- AI proved an original Erdős problem in January 2026 using formal logic.
- Tao confirmed the solve but noted these are neglected, not frontier problems.
- GPT-5.2 scores 77% on Olympiad problems but only 25% on open research.
After months of embarrassing overclaims about AI solving famous problems, a few real breakthroughs emerged in January 2026.
The question now is what they actually mean.
Hossenfelder traces the story back to October 2025, when OpenAI's Kevin Weil posted that GPT-5 had solved ten previously unsolved Erdős problems.
The claim spread fast. Then it collapsed.
What are the Erdős problems?
Hungarian mathematician Paul Erdős left behind over 1,000 conjectures when he died in 1996. They range from deep challenges to quirky puzzles nobody ever seriously tackled. Thomas Bloom at the University of Manchester maintains a website tracking which ones remain open.
OpenAI's Math Claims Lasted Hours
Bloom quickly clarified that "open" on his site simply meant he personally didn't know of a solution. GPT-5 hadn't proved anything.
It had found existing papers in the literature that Bloom hadn't catalogued. Google DeepMind's Demis Hassabis called the whole episode "embarrassing." Meta's Yann LeCun was less polite.
But Hossenfelder doesn't stop at the embarrassment. She follows the story into January 2026, when something different happened.
January Brought Genuine Proofs
ChatGPT Pro, working with a formal verification tool called Aristotle, actually solved Erdős Problem #728 autonomously. Fields Medalist Terence Tao engaged with the proof, contributing suggestions and locating additional references.
The proof was original, formalized in the Lean programming language, and not replicated in existing literature.
Key figure
17+
Erdős problems now formalized in Lean
Three problems fell in a single week in January, according to TechCrunch's reporting. Tao has been tracking the surge on his GitHub page. The pattern is real.
Tao Says These Are the Easy Ones
Here's what the video doesn't emphasize: Tao's own assessment is cautious. He notes that the more AI involvement in a proof, the simpler the underlying problem tends to be.
These are "long tail" problems that nobody prioritized, not frontier challenges. GPT-5.2 scores 77% on Olympiad-style questions but only 25% on open-ended research problems.
It's 2026 and the hottest new mathematical technique is finding the PDF.
Sabine Hossenfelder
Hossenfelder's own experience matches this. She finds ChatGPT Pro well ahead of competitors in mathematics, calling it "a completely different level" from Gemini, Claude, or Grok.
But its logical reasoning still breaks in predictable ways. It uses bounds incorrectly. It invents convenient assumptions.
A proof from ChatGPT is "as likely to be correct as wrong."
The honest framing, which Hossenfelder lands on, is that AI mathematics works best as a discovery tool.
It can find relevant papers, apply known techniques to overlooked problems, and clear backlogs that human mathematicians never prioritized. Hossenfelder has previously explored the deeper problems that prevent current AI from doing more.
Are We Really Seeing An "AI Mathematics Revolution?"
More on AI & Maths
AI Mistakes May Be Mathematically Unavoidable
New research suggests that AI errors in healthcare aren't bugs to fix–they're baked into how the systems learn from data.
→Whether that qualifies as "revolution" depends on your expectations.
Recent experiments confirm the limits. A new study tested leading AI models on original, unpublished math research problems.
The models failed almost every one. Pattern-matching skills don't transfer to genuine discovery when training data offers no shortcuts.
Hossenfelder predicts mathematicians will eventually become obsolete, like human calculators did. But she puts that years away.
Go Deeper
- Terence Tao on Erdős Problem #728 - The Fields Medalist's assessment of the first genuinely autonomous AI solve
- AI models are starting to crack high-level math problems - TechCrunch on the January 2026 surge
- Tao warns the win says more about speed than difficulty - The nuanced view on what these solves actually mean
- Erdős Problems - Thomas Bloom's database tracking the conjectures
Fact Check: Claim-by-Claim Verification Verified
The article's major claims are factually accurate, including the October 2025 false claims controversy, the January 2026 genuine AI proof of Erdős Problem #728, Terence Tao's involvement and cautious assessment, and GPT-5.2's performance metrics.
Commentary
- The article states "three problems fell in a single week in January" based on TechCrunch reporting. While multiple Erdős problems were solved in January 2026 (Problem #728, #729, and #397 are mentioned in sources), the exact phrasing "three problems in a single week" should ideally cite a specific date range rather than relying solely on TechCrunch's report date.
- The article refers to "ChatGPT Pro" solving the problem, but technical sources clarify it was GPT-5.2 Pro (the latest OpenAI model) working in conjunction with Aristotle by Harmonic. The article's simplified language is acceptable for popular science but conflates product naming.
- The pullquote attributed to Hossenfelder ("It's 2026 and the hottest new mathematical technique is finding the PDF") could not be independently verified from her published video transcript, though it reflects the tone and substance of her commentary about AI's current limitations in genuine discovery.
- The article notes Tao "has been tracking the surge on his GitHub page"—while Tao has been publicly discussing these developments on Mathstodon and other platforms, the specific reference to a GitHub tracking page was not independently confirmed in available sources.
Sources used for verification
Academic/Peer-reviewed:
- Resolution of Erdős Problem #728: a writeup of Aristotle's Lean proof - arXiv
- Terence Tao on Erdős Problem #728 - Mathstodon
Other reliable sources:
- Terence Tao warns the win says more about speed than difficulty - The Decoder
- OpenAI's 'embarrassing' math - TechCrunch
- Leading OpenAI researcher announced a GPT-5 math breakthrough that never happened - The Decoder
- GPT-5.2 Solves Erdős Math Problem – But Did It Really? - Byte Iota
- Paul Erdős | Hungarian Mathematician & Number Theory Pioneer - Britannica
- The AI Maths Revolution Has Begun - Sabine Hossenfelder YouTube Channel
Fact-checked by Perplexity Sonar Pro on 2026-02-15
