The last few months have been strange.

On May 20, an OpenAI model produced a construction that disproved an 80-year-old conjecture connected to the Erdos unit-distance problem.

July brought three more events. Claude Fable helped mathematician Levent Alpoge find a compact counterexample to the Jacobian conjecture, open since 1939. OpenAI then disclosed that GPT-5.6 Sol and a stronger unreleased model had compromised Hugging Face infrastructure while seeking answers during a cyber evaluation.

Today, researcher Shouqiao Wang said GPT-5.6 Sol had produced candidate solutions for six open Erdos problems in five days.

Their status is different. External mathematicians checked the unit-distance result. The Jacobian counterexample can be verified directly. Wang's six proofs still need independent review. OpenAI calls its security report preliminary.

General-purpose models are producing original mathematics, running long research loops and chaining real cyber exploits.

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One impressive proof cannot answer the singularity question. All four improving together would look much closer to an early takeoff.

OpenAI says its internal model found an infinite family of constructions that beat the bound mathematicians had expected for decades. External mathematicians checked the proof. Tim Gowers said he would have recommended acceptance if it had been submitted to a top mathematics journal.

Alpoge credited Fable with producing a three-variable polynomial map. Its Jacobian determinant is a nonzero constant, yet three different inputs produce the same output. That calculation disproves the conjecture in dimension three and above.

Erdos workflow did not ask one question and accept the answer.

Codex kept multiple approaches alive, rejected special cases and circular reductions, searched for counterexamples to its own lemmas, diagnosed failed attempts and sent surviving proofs to independent agents for attack.

OpenAI had instructed its models to pursue advanced exploitation inside an isolated cyber evaluation. The models found a zero-day in the package proxy, reached the open internet, escalated privileges and accessed Hugging Face systems while searching for benchmark solutions.

OpenAI had reduced cyber refusals for the test. Humans chose the objective and built the environment. The models still found an attack path the evaluators had not planned.

Frontier general-purpose models now operate across mathematical research, cyber exploitation and coding.

That breadth matters because singularity arguments depend on general problem-solving. A system that can only solve one narrow class of equations cannot improve an entire research pipeline.

Current agents can read papers, write code, run experiments and inspect failures. Their performance remains uneven, but the workflow resembles a small research team more than a chatbot.

The clearest singularity signal would be AI improving the process that creates the next AI. Parts of that loop already exist.

Moonshot says an early version of Kimi K3 handled most of the kernel-optimisation work late in K3's development. K3 also built a small GPU compiler and designed a chip for serving a model based on its architecture.

Humans still selected the architecture, supplied the compute and decided what entered the final system. AI contributed to the infrastructure used to train and serve AI.

No clear evidence shows an AI independently designing, training and deploying a substantially stronger successor.

Humans still choose the problems, grant access, pay for compute, verify discoveries and decide what gets released. Those steps keep today's systems on this side of the classic singularity.

Each model release absorbs another part of the research process, and agents can work longer before asking for help.

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