Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The history of mathematics (e.g., Fermat's Last Theorem, the Poincaré conjecture) demonstrates that problems deemed intractable were solved via unforeseen conceptual innovations.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Selection bias: we remember solved 'intractable' problems but forget thousands abandoned as genuinely unsolvable or fundamentally misconceived.
      ?

      Think about whether this reason is strong or weak

    • 2.Innovations may have been inevitable refinements of existing methods rather than unforeseen conceptual leaps—success doesn't prove necessity of novelty.
      ?

      Think about whether this reason is strong or weak

    • 3.Claim conflates mathematical history with a universal law about problem-solving, but lacks criteria for predicting which problems will yield to innovation.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.FLT and Poincaré remained unsolved for centuries despite intense effort, then fell quickly after new frameworks (modularity, Ricci flow) emerged.
      ?

      Think about whether this reason is strong or weak

    • 2.Conceptual breakthroughs often enable simultaneous solutions to previously isolated problems, suggesting barriers were conceptual, not merely computational.
      ?

      Think about whether this reason is strong or weak

    • 3.Mathematics progresses via paradigm shifts (non-Euclidean geometry, set theory, category theory) that reframe what counts as tractable.
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42