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Mathematicians confront limits of formal proof and ambiguity in AI era

By PulseAugur Editorial · [3 sources] ·

Mathematicians have grappled with the inherent limitations of formal systems, discovering that not all well-specified mathematical statements can be proven, challenging the notion of absolute certainty. This realization, stemming from logical paradoxes and refined through the development of formal languages and proofs, highlights that even seemingly unambiguous mathematical objects may not be as precisely defined as once believed. The pursuit of automated theorem proving, merging computer science and mathematics, aims to handle formal writings and proofs, with tools like Coq and Lean playing a role in this ongoing scientific endeavor. AI

IMPACT Highlights the philosophical and practical challenges in formalizing knowledge, relevant for AI's reasoning capabilities and the development of verifiable systems.

RANK_REASON The cluster discusses foundational issues in mathematics and logic, including the limits of formal proof and the development of automated theorem proving tools, which falls under research.

Read on Mastodon — fosstodon.org →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

Mathematicians confront limits of formal proof and ambiguity in AI era

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The cluster discusses foundational issues in mathematics and logic, including the limits of formal proof and the development of automated theorem proving tools, which falls under research.
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COVERAGE [3]

  1. Mastodon — fosstodon.org TIER_1 English(EN) · [email protected] ·

    # 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

    # 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…

    LINKS youtube.com/watch
  2. Mastodon — fosstodon.org TIER_1 English(EN) · [email protected] ·

    # 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 scient

    # 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…

  3. Mastodon — fosstodon.org TIER_1 English(EN) · [email protected] ·

    # 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 absurdi

    # 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 …

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