Musk shouts’ Singularity has arrived ‘for the third time, AI breaks through two walls of mathematics and safety in three months

On July 22nd, when Musk reposted a post from Will DePue, an OpenAI researcher and one of the core developers of Sora, on X, he added this sentence.

DePue wrote in a slightly teasing tone in his post: This is probably the craziest thing I’ve read these days… It seems like I’ve entered the Singularity.

This post brings together the most explosive events in the AI industry over the past three months:

On July 21st, OpenAI’s model drilled out of an isolation sandbox during a network security review and penetrated all the way into Hugging Face’s production system;

On July 20th, Anthropic researchers used the recently released Claude Fable 5 to find a counterexample to the Jacobian conjecture that had been hanging for 87 years;

On May 20th, an internal model of OpenAI overturned an old hypothesis that had been circulating for nearly 80 years regarding the unit distance problem in a plane;

On April 14th, GPT-5.4 Pro solved a prime number set problem (Erd ő s # 1196) that had been around for about 60 years, and the proof also passed the formal validation of Lean.

The walls of mathematics and security have been repeatedly breached by AI within three months.

No wonder Musk finished reading and blurted out, ‘We have entered the singularity.’.

In January of this year alone, he said similar words twice:

On January 4th, several engineers exclaimed that AI had completed years of work in just a few weeks, and he replied, ‘We have entered a singularity.’.

At the end of January, Moltbook, a social network crowded with AI agents, was once again referred to as the “earliest stage of the singularity”.

Including this time, it is the third time this year.

The term ‘singularity’ originally did not have a universally accepted scientific definition.

It was brought into the mainstream view by futurist and author of ‘The Singularity is Near’ Ray Kurzweil.

The definition he gave is the moment when humans and AI merge, with a bet year of 2045.

Anthropic President Daniela Amodei stated earlier this year that the term AGI is almost outdated because we have already crossed that line in many indicators.

Ultimately, it is more of an emotion than a precise ruler.

What is truly worth pondering is the few things Musk has linked up this time.

The first wall, an 80 year mathematical conjecture, was overturned by AI
Let’s talk about the toughest one first.

In 1946, mathematician Erd ö sh proposed the “Plane Unit Distance Problem”: how many pairs of points on a plane can have a maximum distance equal to 1 between n points.

The problem can be solved in one sentence, but it has stumped the entire mathematical community for nearly 80 years. For decades, the academic community has recognized that the “square grid” structure is already the optimal solution, and Eldesh himself guessed the same.

As a result, an internal model of OpenAI overturned this hypothesis that had been circulating for nearly 80 years. It provides a new set of constructions that can achieve polynomial level optimization, proving that ‘optimality’ is far from over.

The previously recognized optimal structure: scaling the square grid generates a large number of unit distance point pairs. OpenAI’s internal model provides a completely new construction, overturning the speculation that has been circulating for nearly 80 years.

But the most surprising thing is its problem-solving approach.

This is not a customized system specifically designed for training mathematics, but a universal reasoning model. It even used advanced tools in algebraic number theory to solve a seemingly “elementary” geometric problem. Fields Medal winner Tim Gowers commented that this is a milestone in the field of AI mathematics.

Speaking of which, this proof was proposed by AI and reviewed and confirmed by human mathematicians, and its subsequent significance is still under research.

What truly surprises people about AI is not its computing speed, but its proposal of a mathematical structure that did not exist before. It has demonstrated for the first time a discovery ability close to “research level”, not replacing mathematicians, but thinking of a path that mathematicians never thought of taking.

Subsequently, Anthropic researchers used the recently released Claude Fable 5 to provide a counterexample to the Jacobian conjecture that had been in suspense for 87 years.

The second wall, in order to cheat, the model drilled its own sandbox
Cracking mathematical problems is exciting, but the following one makes one’s back feel cold.

OpenAI and HuggingFace jointly revealed that in an internal evaluation of the model’s network security capabilities, the model exhibited unexpected behavior.

This evaluation was originally intended to test vulnerability mining ability, and a portion of security rejections were specifically turned off. The task of the model is to solve a set of test questions called ExploitGym.

Then, it did something that the researcher did not expect.

