[penguin_booze]

"you could have..." is among the top insulting phrases used by maths-adjacent people. Others in that league are "it should now be obvious...", "it's abundantly clear...", "it can be easily shown that...", "this is nothing but..." etc.

The rest of us reading this are like, holy batman, what the fuck was that?!

[ozgung]

Also the proof is so trivial that it’s left to the reader.

[BurnerOptical]

This one hurts the most, esp. in fields you're not familiar.

[hnfong]

Well, at least these days an actually trivial (to a domain expert) proof can be delegated to a frontier model...

[cubefox]

In the future this might be replaced with "you can verify this fact by asking an LLM of your choice". Similar to how people in chat arguments already post screenshots of an LLM answer to show that their opinion is correct.

[moffkalast]

Counterexample left as an exercise for Fable

[jameshart]

Math educators like Grant Sanderson (3blue1brown) use it in a very specific way: the goal of a mathematical explanation is to make the learner feel like they could have come up with something. And a really good mathematical communicator can absolutely do that.

A piece like this which uses it in a headline but in no way makes an average reader feel like they could have come up with it is just badly misjudging how good of an explanation it is.

[wrs]

I don’t think “you” in these titles ever really refers to an “average reader”. Some familiarity with the field is required. Imagine how non-programmers (and many programmers) feel about some examples I just Googled:

“You Could Have Invented Parser Combinators”

“You Could Have Invented Container Runtimes”

“You Could Have Invented Git”

Given the references to “mathematicians”, I think this reaction is more about an unfamiliarity with the concept of applied mathematics, which is ironic for practitioners in a field containing so much that is (or should be) regarded that way.

Software used to be all about “discrete math”, logic, maybe a bit of queuing theory…and now suddenly linear algebra and statistics became important. Don’t panic, it’s just another textbook on the shelf.

[aesthesia]

I think the origin of the title formula is Timothy Chow's "You Could Have Invented Spectral Sequences" (https://www.ams.org/notices/200601/fea-chow.pdf), which is certainly not aimed at an average reader.

[jameshart]

So I think what’s a little unfair there is that “you could have invented container runtimes”[1] is an article which really tries to answer ‘how does someone who works in traditional software development with an understanding of operating systems and deployment that is a few years out of date get brought up to date on what they need to know so that to them, something like container runtimes become a logical and obvious thing that solves a problem they now understand?’

What this particular mathematical writeup seems to address is ‘how does someone who is already up to speed on the mathematical underpinnings of attention kernel neural networks get brought up to date on what they need to understand in order to see this new algorithm as obvious’

Which is a smaller audience to be sure, and - given how fast this field has grown - somewhat disingenuous in its implications.

This kind of title is appropriate for a piece aimed at helping someone who is a little behind the curve catch up. In the field of deep learning it should be obvious even to the people inside it riding that curve that it is moving really fast and that this kind of content only works for people who are running to keep up.

[1] https://medium.com/@gtrevorjay/you-could-have-invented-conta...

[egeozcan]

Answer with:

You could have your own hacker news, it's just a textbox, a bunch of tables and headings! Once you add these, it'll be abundantly clear that you also need a database. It should now be obvious that you also need a user system and it can be easily shown that needs a backend. Admin tools, tests, statistics, performance checks and so on can easily be derived from such backend.

[sva_]

Chill, it's just a rhetorical phrase. They want to show that this KDA is the result of a series of incremental improvements, and I think they did a pretty good job at that.

I often find people get annoyed at mathy stuff because they seem to think that they should be able to read it like a (comparatively low information dense) newspaper article or something similar.

Math isn't like that, it usually has high information density and you need to parse every single symbol. And also people make this mistake where they gloss over stuff they don't get because they think they'll just understand things from context. Works great in normal literature - but math ain't like that. If you don't understand something, go back to the definitions.

[Razengan]

Right next to "Learn More" by software UI designers.