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
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Scott Aaronson and others have shown that known proof tec... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→P ≠ NP is unlikely to be independent of strong formal theories such as PA or ZFC

    Scott Aaronson and others have shown that known proof techniques (algebrization, relativization, natural proofs) are formally blocked from resolving P≠NP, suggesting the statement resists standard mathematical machinery.

    ?Rate how convincing each reason is below to see the overall strength.

    No one has weighed in yet. Be the first to share reasons for or against this statement.

    Sign in or register to share your perspective on this statement.

    Key Terms

    Algebrization(as a blocked approach to P≠NP)
    A proof technique that converts a computational problem into an algebraic (equation-based) problem to make it easier to analyze.
    Formally blocked(describing why certain proof techniques cannot work)
    Proven mathematically to be impossible or prevented by strict logical rules, not just practically difficult.
    Natural proofs(as a blocked approach to P≠NP)
    A proof technique that uses straightforward, intuitive logical reasoning rather than unusual or clever tricks.
    Proof techniques(describing mathematical approaches)
    Standard methods or strategies that mathematicians use to prove that statements are true, like following a recipe to solve a problem.
    P≠NP(as used in computer science and mathematics)

    Next step

    Based on where you are in your exploration

    Explore a random proposition
    Start fresh with something unrelated.
    A famous unsolved question asking whether problems that are quick to check are also quick to solve. Most computer scientists believe they're different, but no one has proven it yet.
    Scott Aaronson(cited as an authority on computational complexity)
    A computer scientist who studies the theoretical limits of computation and has made important discoveries about what kinds of problems computers can and cannot solve.
    Standard mathematical machinery(the conventional approaches that don't seem to work for this problem)
    The usual, well-established methods and tools that mathematicians typically rely on to solve problems.
    relativization(Used here as a technique for defining metaphysical necessity from epistemic necessity by relativizing to some suitable class)
    A method for defining one form of necessity in terms of another by restricting to a suitable class, applicable when the extension of the target property is broader than the base property

    Connections

    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    P ≠ NP is unlikely to be independent of strong formal theories such as PA or ZFC

    Details

    Type
    claim
    Perspectives
    0 (0 for, 0 against)
    Edits
    1 edit

    Open for perspectives

    This idea is waiting for its first supporting or challenging perspective.

    Share the first perspective