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Mathematician Uses AI to Disprove Long-Standing Jacobian Conjecture

Mathematician Uses AI to Disprove Long-Standing Jacobian Conjecture

Levent Alpöge, a mathematician and number theorist, has reportedly disproven the Jacobian conjecture, a significant problem in algebraic geometry, using Anthropic's AI model, Fable 5. The Jacobian conjecture, which dates back to 1939, posits that a polynomial map with a nonzero constant Jacobian determinant should have a polynomial inverse. Alpöge's counterexample, shared during the World Cup final, demonstrates a polynomial map that meets the conjecture's conditions but fails to be invertible. This finding, if verified, would resolve a problem that has challenged mathematicians for decades. The counterexample has been shared online, and the mathematical community is awaiting formal peer review and verification.
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AI Breakthrough: Claude Fable 5 AI Disproves 87-Year-Old Jacobian Conjecture

AI Breakthrough: Claude Fable 5 AI Disproves 87-Year-Old Jacobian Conjecture

A significant development in the field of mathematics has occurred with the help of artificial intelligence. Levent Alpöge, a mathematician at Harvard University, announced via a tweet that the Jacobian conjecture, a mathematical problem that has puzzled experts for nearly a century, is false. This revelation was made possible through the use of the Claude Fable 5 AI, which provided a 216-character counterexample disproving the conjecture. The Jacobian conjecture, proposed by Ott-Heinrich Keller in 1939, suggested that a specific type of mathematical function could work in reverse. It was listed among the most challenging problems for mathematicians in the 21st century by Stephen Smale in 1998. The AI's involvement in solving this problem marks a significant milestone in the application of AI in mathematics.
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Challenges in Cybersecurity as AI Models Advance

Challenges in Cybersecurity as AI Models Advance

The year 2026 has seen a rise in AI-powered cyberattacks, with new AI models possessing capabilities comparable to top human hackers. Efforts to control access to these models, such as the U.S. government's export controls on Anthropic's Mythos and Fable models, have proven to be temporary solutions. As foreign companies develop and release powerful AI models, controlling AI becomes increasingly difficult. The federal government has reduced resources for key cybersecurity agencies, creating a gap that AI companies are attempting to fill. Initiatives like Anthropic's Project Glasswing and OpenAI's Patch the Planet aim to bolster critical infrastructure and software libraries.
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Zscaler Joins Hiroshima AI Process to Enhance AI Security

Zscaler Joins Hiroshima AI Process to Enhance AI Security

Zscaler has joined the Hiroshima AI Process (HAIP) Friends Group Partners’ Community, reinforcing its commitment to advancing secure, transparent, and trustworthy AI adoption. The HAIP, launched under Japan’s 2023 G7 Presidency, aims to promote international discussion on safe AI practices. Zscaler will contribute its expertise in AI security, focusing on risk assessment, security testing, and incident response. The company is also involved in frontier AI security initiatives, collaborating with projects like Anthropic’s Project Glasswing and OpenAI’s Trusted Access for Cyber program.
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Mathematician Uses AI Model Fable 5 to Disprove Jacobian Conjecture

Mathematician Uses AI Model Fable 5 to Disprove Jacobian Conjecture

Mathematician Uses AI Model Fable 5 to Disprove Jacobian Conjecture
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Chinese AI Models Challenge U.S. Dominance with Open-Source Approach

Chinese AI Models Challenge U.S. Dominance with Open-Source Approach

China's leading AI companies, Moonshot and Alibaba, have introduced new AI models that they claim rival the best from U.S. companies like OpenAI and Anthropic. Moonshot's Kimi K3 and Alibaba's Qwen3.8 are being positioned as formidable competitors in the AI landscape, with Moonshot's model boasting 2.8 trillion parameters and Alibaba's 2.4 trillion. These models are being made publicly available, contrasting with the more proprietary approach of U.S. companies. This move is seen as a strategic effort to close the gap in AI capabilities between China and the U.S., as the technology becomes increasingly central to national security and economic power.
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Chinese AI Model K3 Challenges U.S. Tech Industry with Advanced Capabilities

Chinese AI Model K3 Challenges U.S. Tech Industry with Advanced Capabilities

A new artificial intelligence model from China, known as Kimi K3, has surprised the U.S. tech industry with its capabilities, which rival those of leading models like Anthropic's Claude and OpenAI's ChatGPT. Developed by Beijing-based startup Moonshot, K3 has been recognized for its high performance in front-end coding capabilities, according to Arena, a platform for evaluating AI systems. The release of K3 coincides with Chinese President Xi Jinping's address at the World Artificial Intelligence Conference in Shanghai, highlighting China's growing efforts to develop domestic AI technology amidst U.S. restrictions on advanced tech imports. The K3 model is priced higher than previous Chinese models but remains more affordable than OpenAI's GPT-5.6 Sol model. This development has intensified the competition between Chinese and U.S. AI companies, with accusations from U.S. firms like Anthropic and OpenAI regarding the illicit distillation of their technologies by Chinese counterparts.
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Chinese AI Model Challenges U.S. Tech Industry with Competitive Capabilities

Chinese AI Model Challenges U.S. Tech Industry with Competitive Capabilities

A new artificial intelligence model from China, known as Kimi K3, has surprised the U.S. tech industry with its capabilities that rival those of leading U.S. models like Anthropic's Claude and OpenAI's ChatGPT. Developed by the Beijing-based startup Moonshot, K3 has been recognized for its performance in front-end coding capabilities, topping the charts in Arena's AI system evaluations. The release of K3 coincides with Chinese President Xi Jinping's address at the World Artificial Intelligence Conference in Shanghai, highlighting China's advancements in AI amidst U.S. restrictions on technology access. The model's release has sparked discussions about the competitive dynamics between Chinese and U.S. AI companies, with some analysts viewing it as a potential revenue challenge for U.S. firms.
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OpenAI Executive's Comments on China's Kimi K3 Model Ignite U.S. Tech Debate

OpenAI Executive's Comments on China's Kimi K3 Model Ignite U.S. Tech Debate

OpenAI Executive's Comments on China's Kimi K3 Model Ignite U.S. Tech Debate
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Anthropic Settles $1.5 Billion Copyright Lawsuit with Authors

Anthropic Settles $1.5 Billion Copyright Lawsuit with Authors

Anthropic Settles $1.5 Billion Copyright Lawsuit with Authors
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Meta, Anthropic in talks for potential $10 billion compute lease deal, NYT reports

Meta, Anthropic in talks for potential $10 billion compute lease deal, NYT reports

July 17 (Reuters) - Meta Platforms is in talks to lease computing power to Anthropic in a potential deal worth as much as $10 billion over two years, the New York Times reported on Friday, citing three people with knowledge of the discussions.
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Dr. Jill Lepore Discusses AI Backlash and the 'Artificial State'

Dr. Jill Lepore Discusses AI Backlash and the 'Artificial State'

Dr. Jill Lepore, a Harvard professor and New Yorker staff writer, discusses her new book, 'The Rise and Fall of the Artificial State,' which examines the impact of artificial intelligence and systemic measurement on society. Lepore argues that the quantification of human concerns through technology has led to a dehumanizing effect, affecting politics and governance. She highlights the role of Big Tech in shaping the modern state and the potential dangers of AI-driven decision-making. Lepore also addresses the backlash against AI, particularly among college students, and the need for a more human-centered approach to technology.