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  • unification programs in math

    From sobriquet@21:1/5 to All on Sat Feb 22 21:33:41 2025
    It seems that programs like the Erlangen program or the Langlands
    program seek to unify math by bridging certain realms, like number
    theory, algebra, geometry and topology.

    https://ncatlab.org/nlab/show/Erlangen+program https://ncatlab.org/nlab/show/Langlands+program

    https://www.youtube.com/watch?v=xuLCPv6smwo

    Will AI be helpful in condensing math concepts in a unifying
    framework? On an abstract level natural language and mathematics seem
    similar in the sense of a large network of related
    notions/ideas/concepts, where we seek to differentiate and identify
    things in an optimal fashion.
    Naively you would think that if you want to master a particular topic,
    like differential geometry, you should be able to feed hundreds of books
    on the topic or closely related topics into an LLM so it can crunch it
    down to a single comprehensive overview that can be explored
    interactively, where the level of detail in the presentation can be
    customized based on your level of understanding and your background
    knowledge.

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  • From sobriquet@21:1/5 to All on Sat Feb 22 23:32:27 2025
    Op 22/02/2025 om 22:07 schreef Ross Finlayson:
    On 02/22/2025 12:33 PM, sobriquet wrote:

    It seems that programs like the Erlangen program or the Langlands
    program seek to unify math by bridging certain realms, like number
    theory, algebra, geometry and topology.

    https://ncatlab.org/nlab/show/Erlangen+program
    https://ncatlab.org/nlab/show/Langlands+program

    https://www.youtube.com/watch?v=xuLCPv6smwo

    Will AI be helpful in condensing math concepts in a unifying
    framework? On an abstract level natural language and mathematics seem
    similar in the sense of a large network of related
    notions/ideas/concepts, where we seek to differentiate and identify
    things in an optimal fashion.
    Naively you would think that if you want to master a particular topic,
    like differential geometry, you should be able to feed hundreds of books
    on the topic or closely related topics into an LLM so it can crunch it
    down to a single comprehensive overview that can be explored
    interactively, where the level of detail in the presentation can be
    customized based on your level of understanding and your background
    knowledge.

    How about "strong mathematical platonism",
    with regards to a "heno-theory", that makes
    bridges as you mentioned, bridge results,
    what results each of the "fundamental" theories,
    is one theory.

    Then, "theories of one relation", like set theory
    and part theory and ordering theory and identity,
    have various ways of looking at them as fundamental,
    then though that the resolution of mathematical paradox
    makes to arrive at the extra-ordinary, of course.

    The "strong" and "weak" are not necessarily reflective
    terms in mathematics, and "growth" is sometimes "in-growth".

    The, "mathematical platonism" is the usual historical
    account of "a mathematics, the mathematics".



    From AlphaTensor to AlphaSheaf?

    https://www.youtube.com/watch?v=TUJ9tHl4_vw

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