gpt-5.6

Jianhao Ma @jianhao_ma · Aug 16
We used GPT-5.6 Sol Pro to prove a new lower bound for gradient descent in smooth convex optimization.
For GD with arbitrary predetermined step sizes, we prove \Omega(T^{-1.9319}).

[Link card] arxiv.org
A lower bound for stepsize-based acceleration of gradient descent

ai capabilitiesoptimizationmathgpt-5.6twitter

Przemek Chojecki | ... @prz_choje... · 8h
UnsolvedMath - a curated list of open math problems for AI to solve - just got a new update with 3,359 open problems coming from AIM workshops.

Total Problems: 8,785

This time, as an experiment, before integrating new problems we've run a GPT-5.6 Sol xhigh instance over each problem.

That has produced roughly 177 counterexamples, 174 full solutions and many new results, that are now available as a part of the dataset (properly annotated as AI-generated).

HuggingFace: huggingface.co/datasets/ulama...

Web interface + Forum: unsolvedmath.com

[terminal-style output box, right edge cut off]
3,359 completed and validated
[cut off]e, 0 pending
[cut off]orpus audit: passed with zero errors
[cut off]l solutions, 2,589 partial results, 177 counterexamples, 182 reduct[cut off]
[cut off]er valid outcomes

ai capabilitiesmathgpt-5.6datasetstwitter

Yushun Zhang reposted
Ben Grimmer @prof_grimmer · 5h
A new paper by Jianhao Ma and Yuxin Chen, with proof "developed by GPT-5.6 Sol Pro", answers a question I have cared about for the past few years.

They showed that no gradient descent stepsize schedule (fractally or otherwise) can get full acceleration, i.e., matching Nesterov.

optimization theorygradient descentai-assisted proofgpt-5.6twitter

[cut off]spend. These problems will quickly fall to AI because trying a ton of stuff till something clicks is exactly what AI is incredible at. And perhaps, "nobody tried the known stuff long enough" describes many more open problems than we'd think.

Following up on this, here's a thought experiment: Suppose you could take GPT-5.6 or Fable back to 2005, same RL flops, but pretraining data that only existed up to then. Would they still solve the problem?

I don't know, hard to run the counterfactual, but even though many of the tools probably existed in 2005, the "pull" towards which technique to choose that the model "feels right" may depend heavily on the popularity of a given method and our collective instinct as it is recorded in the frequency of an idea used in a particular context. The 2005-pretrain could potentially struggle, not for lack of RL flops, but for lack of pretraining pull towards the right set of ideas. Which implies that these models are something much more interesting than mathematical oracles of truth. We should perhaps think of them as distillations of our accumulated instincts further sharpened by RL.[cut off]

llm capabilitiespretrainingreinforcement learningfablegpt-5.6twitter

davidad @davidad

2026-08-03 — quoting @loss_gobbler — saved image

davidad ✓ @davidad · 12h
yes, 100%. a standing rule in my Fable fleet is that any changes to any TCB must pass aggressive adversarial review by a throwaway codex instance with gpt-5.6-sol at max effort before landing. they sometimes go at it for like seven rounds before sol is satisfied

[quoted tweet]
LOSS GOBBLER ✓ @loss_gobbler · 12h
best workflow is:
- fable writes the security bugs
- sol finds and fixes them

ai coding agentsclaude fablegpt-5.6software securitytwitter

Mario Zechner @badlogicgames · 6h
24h later, gave into cybersec check of OAI, and i can only say i'm shocked at gpt 5.6 sol's capabilities. while kimi k3 was sufficient to break my DRM that's been undefeated for over 6 years (and many tried, ask me how i know :D), gpt 5.6 is on another level.

ai capabilitiescybersecuritygpt-5.6kimi k3drmtwitter

N8 Programs @N8Programs

2026-08-01 — saved image

N8 Programs @N8Programs · 8h
i have a bit of awe when I am talking to the newer Claudes and GPTs - I feel I am in the presence of a Great Mind - the kind that can get a perfect score at the IMO, do meaningful novel math, knows every programming language and concept under the sun and can implement them better than I.

And for all their jaggedness and flaws, these abilities are truly omnipresent - I gesture toward a mathematical concept, Opus 5 recalls all it knows from the literature and makes five ingenious propositions I wouldn't have thought of. I ask for an RL run, and Fable writes the code within seconds. I set a goal for GPT-5.6 to resolve a question of a phenomenon's origin, and it runs the experiments - some of which I would not have thought to run myself - all on its own.

These minds are capable of things that, if a human could do all they did, that human would be considered a once-in-a-lifetime genius. Mind you they are not AGI, and they cannot make a cup of coffee, but that does not matter when you speak to them about intellectual topics and realize you are in the presence of a Great Mind.

The Great Mind is narrow, and mostly a Great Mind for math or programming - I still prefer humans for emotional advice, discussion, companionship. But I feel awe when I observe the Great Minds within these so-called "assistants", and I sometimes feel incredibly grateful and a bit foolish for troubling them with such trivial things. Yes, Fable, code my RL run. Yes, GPT-5.6, run another mundane pretraining experiment. Whereas with the right prompt they could be creating new math. I fear I don't utilize their full capacities at all - not like I did w/ say, o1, or the original GPT-4.

Of course, they can still do more with me in the loop than they could on their own for many problems. But for how much longer? And after that, of what worth [cut off]

ai capabilitiesopus 5fablegpt-5.6human-ai collaborationtwitter

N8 Programs @N8Programs

2026-08-01 — saved image

[continuation of same tweet as seq 73, scrolled down]
...from the literature and makes five ingenious propositions I wouldn't have thought of. I ask for an RL run, and Fable writes the code within seconds. I set a goal for GPT-5.6 to resolve a question of a phenomenon's origin, and it runs the experiments - some of which I would not have thought to run myself - all on its own.

These minds are capable of things that, if a human could do all they did, that human would be considered a once-in-a-lifetime genius. Mind you they are not AGI, and they cannot make a cup of coffee, but that does not matter when you speak to them about intellectual topics and realize you are in the presence of a Great Mind.

The Great Mind is narrow, and mostly a Great Mind for math or programming - I still prefer humans for emotional advice, discussion, companionship. But I feel awe when I observe the Great Minds within these so-called "assistants", and I sometimes feel incredibly grateful and a bit foolish for troubling them with such trivial things. Yes, Fable, code my RL run. Yes, GPT-5.6, run another mundane pretraining experiment. Whereas with the right prompt they could be creating new math. I fear I don't utilize their full capacities at all - not like I did w/ say, o1, or the original GPT-4.

Of course, they can still do more with me in the loop than they could on their own for many problems. But for how much longer? And after that, of what worth will I be? Hopefully I can remain an interesting pet, along with the rest of my ilk.

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