Awesome! Thanks! Would you welcome feedback on the symbols, along with suggestions? It's clear that you put thought and effort into this.

I like these, but I have to look up what most of them mean.  It would be helpful to show them named in this post. 

Recursion/induction is like a loop with an off-ramp. Like a letter Q. 

Maybe proof by contradiction is like an inverted house of cards. You make an assumption, and then look for ways to knock it down. 

proof by probability feels like a gauge, like a line with an arrow that indicates a threshold. 

Direct proof is a square. It just sits there on its own. 

I don’t know one directly for contraposition, but it involves negative space like the image of the faces and vases. 

Here’s an odd suggestion: make it in a Choose Your Own Adventure style. The joy of that format is that you can compare and contrast different possible worlds. You only need a handful of branching paths, especially when you already have two major ones. 

I wish mathematicians would take a page out of computer science/software engineering, where we’ve collectively decided that single-character variable names are bad practice. 

I do understand the value and beauty of a terse notation, especially when hand-writing it, but I can also appreciate similar beauty of well-structured and self-documenting code, especially within an code editor that uses a language server that can provide context for any symbol. White space hints at structure and comments clarify the more difficult to parse sections of code  

I’m constantly algebraicly manipulating symbols. We generally call it refactoring, but it’s the same thing up to an isomorphism. I aim to write my code in such a way to minimize the cognitive load on the reader. Using single-character symbols adds a whole layer of cognitive load where the reader needs to keep a mental map of what each symbol represents, especially when the convention chooses an arbitrary symbol, rather than at least using abbreviations. This feels especially onerous for students who are trying to learn the concepts behind the symbols, while trying to keep track of what each symbol represents  

This is really is just a general rant. You did a good job with your explanation. It balances technical nuance with approachability. That really is why I even had this thought to begin with.

Thanks for sharing!

I’d be worried about further disenfranchisement of the poor. I won’t claim that this is a fatal flaw, but I think it should be addressed.

To make it more concrete, a fictional scenario:
To someone who sleeps outside with no income, selling their vote for $1000 to some rich dude sounds like a good deal, especially when that vote has a negligible chance of winning them a better situation. 

That’s okay on an individual level of choice, but scaled up it’s a misalignment of incentives. 

This does seem like a good idea for small organizations, but at some scale, I expect bad actors to break the system.

Even without an A/B comparison, if policies came with measures of success, that would go a long way to steering into better policies. Do school vouchers improve outcomes for students? It seems plausible, but we should be able to track graduation rates, and GPAs. Maybe we can even agree that that is an important goal. If after 5 years, those measures are not showing significant improvement, we can conclude that the voucher program didn’t meet its goals, and at the very least the policy needs to change, if not directly reversed. 

It’s not perfect, as there can be confounding effects, but by tying the life of a policy to success metrics (that hopefully would be easier to agree on), we can at least we can show progress, and rule out the worst ideas. 

How do you think this applies to paid YouTube accounts? I have one, and I don’t ever see YouTube ads. I still see the in-video ads that the artists insert into their videos, but even then I can skip them easily, and YouTube actually makes that easier, since I can skip forward twice and I get a button to skip the segment. 

YouTube is pretty far along the enshitification curve. I don’t see them changing things enough to turn that ship around.