Topic
3 stories
Mathematicians have shown that no electoral system can perfectly balance local representation, proportional national results, and a fixed-size parliament once enough parties compete. A newly proposed voting method could soften these unavoidable trade-offs and produce outcomes that are much closer to fair.
Researchers have found a way to build much larger “twisted” oxide materials while precisely controlling how their atomic layers line up. Because these materials can be made over large areas and transferred onto different surfaces, the technique could help turn twistronics from a laboratory curiosity into a practical platform for next-generation electronics.
A mathematician working at Anthropic says he used the AI model Claude Fable 5 to uncover a remarkably simple counterexample to the Jacobian conjecture, a famous problem that has resisted mathematicians for more than a century. The result shows that the conjecture is false in three dimensions and above, although the original two-dimensional version remains unsolved.