What does mathoverflow tell us about the production of mathematics?
What does mathoverflow tell us about the production of mathematics?
复制标题
关于数学的产生，mathoverflow 告诉我们什么？
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Pease
中科院分区：
文献类型：
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作者：
U. Martin;A. Pease
传统上，最高水平的数学研究被视为一项单独的活动。然而，数学家自己的新创新开始利用社会计算的力量来创造新的数学生产模式。我们研究这样一个系统的有效性，并利用人工智能和基于计算机的数学提出增强建议。我们分析了研究数学家社区问答系统 mathoverflow 中问题样本和答案的内容。我们发现 mathoverflow 非常有效，我们 90% 的样本问题得到了完全或部分回答。典型的回应是非正式的对话，允许错误和猜测，而不是严格的数学论证：我们的样本讨论中有 37% 承认错误。响应通常呈现受访者已知的信息，并且很容易被其他用户检查：因此 mathoverflow 的有效性来自信息共享。我们的结论是，通过人与机器的结合来扩展数学溢出的力量和范围，给人工智能和计算数学带来了新的挑战，特别是如何处理错误、类比和非正式推理。
The highest level of mathematics research is traditionally seen as a solitary activity. Yet new innovations by mathematicians themselves are starting to harness the power of social computation to create new modes of mathematical production. We study the effectiveness of one such system, and make proposals for enhancement, drawing on AI and computer based mathematics. We analyse the content of a sample of questions and responses in the community question answering system for research mathematicians, mathoverflow. We find that mathoverflow is very effective, with 90% of our sample of questions answered completely or in part. A typical response is an informal dialogue, allowing error and speculation, rather than rigorous mathematical argument: 37% of our sample discussions acknowledged error. Responses typically present information known to the respondent, and readily checked by other users: thus the effectiveness of mathoverflow comes from information sharing. We conclude that extending and the power and reach of mathoverflow through a combination of people and machines raises new challenges for artificial intelligence and computational mathematics, in particular how to handle error, analogy and informal reasoning.