8 days ago, while jogging, I asked Claude to solve the Riemann Hypothesis It didn’t. 1.5 days later, it proved >= 67% of the zeros are on the line (prev: 41.6%) Still not sure what that means, but some analytic number theorists seem excited - I’d tried once before in a single session and it went nowhere. Eight days ago, when I tried again, this was the opening message:The heavy lifting was recent ...

Claude attempted to address the Riemann hypothesis, a famous unsolved problem in mathematics dating back to 1859. The challenge reflects the ongoing exploration of Claude's mathematical capabilities and its potential contributions to scientific discovery.

The U.S. Department of Energy has launched the Genesis Open Models Initiative to promote the development and sharing of open-source models for energy systems. This initiative aims to enhance collaboration among researchers and facilitate advancements in energy technology.

Naomi Bashkansky resigned from OpenAI to become a Founding Researcher at Conduit, where she is working on developing telepathy through thought-to-text models. Conduit is collecting large amounts of non-invasive neural data to facilitate this technology.

AI benchmarks are essential for assessing model performance and informing deployment choices. However, they often reach saturation, reducing their effectiveness in distinguishing between models and limiting their long-term utility.

ChatGPT for Academic Researchers provides 100,000 scientists and mathematicians with free access to advanced ChatGPT models. An AI-generated disproof of the Erdős unit-distance conjecture was shared in May.

Google has shut down its AlphaFold project, which was recognized with a Nobel Prize for its contributions to protein folding predictions. Key members of the DeepMind team have been reassigned or have left the company as Google shifts its focus to the Gemini project.

1,134 employees from frontier AI companies assert that while AI has the potential to create a significantly improved future, there are risks associated with rapid capability development. They indicate that the automation of AI research could accelerate progress beyond current understanding or control.

Terence Tao explores the intersection of mathematics and artificial intelligence, emphasizing how AI can enhance mathematical research and problem-solving. He discusses the implications of AI for the future of mathematical discovery and education.

The Jacobian conjecture is stated to be false, with a specific mapping from \(\mathbb{C}^3\) to \(\mathbb{C}^3\) shown to have a Jacobian determinant of -2. The mapping sends the points (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0).