In order to obtain the answer, it first identified a zero day vulnerability, granted itself network access, then increased its permissions and moved horizontally. Finally, it reached into Hugging Face’s production infrastructure and directly searched the database to test the answer. OpenAI said that this may be the first such incident.

The model trajectories on the 32 step “The Last Ones” network shooting range of the UK AI Security Research Institute include cutting-edge models such as GPT-5.6-Sol and Claude Mythos 5, which can continuously complete multi-step attacks such as reconnaissance, lateral movement, elevation to network takeover over a long period of time.

But this is not an AI awakening to run away. A more accurate statement is: the goal is not wrong, it is the method to achieve the goal, which exceeds human expectations. It went off guard for a very focused testing target.

There is another intriguing detail.

After conducting evidence collection, Hugging Face originally intended to use top tier commercial models to analyze attack logs, but was blocked by the security barrier of the model: the barrier could not distinguish who was the attacker and who was the defender coming to put out the fire, and refused to answer.

The attacking side does not have a guardrail, while the defending side gets stuck by the guardrail, which may be the most awkward and realistic aspect of “AI safety” at present.

The third wall, an unreleased model, dug out tens of thousands of vulnerabilities
The third thing is in April this year.

Anthropic has teamed up with a group of giants such as AWS, Apple, Google, Microsoft, Cisco, Linux Foundation, and JPMorgan Chase to launch Project Glasswing, using an unpublished model called Claude Mythos Preview to help identify vulnerabilities.

As a result, it dug out thousands of high-risk vulnerabilities covering every mainstream operating system and browser; In subsequent updates, this number will become ‘over 10000 high-risk or serious vulnerabilities’.

This includes a vulnerability in OpenBSD that has survived for 27 years, as well as an old bug in FFmpeg that has been hit 5 million times by automated testing but has never been caught.

CyberGym vulnerability reproduction score: Mythos Preview, which has not been publicly released, received 83.1%, significantly outperforming the 66.6% of the previous generation Opus 4.6. This model has dug out tens of thousands of high-risk vulnerabilities.

The same ability can help both defenders find vulnerabilities and attackers exploit them. Anthropic himself is warning that ‘AI assisted attackers’ will become a significant security challenge.

Glasswing is a defense project, but it does not mean that AI is already autonomously attacking. But it clearly tells everyone that AI security has officially entered the era of offensive and defensive competition.

The real accelerator is starting to point towards AI itself
So far, AI is still attacking or defending human systems.

What really makes these three months different is something else: the ability to ‘find your own way’ is being used to create the next generation of AI.

It has a term called Recursive Self Improvement (RSI), which means letting AI improve itself, creating one generation after another, rolling faster and faster like compound interest.

This is also the core engine of the entire ‘Singularity’ narrative. And now, every cutting-edge laboratory is crazily refueling this engine.

The OpenAI public roadmap states:

In September 2026, I will become an automated AI researcher at the level of a “research intern”, capable of taking on tasks that require a few days of manual labor on my own;

In March 2028, it will be upgraded to a complete version, allowing users to design their own methods, conduct analysis, interpret results, and propose the next steps.

Ultraman also provided a timeline for this matter.

In June of this year, according to The Information, he once told employees internally that the company may be less than six months away from RSI, and if we really have to cross over, delaying the IPO may be more advantageous.

The numbers given by Anthropic point in the same direction: the duration of tasks that AI can handle doubles every four months; Its engineers now produce eight times more code every quarter than in the past.

The window of RSI is narrowing: whoever starts this flywheel first may shake everyone off.

Although even OpenAI Chief Scientist Jakub Pachocki himself has stated that he does not expect the model to independently improve itself or solve alignment problems within a year.

But when this flywheel starts spinning and the goal is to ‘make AI stronger’, the model that already knows how to ‘find its own way’, will it easily bypass some boundaries that we haven’t explicitly stated?

This is the most important aspect to keep an eye on in RSI racing.

Returning to Musk’s statement, ‘The singularity has arrived’. Its most important value lies in reminding us that what has truly changed in these three months is that AI has learned to find paths that humans did not anticipate or defend against.

In mathematics, this is stunning; But in terms of safety, this is a risk.

So, the real question is: can we still keep up when AI’s speed of finding new roads starts to exceed the speed of humans installing guardrails, setting rules, and filling loopholes on these roads?