPSRC EP/K040251/2Mathematics is recognized as a profound intellectual achievement, with impact on many aspects of wealth creation and quality of life, and as unique cultural capital, drawing crowds to exhibitions and public lectures. For centuries, the highest level of mathematics has been seen as an isolated creative activity, to produce a proof of a difficult theorem for review and acceptance by research peers. However, at a remarkable inflexion point, new technology is radically extending the power and limits of individuals. Websites such as the polymath or mathoverflow sites allow researchers to collaborate with each other, and "show their working", so that others outside their specialist field can engage with their research and get early insight into things that might be useful. Now routinely used for verification of hardware and software designs, and in cyber-security, computer proof goes beyond symbolic computation, or numerical simulation, to generate mathematical arguments too complex for humans to grasp, and to check these chains of inference from first principles. These phenomena have typically been viewed as distinct, linked only by their relationship to mathematics. Yet they have many common features, not least, as we showed in the original project, their dependence, ultimately, on human and social issues of mathematical judgement and creativity. In this proposal, to extend our current research, we view these phenomena as a united whole, in which people and computer systems combine into a single problem-solving entity, where individuals interact with each other, and with computers which draw on a single "engine" of computer proof. We call this model of the production and application of mathematics the "social machine of mathematics" based on the new paradigm of "Social machines", identified by Berners-Lee about 20 years ago.We focus on two research questions: === "Beyond Inference": how can we give human mathematicians the benefits of computer proof, while shielding them from its complexity?=== " Towards impact: how can we evaluate the impact and cultural capital of foundational research?

这是奖学金的延伸：“MathSoMac：数学的社会机器”，这是一个既定的职业奖学金，2014-2018年，EPSRC EP/K 040251/2数学被认为是一个深刻的智力成就，对财富创造和生活质量的许多方面产生影响，并作为独特的文化资本，吸引人群参加展览和公开讲座。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，以证明一个困难的定理，供研究同行审查和接受。然而，在一个显著的转折点上，新技术正在从根本上扩展个人的权力和限制。像polymath或mathoverflow这样的网站允许研究人员相互合作，并“展示他们的工作”，这样他们专业领域之外的其他人就可以参与他们的研究，并尽早了解可能有用的东西。现在，计算机证明通常用于验证硬件和软件设计，在网络安全中，计算机证明超越了符号计算或数值模拟，产生了人类无法理解的复杂数学论证，并检查了这些从第一原理推断的链。这些现象通常被认为是不同的，只有通过它们与数学的关系才能联系起来。然而，它们有许多共同的特征，尤其是，正如我们在最初的项目中所展示的那样，它们最终依赖于人类和社会的数学判断和创造力问题。在这个提议中，为了扩展我们目前的研究，我们将这些现象视为一个统一的整体，在这个整体中，人和计算机系统联合收割机结合成一个单一的解决问题的实体，在这个实体中，人与人之间相互作用，并且与计算机之间相互作用，计算机证明的单一“引擎”。我们把这种数学生产和应用的模式称为“数学的社会机器”，这是基于伯纳斯-李在20年前提出的“社会机器”的新范式。我们关注两个研究问题：“超越推理”：我们如何让人类数学家享受计算机证明的好处，同时又让他们免受其复杂性的影响？“走向影响：我们如何评估基础研究的影响和文化资本？