数学家们一直在努力应对形式系统的固有局限性，发现并非所有明确定义的数学命题都可以被证明，这挑战了绝对确定性的观念。这一认识源于逻辑悖论，并通过形式语言和证明的发展得以完善，突显出即使是看似明确无误的数学对象也可能不像人们曾经认为的那样精确定义。自动化定理证明的追求，融合了计算机科学和数学，旨在处理形式化的书写和证明，其中Coq和Lean等工具在此持续的科学探索中发挥着作用。 AI
影响 强调了知识形式化的哲学和实际挑战，这与AI的推理能力和可验证系统的开发息关。
排序理由 该集群讨论了数学和逻辑的基础性问题，包括形式证明的局限性和自动化定理证明工具的发展，这属于研究范畴。
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# Math # AI 6/n This is slightly off topic here, but I wish to make a digression and mention that mathematicians also discovered with quite a surprise that not everything can be proved: there are seemingly natural mathematical statements (the one which are well specified, without…
# Math # AI 5/n After World War 2, the development of computers made possible that computers handle formal writings and formal proofs, and this started a scientific field (at the interaction of mathematics and computer science) of automated theorem proving. This is quite an inter…
# Math # AI 4/n After this logical disaster, mathematicians took a great more care to elaborate the way they can argue so that they don't fall into such absurdities. And they devised a way for that, which is the idea that mathematics could be (should it be?) framed in a specific …