January 14th, 2026. The day the number crunchers finally started out-crunching us. Not just with spreadsheets and algorithms, but with the kind of abstract, creative problem-solving that used to be the exclusive domain of tweed-clad geniuses scribbling on blackboards. OpenAI’s GPT-5.2 and Google’s AlphaEvolve, two titans of the AI world, just cracked a significant set of Paul Erdős’s notoriously difficult unsolved mathematical problems.
For the uninitiated, Paul Erdős was a Hungarian mathematician who lived and breathed numbers. He wasn’t just good at math; he was math, wandering the globe like a mathematical Johnny Appleseed, posing problems, collaborating with anyone who’d listen, and leaving behind a legendary collection of over 1,000 unsolved conjectures. These weren’t your average textbook questions; they were deep, fundamental puzzles that had stumped mathematicians for decades. Think of them as the mathematical equivalent of the Gordian Knot, or perhaps the final level of a super-hard video game that nobody could beat.
And now, AI has not only beaten the game, but it’s also started designing its own levels. Since Christmas Day 2025, fifteen of Erdős’s problems have been solved, and AI models contributed to eleven of those solutions. Eleven! That’s like Spock suddenly becoming a stand-up comedian – a complete and utter paradigm shift.
So, what exactly happened? How did these digital brains manage to achieve something that had eluded the best human minds for so long? The answer, as always with AI, is a complex interplay of factors. First, the AI models themselves have become exponentially more powerful. GPT-5.2 and AlphaEvolve are not your average language models; they possess enhanced reasoning abilities that allow them to navigate the intricate world of abstract mathematical concepts. They can see patterns, make connections, and formulate hypotheses in ways that were previously unimaginable.
But brute force alone isn’t enough. Even the most powerful AI needs tools and guidance. That’s where formal verification systems like Lean and Harmonic’s Aristotle come in. These systems act as rigorous fact-checkers, meticulously verifying every step of a mathematical proof to ensure its accuracy and reliability. Think of them as the Vulcan logicians to the AI’s more intuitive, sometimes impulsive, Captain Kirk. This collaboration between AI intuition and formal verification is what made the breakthroughs possible.
The process is a bit like a super-charged version of collaborative problem-solving. The AI generates potential solutions, and the verification system ruthlessly tests them, flagging any errors or inconsistencies. This iterative process continues until a valid proof is found. It’s like a digital Socratic dialogue, with the AI and the verification system pushing each other to reach a deeper understanding of the problem.
Implications: Are We Witnessing the Dawn of True AI?
The implications of this achievement are profound. It suggests that AI systems are making significant strides towards general intelligence, demonstrating capabilities that were once thought to be the exclusive domain of human mathematicians. The ability of AI to autonomously solve complex problems indicates a potential revolution in mathematical research. Imagine a future where AI acts as a powerful tool for mathematical discovery, generating new theorems, identifying hidden patterns, and accelerating the pace of scientific progress. It’s like giving mathematicians a superpower, allowing them to explore uncharted territories of the mathematical universe.
Of course, there are caveats. The work remains within a constrained domain, and human verification is still required. But even with these limitations, the implications for the future of AI in abstract reasoning and problem-solving are enormous. This development may accelerate timelines for developing AI systems capable of operating autonomously in complex domains, from scientific research to engineering design to even, dare we say it, writing catchy blog posts (though hopefully not this one!).
The Ethical and Philosophical Quandaries
This raises some important questions. What does it mean to be intelligent? If an AI can solve complex mathematical problems, does that mean it’s truly “thinking”? And if so, what are the ethical implications of creating machines that are capable of surpassing human intelligence? These are not just abstract philosophical questions; they have real-world consequences for how we develop and deploy AI. As AI becomes more powerful, we need to ensure that it’s aligned with human values and that it’s used for the benefit of humanity. It’s the classic “with great power comes great responsibility” scenario, only this time, the power is exponentially greater.
And let’s not forget the economic impact. If AI can automate mathematical research, what does that mean for the future of mathematicians? Will they become obsolete, replaced by tireless digital algorithms? Or will they adapt and evolve, using AI as a tool to enhance their own abilities? The answer, most likely, is a combination of both. Some jobs will be automated, but new opportunities will also be created. The key is to prepare for these changes by investing in education and training, ensuring that people have the skills they need to thrive in the age of AI.
The Road Ahead
The cracking of Erdős’s problems is not just a technological milestone; it’s a cultural one. It’s a reminder that AI is rapidly changing the world around us, and that we need to be prepared for the challenges and opportunities that lie ahead. It’s a bit like that scene in “2001: A Space Odyssey” when the ape-man discovers how to use a bone as a tool. It’s a moment of profound transformation, a glimpse into a future where the boundaries between human and machine intelligence become increasingly blurred. And while that future may be uncertain, one thing is clear: it’s going to be fascinating.
Discover more from Just Buzz
Subscribe to get the latest posts sent to your email.
