Jesus Christ, AI journalism is so bad right now. Exhibit one, Gizmodo is raving about an article that 'proves' LLMs have a "mathematical limit" and can't possibly do tasks that are too complex. Let's look at the actual paper, shall we? gizmodo.com/ai-agents-ar...

So first thing to note is that it's an Arxiv preprint, meaning it has no peer review. Also, it's the only paper by the two coauthors. (Gotta give props to Gizmodo, at least they linked the paper. Some places don't do that and it's infuriating) arxiv.org/abs/2507.07505

So how can an 2^k step problem be solved in n^2 operations????!?!! This is a pretty egregious misunderstanding, assuming "one output" is the same as "solving a problem". I'm no LLM expert, but to my layfolk understanding, LLMs output one token, over and over again *in sequence*

So how does an LLM output 2^k strings? By outputting one character at a time, k*2^k times. It doesn't matter if this takes quadratic time, it's still solvable! (You could argue that this overflows the context window, but the strings have an ordering! LLM just needs to know *last* string printed)

An analogy: it is impossible for computers to uppercase a string, because iterating through a string is an O(n) operation and a CPU cycle can only do O(1) work. (BTW their [7] reference in that screenshot does to one of the author's personal blogs. It doesn't list the calculations they claimed)

One more basic misunderstanding of the problem domain: "if a problem takes O(n^3) to solve, it must take O(n^3) to verify a solution" Our best algorithm for solving 3SAT is ≈O(1.4^n) (n being number of variables). That's exponential. But we can CHECK IF A SOLUTION IS CORRECT in linear time.

Now, I want to be clear, I'm not mad at Gizmodo for taking all the paper claims at face value. You don't need to know a lot of CS to realize this paper is bunk, but you need to know at least *some* CS. No, I'm mad because they didn't bother to google the author. Because if they did...

...they'd know the paper was written by A HIGH SCHOOLER. First result on Kagi is his LinkedIn profile. He started college THIS YEAR. Two months AFTER publishing this preprint! And no, he doesn't have any attestable experience in computer science He's, like, a linguistics and entrepreneurship guy

So that's why AI Journalism sucks. Journalists see an article that affirms their priors, don't have the experience to fact check it, don't bother to do the basic due diligence of making sure the author isn't an actual child, and push it to their audience as proving a "mathematical limit" of LLMs

Maybe I'm being too optimistic. Maybe they did check and did know that their source was AT MOST eighteen years old and published it anyway

(I'm picking on anti-AI journalism here but pro-AI journalism is equally as bad on this matter)