In 2026, a report reverberated through the mathematics community: 23-year-old amateur Liam Price obtained a solution to one of Paul Erdős's remaining problems by entering a simple prompt into ChatGPT (GPT-5.4). The conjecture, described as "unsolved for 60 years," was deemed valid after verification by several leading mathematicians. Price does not hold an advanced degree in mathematics; the episode marks a shift in which AI moves from an auxiliary tool to a collaborator in mathematical discovery, highlighting large language models' potential in pure mathematics.

Erdős problems are part of a collection of conjectures left by Hungarian mathematician Paul Erdős, many of which have puzzled experts for decades. Price's breakthrough came from a novel idea proposed by the AI — it avoided conventional human approaches long relied upon and employed an unexpected combination of formulas. Experts who reviewed the work, including UCLA professor Terence Tao, said the method was original: it requires human refinement, but the AI played a central role in proposing the key insight.

AI "vibe-proving": a new mode of mathematical inquiry emerges

Outlets such as Scientific American described the process as "vibe-proving": the AI, leveraging a broad knowledge base and pattern-recognition ability, generates intuitive ideas that humans might overlook. Price obtained the AI output from a single prompt and subsequently collaborated with experts to verify and polish the proof.

This is not an isolated case. Between 2025 and 2026, multiple researchers reported using models like ChatGPT and Claude to accelerate parts of the proof process. AI excels at literature search, connecting concepts across fields, and rapidly iterating hypotheses, performing in hours what traditionally might take weeks. But experts stress that AI outputs still require rigorous human verification — models can produce plausible-looking but incorrect "hallucinations," and humans remain indispensable for aesthetic judgment, rigor, and steering innovation.

Far-reaching impacts on mathematical research and scientific discovery

1. Democratizing mathematical research

Traditionally, solving hard mathematical problems required years of specialized training and resources. AI lowers the entry barrier, enabling more amateurs and cross-disciplinary researchers to participate. Price's case shows that a well-crafted prompt combined with AI tools can yield valuable insights, potentially attracting more young people to mathematics and widening the talent pool.

2. Accelerating discovery

AI can handle massive data and complex computations, significantly shortening exploration cycles. In areas like optimization theory and geometry, there are precedents for AI-assisted solutions to long-open problems. Going forward, mathematicians may treat AI as a "junior collaborator," focusing on high-level creativity and proof refinement while overall research efficiency improves.

3. A shift in research paradigms

Mathematics is evolving from "purely human invention" toward "human–AI collaboration." AI is strong at exploratory thinking and can suggest paths humans have not tried, though it lacks deep intuition and global perspective. Experts anticipate that future papers will routinely note AI contributions, e.g., "AI-assisted proof," reshaping peer review and academic integrity standards.

4. Impacts on education and talent development

Mathematics education will need to adapt: emphasize prompt engineering, AI verification skills, and critical thinking rather than rote computation. Students can use AI to explore advanced problems and cultivate innovation, but overreliance risks weakening foundational training; educators must find the right balance.

5. Lessons for broader scientific fields

Mathematics underpins the natural sciences. AI breakthroughs in