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NNTP-Posting-Date: Sun, 23 Jun 2024 02:58:25 +0000
Subject: Re: it's a conceptual zoo out there
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sat, 22 Jun 2024 19:58:39 -0700
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On 06/22/2024 06:36 PM, sobriquet wrote:
>
> In particle physics, people used to refer to the particle zoo since
> there was such a bewildering variety of elementary particles that were
> being discovered in the previous century.
> Eventually things got reduced to a relatively small set of fundamental
> fermions and bosons and all other particles (like hadrons or mesons)
> were composed from these constituents (the standard model of particle
> physics).
>
> Can we expect something similar to happen eventually in math, given
> that there is a bewildering variety of concepts in math (like number,
> function, relation, field, ring, set, geometry, topology, algebra,
> group, graph, category, tensor, sheaf, bundle, scheme, variety, etc..).
>
> https://www.youtube.com/watch?v=KiI8OnlBTKs
>
> Can we kind of distinguish between mathematical reality and mathematical
> fantasy or is this distinction only applicable to an empirical science
> like physics or biology (like evolution vs intelligent design)?

It's mostly the milieu of model theory what relates among them.

Logically then that's mostly relations.

The "stronger" and "weaker" theories
are both "weaker" and "stronger",
proving more with less, less with more,
less with less, more with more.

Then "Foundations" has the usual goal of being "a 'the' theory".

"A Theory"


https://www.youtube.com/watch?v=WT7yUJYtTz8&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY&index=43


There still is a "Particle Zoo", there's a "Wave Zoo", too.
"Resonance theory" is above wave theory about "particle-wave"
duality. Energy's conserved, yet it's also in a form, and
the interactions and transitions are various.


I basically look at it as geometry, arithmetic, algebra,
number theory, topology, and function theory, operator calculus.


I.e. the discrete is embedded in the continuous.