"Are you an expert?" is a perfectly respectful question.

Everyone has a different perspective, based on their math background. From the OP's perspective, the formalization of this problem statement was apparently worth talking about. On the other hand, for you it's just a homework problem that belongs in an intro class.

Let's just be generous and try to accept these differences.

My comment was exactly about the required math background though. Anyone who's completed an intro to proof class would find that kind of statement easy to formalize because they would have had to write similar statements for homework. That provides some context: everyone who's interested in computer theorem provers probably has some experience with proofs, so formalizing that statement should be easy for them. i.e. (for this kind of problem) it's not really "the hard part" for people who are seriously working on this stuff.

I think it's reasonable to ask whether LLMs formalize theorems correctly. And I'm not sure that saying "this one is easy" answers that question.

>That's what's covered by the "assuming you have formalized the statement correctly" parenthetical.

Sure. But it's fair to ask how to validate that assumption.

Skilled humans must understand the problem and write the theorem statement.

This answer is too grown-up for the forum.

“It takes a thousand men to invent a telegraph, or a steam engine, or a phonograph, or a photograph, or a telephone or any other important thing—and the last man gets the credit and we forget the others. He added his little mite — that is all he did. These object lessons should teach us that ninety-nine parts of all things that proceed from the intellect are plagiarisms, pure and simple; and the lesson ought to make us modest. But nothing can do that.”

― Mark Twain

Yeah, it's all about the inflection point. Otherwise how are you even dispositive?

> many times I have seen something advertised, thought "I want that!" and bought it and sometimes that thing became my new favorite.

This happens. It matters to you and to the people paying for those ads … if they could really quantity it.

But it’s too tiny to matter to the media outlets. You’re talking about real clicks, which are already a small fraction. Real clicks on ads that actually offer anything desirable … that’s just too small a part of total clicks. Nobody can make much money on that 0.5% (?) of the traffic, no matter how idealistic they are. Fake clicks on misleading ads are the bread and butter of the market.

As a vendor, expecting online advertisers to get you customers efficiently is like expecting a real estate agent to get you the best sale price. They care about their own revenue, not yours.

Look at even Amazon's own site. They're hardly bothering to show you real stuff that you actually want. Either they're completely incompetent, or that's just not where the money is.

Genuine clicks on useful ads are a tiny part of ad revenue. There’s no incentive for media to work on that slice of clicks.

Amazon did borrow money, for a long time.

To become the next Uber, do I just need to run huge losses?

I think you're saying that just running up huge losses is sufficient to create a successful company? But that you personally wouldn't want to run up huge losses? Not sure.

nah, I am saying that many (super) successful businesses ran in red financially for a very long time. I would not run a business that way but I am also (fortunately) not a CEO of a multibillion dollar company