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counterexample

4 articles · Page 1 of 1
Machine Learning Algorithms & Natural Language Processing
Machine Learning Algorithms & Natural Language Processing
Jul 23, 2026 · Artificial Intelligence

How GPT‑5.6 Refuted a 30‑Year‑Old Math Conjecture with a 58‑Word Prompt

Using only a 58‑word prompt across four dialogue rounds, GPT‑5.6 Pro generated a concrete counterexample that disproves the 30‑year‑old Dinitz‑Garg‑Goemans unsplittable‑flow conjecture, illustrating how minimal prompting can drive AI to produce non‑trivial mathematical discoveries.

AI promptingDinitz-Garg-Goemans conjectureGPT-5.6
0 likes · 9 min read
How GPT‑5.6 Refuted a 30‑Year‑Old Math Conjecture with a 58‑Word Prompt
Machine Learning Algorithms & Natural Language Processing
Machine Learning Algorithms & Natural Language Processing
Jul 21, 2026 · Artificial Intelligence

AI’s Fable 5 Overnight Refutes Jacobian Conjecture, Dashing Zhang Yitang’s 7‑Year Quest

An Anthropic AI model, Claude Fable 5, produced a concise counterexample that disproves the 87‑year‑old Jacobian conjecture, sparking worldwide reaction and highlighting both the mathematical breakthrough and the poignant story of Zhang Yitang’s seven‑year effort.

AI mathematicsClaude Fable 5GPT-5.6
0 likes · 9 min read
AI’s Fable 5 Overnight Refutes Jacobian Conjecture, Dashing Zhang Yitang’s 7‑Year Quest
IT Services Circle
IT Services Circle
Jul 21, 2026 · Artificial Intelligence

How Claude Fable 5 Disproved a 142‑Year‑Old Jacobian Conjecture with Three Simple Formulas

A mathematician named Levent Alpöge announced on X that Claude Fable 5 generated a three‑dimensional counterexample to the 142‑year‑old Jacobian Conjecture, which was instantly verified with Mathematica, updating the Wikipedia entry and highlighting AI’s growing role in solving deep mathematical problems.

AIClaude Fable 5Jacobian conjecture
0 likes · 9 min read
How Claude Fable 5 Disproved a 142‑Year‑Old Jacobian Conjecture with Three Simple Formulas
Machine Heart
Machine Heart
Jul 20, 2026 · Artificial Intelligence

One Tweet, One Counterexample: Did Claude Fable 5 Disprove the 85‑Year‑Old Jacobian Conjecture?

A tweet by Anthropic researcher Levent Alpoge, aided by the Claude Fable 5 model, presented a simple polynomial map whose constant Jacobian determinant of –2 sends three distinct points to the same image, providing a concrete counterexample that refutes the Jacobian conjecture that has challenged mathematicians for 85 years.

AI in mathematicsClaude Fable 5Jacobian conjecture
0 likes · 11 min read
One Tweet, One Counterexample: Did Claude Fable 5 Disprove the 85‑Year‑Old Jacobian Conjecture?