Showcasing practical examples, projects, and case studies demonstrating how AI models and tools are being applied across various fields.
The fraction 355/113 gets astonishingly close to π using just three digits in its denominator. It also points to a question mathematicians have struggled with for decades: how often can fractions achieve that kind of accuracy as their denominators grow? OpenAI’s manuscript The Irrationality Exponent of π Is 2, dated September 24, 2026, claims an … Read more
A cube looks ordinary until you ask a question mathematicians have spent decades trying to answer: can any symmetric convex shape beat it at a particular geometric balancing act? The Mahler conjecture concerns a shape and its polar, a mathematical partner whose size changes in response to the original. Multiply their volumes, and you get … Read more
A flat surface, a fixed distance, and a handful of colors. That sounds like an afternoon puzzle. Mathematicians have been wrestling with it since 1950. The Hadwiger–Nelson Problem asks how many colors are needed to color every point in the plane so that points exactly one unit apart never share a color. OpenAI’s manuscript, The … Read more
Randomness is a useful shortcut in computing. A few coin flips can help a memory-starved algorithm explore possibilities without recording every step. For decades, theoretical computer scientists have asked whether those random bits provide genuine extra power when an algorithm has almost no working memory. OpenAI says the answer is no. In a 108-page manuscript … Read more
Hilbert’s 10th problem has acquired a striking AI twist. OpenAI has published a proposed proof concerning its rational-number extension: whether an algorithm can always determine if a polynomial equation has a solution made of fractions. The paper’s answer is no. That sounds odd for a breakthrough. An AI system helps produce mathematics explaining why algorithms … Read more
A graph can give every vertex exactly two selected connections and still leave you going around several separate loops. Getting one loop through the entire graph is the hard part. For decades, that distinction has kept a deceptively simple mathematical question open. Barnette’s Conjecture asks whether every cubic, bipartite, planar, 3-vertex-connected graph contains a Hamiltonian … Read more
The improvement is so small that rounding it casually would erase it. The mathematical claim is large enough to challenge a conjecture that has stood since 1971. OpenAI integer multiplication research claims an exact, deterministic algorithm for multiplying two (n)-bit integers in less than (n\log n) asymptotic time. The saving sits in the exponent of … Read more