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Of course the deep concern is that there's a way to elegantly prove the existence of an ugliest possible proof.
Bonus panel
this post was submitted on 25 Mar 2025
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Saturday Morning Breakfast Cereal
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Posts and discussion about the webcomic Saturday Morning Breakfast Cereal by Hugo Award-winning author Zach Weinersmith (and related works)
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Can someone explain this to me like i'm ~~5~~ 16? This went waaay over my head.
Mathematicians generally look for "elegance", i.e. simple rules that have a lot of explanatory power. If you can simplify a bunch of disparate things into one simple theory, that's a good thing. See Maxwell's equations as an example in physics:
The comic jokes about seeking the opposite, intentionally searching for rules that provide no explanatory power and would literally destroy the universe to compute. Pure mathematicians don't like it because it lacks elegance, and applied mathematicians don't like it because it's impossible to actually use.
ELI5 version is that it's the mathematical version of one of those useless boxes, intentionally made to be useless:
Alright, that makes sense! Thank you for the explanation!
So the third branch mentioned in the comic would be the unpure, inapplicable variant, whereas the first would be theoretical/pure mathematics and the second branch would be applied math?
Yep, exactly!