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In _A Mathematician’s Apology_, G. H. Hardy argues for the virtue of mathematics as a beautiful aesthetic pursuit with intrinsic value that is not dependent on any kind of applied utility. He talks about various fields that in his view will •never• have any sort of practical application, and the two examples he gives are…number theory and relativity.

Oops!

Ah, I see some Wikipedia editor noticed the same thing — and I’m slightly misremembering what Hardy said (though the “oops” still applies!).
https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology#Critiques

Number theory and relativity are great examples not just of how theories find surprising applications, but how ethically decoupled the applications are from the theory.

Number theory gave us encryption, but also blockchain.

Relativity gave us accurate GPS, but also nuclear weapons.

You just can’t know. Simultaneously hopeful and grim news for the theoretician who wonders whether their abstruse work might have tangible, practical value! Hardy’s “focus on the beauty” stance may be the wise one.

@inthehands then you have the connections between number theory and relativity.

https://www.youtube.com/watch?v=MnS4hduP5xg

Is that connection relevant to anything? Probably, but I have no idea how.

@inthehands I've collected some notes about how I stumbled into this curiosity here:

https://github.com/constructive-symmetry/constructive-symmetry/blob/master/T002_Tools_of_Math_Construction/Part03_Aggregate_Theory.md

@inthehands I really enjoyed finding what seems to me to be a really strong argument that very carefully selected examples from number theory and abstract algebra are in fact a really important part of the early childhood math curriculum. Thus the Aggregate Theory of Concrete Mathematics, which emphasizes applying iterative deepening as a learning/study strategy to the Stern-Brocot Tree, Pascal's Triangle, Symmetry Group of the Square, and computer programming.