[JumpCrisscross]

> Whether or not humans ever mastered mathematics, what is and isn't mathematically true would not change...[we] can create notation and formalisms, but they do not invent the truths those mathematics represent

This is a big philosophical question. (Kant would agree with you. Some of his detractors would not.)

Setting that aside, I agree with your criticism of the claim that mathematics only exists to solve concrete problems. Mathematical fiction, e.g. exploring how a system following nonsense rules might behave, is perfectly good math. It's interesting, potentially beautiful, first and foremost; it might also be useful, though that's of secondary concern. (It has an uncanny knack for being so [1].)

To say math must serve physical reality is to discard its artistic side, perhaps essence; that's disappointing, debilitating and reductive.

[1] https://aapt.scitation.org/doi/abs/10.1119/1.2402156?journal...

[thwayunion]

With respect to aesthetics, to each their own. I do find some mathematics beautiful. In fact, "I am bored" is a real problem and mathematics can be used to solve that problem by being a tool that tickles our brains in pleasant ways.

The "tool" and "problem" here are meant as comments on the metaphysical content of mathematics, not some sort of statement that mathematics is for engineering and that's all.

In particular: I'm commenting on the imbued/latent metaphysics of Wolfram's post, which goes beyond mere artistic appreciation. If his framing were "and look how pretty cellular automata are!" then I guess my reaction would be "yeah they are quite cool aren't they?"

I find Church-Rosser quite beautiful and also think Wolfram puts way too much metaphysical weight into the behavior of confluent rewrite systems. Similarly, some Psalms are beautiful and the story of Jesus is very nice but god does not actually exist. There's no contradiction there -- you can take the beauty and spit out the metaphysics.