Mathematicians put AI to work on Fermat's last theorem At an event in London, mathematicians have made unexpectedly fast progress on formalising Fermat's last theorem using AI In the lobby of a central London hotel, tourists are bracing themselves for a day of sightseeing in a heatwave. Meanwhile, staff are resetting the dining room after breakfast. And in a windowless meeting room, assembled academics are contemplating whether humans have a role to play in the future of mathematics, now that AI can prove theorems by itself. The general mood in the room is one of bewilderment at the recent jump in computer intelligence and excitement about the potential it unlocks - and perhaps a slight unease about what the future holds for them personally. Twenty-five researchers from diverse fields and countries are here to spend a week working on formalising Fermat's last theorem with cutting-edge AI models.

As AI reshapes how work gets done, organizations with strong process frameworks are best positioned to lead and maintain operational rigor at scale. Frameworks like Lean Six Sigma and business process management (BPM) first gained traction because they promised clarity in the chaos--a structured way to bring order to messy, sprawling operations. Lean Six Sigma emphasized statistical rigor and quality control; BPM created end-to-end maps of how work should flow across departments. Both offered a repeatable way to embed habits of measurement, analysis, and accountability into day-to-day company culture. But today, those time-tested playbooks are evolving as companies seek to embed AI into established process excellence methodologies. By some estimates, the market for AI-powered process optimization is projected to exceed $113 billion within the next decade.

The increasing societal integration of Large Language Models (LLMs) and agentbased AI demands a new civic competency: adversarial reasoning. This position paper argues that K-12 AI education must move beyond passive literacy to actively equip students with skills in responsible adversarial prompting and ethical system "hacking." Such capabilities are essential for citizens to critically probe AI systems, understand their inherent limitations, identify manipulative patterns, and hold them accountable. We posit that cultivating a generation skilled in "red-teaming" AI is vital for maintaining transparency, preventing undue influence, and fostering a democratic engagement with these transformative technologies.

Kolmogorov-Arnold Networks (KANs) have demonstrated remarkable expressive capacity and predictive power in symbolic learning. However, existing generalization errors of KANs primarily focus on approximation errors while neglecting estimation errors, leading to a suboptimal bias-variance trade-off and poor generalization performance. Meanwhile, the unclear generalization mechanism hinders the design of more effective KANs variants. As the authors of KANs highlighted, they ``would like to explore ways to restrict KANs' hypothesis space so that they can achieve good performance''. To address these challenges, we explore the generalization mechanism of KANs and design more effective KANs with lower model complexity and better generalization. We define \textit{Lipschitz complexity} as the first structural measure for deep functions represented by KANs and derive novel generalization bounds based on \textit{Lipschitz complexity}, establishing a theoretical foundation for understanding their generalization behavior. To reduce \textit{Lipschitz complexity} and boost the generalization mechanism of KANs, we propose Lipschitz-Enhanced KANs ($\textbf{LipKANs}$) by integrating the Lip layer and pioneering the $L_{1.5}$-regularized

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Bilevel optimization has emerged as a technique for addressing a wide range of machine learning problems that involve an outer objective implicitly determined by the minimizer of an inner problem. While prior works have primarily focused on the parametric setting, a learning-theoretic foundation for bilevel optimization in the nonparametric case remains relatively unexplored. In this paper, we take a first step toward bridging this gap by studying Kernel Bilevel Optimization (KBO), where the inner objective is optimized over a reproducing kernel Hilbert space. This setting enables rich function approximation while providing a foundation for rigorous theoretical analysis. In this context, we derive novel finite-sample generalization bounds for KBO, leveraging tools from empirical process theory. These bounds further allow us to assess the statistical accuracy of gradient-based methods applied to the empirical discretization of KBO. We numerically illustrate our theoretical findings on a synthetic instrumental variable regression task.

The outspoken longevity scientist David Sinclair has been predicting that one day, you'll go to the doctor and get a prescription that will make you 10 years younger. Now has learned that he has plans to launch human tests of an oral reprogramming drug as part of a $101 million competition organized by the XPrize Foundation. The foundation is offering cash awards to teams able to "restore" a person to an earlier apparent age, as measured by improvements in immune, cognitive, and muscle function. The grand prize goes to any team able to show a 10-year (or greater) relative improvement after one year of treatment. Reached by phone, Sinclair, a biologist at Harvard Medical School, confirmed that he plans to give an oral drug mixture to volunteers in a bid to seek "evidence for age restoration in humans."

Could humanoid robots be heading for the battlefield? I've come to an industrial space in a tech-heavy area of San Francisco expecting to see a menacing humanoid robot solider doing something combat-like: the future of land-based warfare, perhaps. Instead, the black shiny faceless Phantom robot is engaged in free play, manipulating a bunch of coloured kids blocks. We need data from it just interacting with its environment [and] this is today's menu, explains Sankaet Pathak, co-founder and CEO of two-year-old start-up Foundation Robotics, which is developing Phantom for military and civilian applications. Later he pushes its 80kg steel-covered body around the room to demonstrate its stability and shows me how it walks.

Here's Exactly How That Happened The definitive story of how Claude Code and OpenClaw kicked off computing's biggest transformation possibly ever. "Hi, my name is Peter, and I'm a Claudeholic." It was August 2025 and Peter Steinberger was addressing a meetup in London called Claude Code Anonymous. Steinberger and some fellow addicts had arranged the event to network with people like themselves--techies swept up by coding tools such as Anthropic's paradigm-busting Claude Code. "I dedicate pretty much all my waking time to this, yet it doesn't feel enough," he told the gathering in a cozy, brick-walled room. A few months later, Anthropic released a new version of Claude Code, and the ranks of Claudeholics exploded . Called Opus 4.5, it could handle more complicated programming tasks, retain much more in its memory, run for many hours on end, and manage a team of AI subagents. Anthropic has what it describes as a "notoriously difficult" take-home exam for prospective engineering hires; in a head-to-head comparison of those people and its models, Anthropic claimed that Opus 4.5 "scored higher than any human candidate ever," which "raises questions on how AI will change engineering as a profession."

Enterprise AI hinges on high-accuracy outputs, requiring better data context, unified architectures, and rigorous measurement frameworks, says Bavesh Patel, senior vice president at Databricks, and Rajan Padmanabhan, unit technology officer at Infosys. Artificial intelligence may be dominating boardroom agendas, but many enterprises are discovering that the biggest obstacle to meaningful adoption is the state of their data. While consumer-facing AI tools have dazzled users with speed and ease, enterprise leaders are discovering that deploying AI at scale requires something far less glamorous but far more consequential: data infrastructure that is unified, governed, and fit for purpose. That gap between AI ambition and enterprise readiness is becoming one of the defining challenges of this next phase of digital transformation. As Bavesh Patel, senior vice president of Databricks, puts it, "the quality of that AI and how effective that AI is, is really dependent on information in your ...