When checking that solutions to certain problems are correct, it turns out, you can’t get around the inherent complexity of ...
Mistral AI has released Leanstral 1.5 as a free Apache-2.0 model for Lean 4 verification. Lean 4 is a proof-assistant and programming environment for machine-checkable proofs, and proof engineering ...
Artificial intelligence was beaten by humans in solving 10 complicated mathematical problems within the “First Proof” project. The project was ...
In quantum mechanics, the geometry of quantum states has emerged as a powerful framework for understanding phenomena ranging ...
Noether's work helped prove the conservation of energy in physics, a key foundation for Einstein's theory of relativity ...
Artificial intelligence is mastering the kinds of projects that have long helped to build the careers of young mathematicians. What does that mean for their future? Credit...Illustrations by Yoshi ...
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An OpenAI Model ‘Disproved’ a Famous Math Conjecture. This Mathematician Couldn’t Leave It Alone
Mathematician Will Sawin discusses his experience reviewing and refining a mathematical proof devised by OpenAI's internal model—and what that could mean for mathematics.
In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in discrete geometry that had stumped human mathematicians for the last 80 ...
This marks one of the clearest examples so far of AI helping to solve a longstanding mathematical problem that had stumped the experts. Written for you by our author Paul Arnold, edited by Gaby Clark, ...
On May 20, 2026, OpenAI announced that its internal AI model had disproven a long-held prediction regarding the 'unit distance problem,' a central unsolved problem in discrete geometry. The unit ...
Abstract: Nonlinear PID control systems for a quadrotor UAV are proposed to follow an attitude tracking command and a position tracking command. The control systems are developed directly on the ...
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