Re: it's a conceptual zoo out there

sobriquet explained :

Op 23/06/2024 om 14:32 schreef FromTheRafters:

sobriquet pretended :

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)?

 I don't think so because regarding physics there is one goal, to model reality, and I believe only one reality to deal with. With mathematics there are endless abstractions such as the idea of endlessness itself in its many forms.

>
I think there is still a general trend towards unification in both math and science.
In both cases things get discovered and explored and when things are
explored in more detail, often connections are discovered between seemingly unrelated fields that allow one to come up with a unified framework that underlies things that initially seemed unrelated.
>
https://www.youtube.com/watch?v=DxCWRAT0WKc

Another example is/was Fermat's Little Theorem which was thought at the time to be a 'gewgaw' or a 'bauble' but now is important in information theory.