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From: sobriquet <dohduhdah@yahoo.com>
Newsgroups: sci.math
Subject: Re: unification programs in math
Date: Sat, 22 Feb 2025 23:32:27 +0100
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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