Re: it's a conceptual zoo out there

On 23/06/2024 16:37, sobriquet wrote:

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).
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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..).
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https://www.youtube.com/watch?v=KiI8OnlBTKs
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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)?

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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
 

What does happen is that lecturers teach their material to students year upon year upon year, and over time the ideas and methods are distilled to become more efficient from a teaching perspective. Theorems that were once long and complicated are approached in a more efficient way, and the proofs may turn out to be quite short.  Often the shortness hides a wealth of smaller results, but still there is a big improvement in understandability, and the connections between areas become better understood.
I doubt all the above would be unified into /just/ one concept, because they reflect different interests in what is being studied.  That doesn't mean they won't be seen as aspects of some simpler ideas - for example when I studied maths all the above were seen as sets.  However that didn't mean there was just one course (on set theory) that covered all the above - even though you might say "aha - everything is just a set, so that's it."  (At that time category threory was a bit too new to base the entire degree on, but I imagine these days category theory provides a similar (better?) unififying view of the various areas, like set theory in my study days.  But still there are numbers, topologies, sets, manifolds, rings etc.).
Mike.