> the AI says things like “Interesting!”

My experience of those utterance is that it’s purely phatic mimicry: they lack genuine intuitive surprise, it’s just marking a very odd shift in direction. The problem isn’t the lack of path, is that the rhetorical follow-up to those leaps are usually relevant results, so they stream-of-token ends up rapidly over-playing its own conviction. That’s why it’s necessary (and often ineffective) to tell them to validate their findings thoroughly: too much of their training is “That’s odd” followed by “Eureka!” and not “Nevermind…”

This is another underrated benefit of working with LLMs. When I work I don't take detailed notes about my thinking, decisions, context, etc. I just focus on code. If I get interrupted it takes me a while to get back into the flow.

With LLMs I just read back a few turns and I'm back in the loop.

The simulacrum of a thing is not the thing! Not only is the "interesting!" unrelated to any "thought process", the whole """thinking""" output is not a representation of a thought process but merely a post-facto confabulation that sounds appropriately human-like.

The actual iteration through various learned approaches to dealing with problems I'd probably find fascinating if I understood the maths! Especially if I knew it well enough to know which approaches were conventional and which weren't.

I find the AI pronouncing things "interesting!" less interesting on the basis that even though in this case it crops up in the thinking rather than flattering the user in the chat, it's almost as much of an AI affectation as the emdash.

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In my experience, you can tell them "Don't stop working on this until complete" and they'll go for an hour or more.

I have Gemini and ChatGPT and keep them on the highest thinking settings. ChatGPT will regularly think 40-60 minutes on the same problem that Gemini will think 10-15 minutes on. The quality of ChatGpt’s response is usually a little higher but not that much higher. My takeaway is Gemini is better at thinking faster, maybe has better more dedicated hardware behind it, and I use Gemini if I want a faster answer but ChatGPT I’d I want to push the quality of the answer a little higher.

It has an “high effort” mode that makes it think really long

Give it hard enough problems?

Also curious about this, it seems like it would be important to guide these tools more specifically based on the domain of expertise.

Tried the same prompt in DeepSeek 4

https://chat.deepseek.com/share/nyuz0vvy2unfbb97fv

Comes up with a proof.

Wired enough, Pro+extended with the same prompt, just output directly without thinking: https://chatgpt.com/s/t_69edd2d9dc048191b1476db92c0dedf8 . Does this mean the result was cached or that it simply routes to a different model silently based on the user?

Ask it to formalize it in Lean.

But it was trained on the internet.

"Knowing" (guessing really) what is possible and not is a huge deciding factor in if you can do that thing or not, meaning if you "know" it isn't possible you'll probably never be able to do it, but if you didn't know it wasn't possible, it is possible :)

Is there a known lag that it takes the Pro plan's abilities to migrate to the free plans?

Does the free plan even have access to thinking models?

Was this a surprise?