论文标题
Voevodsky的未完成的项目
Voevodsky's Unachieved Project
论文作者
论文摘要
在2003年在获得田野勋章后不久的一系列演讲中，他在代数几何学中的结果Vladimir Voevodsky（1966-2017）确定了数学的两个战略目标，他计划在进一步的研究中追求这一目标。第一个目标是开发“计算机化的数学知识库”，该库支持自动证明验证。第二个目标是“桥梁纯净和应用数学”。 Voevodsky对第一个目标的研究带来了新的数学基础。鉴于2004年的第二个目标Voevodsky开始开发人口动态的数学理论，该理论涉及分类概率理论。后一个项目没有带来公开的结果，并在2009年被Voevodsky放弃了，当时他决定将自己的努力集中在单价基础和密切相关的主题上。在本文基于Voevodsky的档案资源的本文中，我介绍了Voevodsky对数学及其与自然科学的关系的观点，批判性地讨论了这些观点，并暗示了Voevodsky在应用数学中的思想和方法如何可以进一步发展和追求。特别关注Voevodsky的原始策略，即弥合纯数学和应用数学之间的持续差距，计算机和计算机辅助数学具有重要作用。
In a series of lectures given in 2003 soon after receiving the Fields Medal for his results in the Algebraic Geometry Vladimir Voevodsky (1966-2017) identifies two strategic goals for mathematics, which he plans to pursue in his further research. The first goal is to develop a "computerised library of mathematical knowledge", which supports an automated proof-verification. The second goal is to "bridge pure and applied mathematics". Voevodsky's research towards the first goal brought about the new Univalent foundations of mathematics. In view of the second goal Voevodsky in 2004 started to develop a mathematical theory of Population Dynamics, which involved the Categorical Probability theory. This latter project did not bring published results and was abandoned by Voevodsky in 2009 when he decided to focus his efforts on the Univalent foundations and closely related topics. In the present paper, which is based on Voevodsky's archival sources, I present Voevodsky's views of mathematics and its relationships with natural sciences, critically discuss these views, and suggest how Voevodsky's ideas and approaches in the applied mathematics can be further developed and pursued. A special attention is given to Voevodsky's original strategy to bridge the persisting gap between the pure and applied mathematics where computers and the computer-assisted mathematics have a major role.
