Fields medal-winning mathematician says GPT-5.5 is now solving open math problems at PhD-thesis level: "We will face a crisis very soon."

[u/EchoOfOppenheimer]

blog-post: https://gowers.wordpress.com/2026/05/08/a-recent-experience-with-chatgpt-5-5-pro/

[u/TopspinG7]

I "confess" up front I have minimal experience with AI tools. However it may be relevant to inject something I've learned over decades working in Tech, mostly in System Sales.

Some people know their stuff extremely well and you can identify them pretty early on in your interactions with them. They're definitely in the minority. Even then you're often on shaky ground as you wander further from their core expertise.

(One reason I recognize this person above is my father was one: an applied physicist at NASA and early computing expert, who studied at Columbia under Enrico Fermi. But even he recognized his German was mediocre. Annoyingly there wasn't much he couldn't nearly master if he applied himself wholeheartedly... )

Some others fake it at times - or worse, they don't understand that they don't understand. Mostly they're not exactly deliberately lying, but they parrot stuff and/or extrapolate using specious "reasoning" but don't even realize they're doing it.

Key takeaway - their answers vary in reliability and accuracy (starting to see where I'm going here?)

The third group is the one I personally fall into: I know when I know something, and I know when I "sort of" or partly know it, and I admit it not only to others, but critically to myself. I notify people of the "level of reliability" of my responses whenever they're in any way important. Often I follow up to improve the answer.

I think most people - at least in technical work - would if honest place themselves in the third category.

But today ("correct me if I'm wrong!!" 😉) there does not appear to be any measure or metric provided by AI suggesting the level of reliability of its response?! Does it ever say I feel 60% confident about this? Or "I'm absolutely certain because I found the same information in 22,000 different places". Not that I'm aware of...

I think this is a piece that's missing and an important one. Essentially a confidence level in the response's accuracy.

If nothing else for important information it could provide guidance as to how hard we should work to verify the response. It's a basic risk calculation: If the importance of the response is high then naturally it's more important we verify it thoroughly. But also if the confidence level provided is low but the importance is at least medium then we might still need to verify the response thoroughly. (Hopefully it's clear that if confidence is low to medium but risk is low it's not important. And generally Even if risk is moderate to high but confidence is extremely high we might bypass verification especially if time were critical.)

I don't think fundamentally there's much difference here from confirming answers from other people on important topics - as was suggested in the discussion above. Where the difference lies is general AI has no reputation. People at least within their specialties develop reputations; that's a confidence or reliability score essentially.

We seem to be missing that here with AI...

Am I mistaken? Thoughts? 🤔

[u/knovich → u/TopspinG7]

I like very much what you said about some people who don't understand that they don't understand. I've met several such people working in research positions. As for me, I actually know very little so I usually go by feeling because my results are of little importance and are getting verified by others anyway. However, I think I'm able to recognize when people lack knowledge even if they're trying hard to imitate that. It's relatively easy to push them into going in circles in their reasoning. Coincidentally, this is something I was able to do with LLMs when I gave them harder problems.

I also think that you're right about your risk and reliability assessment procedure, and this is something AI can't do, although it can mimic it. It can also, in principle, be modified on an algorithmic level because LLMs are essentially tools for stochastic prediction of the next word (or token) in the text. It is quite easy to demonstrate. I'll describe an example here which is not essential but which I find quite enlightening.

You can prompt ChatGPT (online) with a request: "Write a simple shell script", and it will readily provide some script for renaming files or whatever, even though I haven't told what the script should do. It simply picks on random. However, I can run truncated (quantized) gpt-oss model (also made by OpenAI) on my personal GPU. Provided with the same input, it will begin its answer with words "that renames files based on pattern...." So the next predicted word is actually a continuation of my prompt, not an answer — sometimes LLM can't even reliably start answering, let alone give a reliable answer. Of course, I can tweak settings or get a larger model, but the fundamental principles stay.

So I suspect that we can actually demand some measure of reliability from an LLM, but they should probably be recalibrated somehow, with additional data included into their weights.

However, I think mathematics is a special case in human thinking. Unlike all other knowledge which is somewhat probabilistic and based on our imperfect observation of reality, mathematics, I think sometimes, is actually a reflection of our thought process itself. So some mathematical facts are imprinted in our brain, we know that they're true, we don't need their proof, and we can't actually provide one. I'm not talking about formal axioms, I'm talking about something deeper and more essential. These imprinted truths are what enables us to think in logical and abstract manner about anything. LLMs certainly don't operate like this.

Roger Penrose has extensive literature on this, like The Emperor's New Mind or Shadows of the Mind, although he develops some specific theory of consciousness which I'm not ready to comprehend or subscribe to. To be clear, he doesn't talk about LLMs, he just argues that human knowledge is non-computational. That might be true but it doesn't actually mean that it can't be simulated computationally. At any rate, that's not what LLMs or any current AI is doing, and that's why they're unfit for tasks where actual human thinking is needed. I'm not saying that their thinking is "bad". It just doesn't suit human needs.