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Latest Articles
OpenAI Reports Internal Model Disproved an 80-Year-Old Geometry Problem
9+ hour, 32+ min ago (505+ words) According to OpenAI's report on the discrete geometry result, the internal model was not specifically trained for mathematics. OpenAI describes it as a general-purpose reasoning model and says external mathematicians validated the result. The company has not identified the model…...
The Transport Principle: Dividing by Zero in Geometric Algebra
20+ hour, 47+ min ago (1792+ words) The equations of gravity divide by zero at the centre of a black hole. This is the mathematics that refuses to stop there: no …...
The Pythagorean Triple Machine
1+ day, 4+ hour ago (21+ words) Discover how a simple algebraic trick factoring a difference of squares generates every Pythagorean triple, from 3-4-5 to infinity....
The Guilty Rapture of Geometry
4+ day, 20+ hour ago (29+ words) On representation, distinguished points, and the forms that quietly replace the world • • • I. THE RAPTURE Whenever we find a geometric analogue for a difficult …...
Mathematical Breakthrough Applied to AI: GeoLAN Addresses the 'Black Box' Problem Using the Kakeya Conjecture
1+ week, 9+ hour ago (1586+ words) Author and source: Leiphone The mathematics community and the AI community have strongly collaborated. Pure mathematical achievements at the highest level have already been directly applied to large model training. A Xiaohongshu creator named Z9 discovered while reviewing papers that the…...
Euclid’s Form: What It Really Guarantees
1+ week, 1+ day ago (37+ words) The Problem — the statement that seemed obvious “How would you prove that not every number of the form N = (p₁ · p₂ · p₃ ··· pₙ) + 1 is …...
Would You Be a Student of Sotce?
1+ week, 5+ day ago (407+ words) i-d.co Now reading: Would You Be a Student of Sotce? “I have the post-school blues for sure,” Sotce tells me as we log onto Zoom. It’s only been a few days since the school emptied out, and the chalkboard…...
How Do You Take the Root of a Triangle?
1+ week, 5+ day ago (36+ words) You’ve Never Heard of Triangular Roots. If this is your first time coming across the term “triangular roots,” then you are where I was six months …...
Monkeys are surprisingly good at geometry
1+ week, 6+ day ago (343+ words) Published Jul 20, 2026 3:00 PM EDT “What surprised us wasn’t just that monkeys could do the task. It was that monkeys, children and adults seemed to think about geometric relationships in fundamentally the same way,” Jessica Cantlon, a study co-author, a cognitive…...
Engineers building Solar panels are using exact replicas of honeycombs made by Bees to ensure...
1+ week, 6+ day ago (238+ words) The Times of India Bees may have helped solve one of solar energy's biggest problems According to a report by Ecoportal, engineers have developed a new type of solar panel using the honeycomb pattern that bees have mastered for millions…...