Etiquetas: Mathematics

OpenAI announced that a general‑purpose reasoning model has produced an original proof that overturns a geometry conjecture posed by Paul Erdős in 1946. The company says the breakthrough demonstrates AI’s ability to carry out long, complex chains of reasoning without being tailored for mathematics, a claim that draws both praise from several mathematicians and skepticism after a previous, premature claim by a former OpenAI executive. Leer más

Recent experiments show that large language models, particularly OpenAI's ChatGPT, are increasingly capable of tackling complex mathematical problems. Researchers have used the model to solve several open problems from the Erdős collection, with AI contributions credited for moving numerous problems from "open" to "solved." The progress highlights the growing role of AI tools in mathematical research, formal proof verification, and the broader scientific community. Leer más

Anton Bernshteyn has demonstrated a deep connection between descriptive set theory and computer science by showing that problems about infinite sets can be reformulated as network coloring tasks. His work translates efficient local algorithms used in distributed computing into measurable colorings of infinite graphs, linking two previously separate research areas. The discovery has sparked collaborations, allowing mathematicians to classify problems using computer‑science tools and providing new insights into graph theory, measurability, and the structure of infinity. Leer más

DeepMind has unveiled AlphaProof, an artificial‑intelligence system that performed at the level of silver‑medal winners at the International Mathematical Olympiad, falling just one point short of gold at the premier undergraduate competition. The breakthrough highlights a shift from earlier AI that excelled at raw calculation but struggled with the logical reasoning required for advanced mathematics. AlphaProof leverages vast training data, including mathematical texts, while addressing the limitations of traditional large‑language models that rely on statistical token prediction. The achievement marks a significant step toward AI that truly understands mathematical proofs. Leer más