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An AI, in collaboration with a mathematician, has produced a one-page proof for a long-standing Erdős problem (#119), claiming the $100 bounty originally offered by Paul Erdős. The problem concerns the maximum modulus of polynomials with zeros on the unit circle. The new result, generated with the help of GPT-5.6 Sol and posted on the erdosproblems.com forum, is notably simpler than a famous 44-page proof by József Beck published in the Annals of Mathematics in 1991, which addressed a related but distinct part of the problem. Thomas Bloom, a mathematician and the maintainer of the Erdős problems website, stated that the AI's proof uses straightforward harmonic analysis techniques and contains "interesting ideas," suggesting the problem was less inherently difficult than previously believed. This follows other recent AI-assisted proofs, such as for the Cycle Double Cover conjecture. The development has sparked debate within the mathematical community. While some argue AI has hit a wall in pure mathematics, others point to incremental but genuine progress on tough problems, indicating that AI's relentless, non-intuitive exploration can uncover overlooked paths that human mathematicians might dismiss after initial failures. This event highlights a potential shift: some "open" problems may persist not due to sheer difficulty, but due to the limits of human patience in exploring all possible avenues.

"AI Era, Industrial Revolution and Future Civilization: An Interview with Zhang Dingwen – The Future Does Not Belong to Those Who Chase" In this interview, entrepreneur Zhang Dingwen reflects on his entrepreneurial journey and philosophy, moving beyond discussions of financing or success to emphasize understanding the "era" itself. He argues that true entrepreneurs should not chase short-term trends ("winds"), but position themselves in the direction of long-term technological and societal evolution. Zhang shares key lessons from his early days, including the realization that user value does not automatically translate to commercial value. For him, the core of entrepreneurship is not building a company but constantly upgrading one's own "cognition" – the ability to interpret information, ask the right questions, and understand the underlying "causes" behind business outcomes, not just the effects. His thinking has evolved from a focus on creating good products to a strategic focus on building "entrances" – platforms that naturally connect users to digital services. He sees smart wearables, like watches, not merely as hardware but as potential future gateways combining technological, financial, social, and even fashion attributes to create sustained user relationships and ecosystems. Ultimately, Zhang's vision transcends individual products or companies. He discusses business competition in three stages: product, platform, and finally, "civilization" – where the greatest companies influence how society operates by defining new rules and ways of life. He believes the mission of a truly great enterprise is to solve problems of its time, build enduring trust, and contribute lasting value, leaving behind not just wealth but a positive impact on how the world works. The future, he concludes, belongs not to the fastest, but to those with the correct long-term direction and a commitment to continuous learning and evolution.

Japan's cabinet has introduced the 2026 Basic Policy on Economic and Fiscal Management and Reform, shifting its primary fiscal target. The new framework moves away from the traditional annual primary balance goal and instead prioritizes a stable reduction of the debt-to-GDP ratio. This change is tied to a strategy of increased "responsible proactive fiscal" spending, aiming to boost long-term growth through investments in strategic sectors like AI, semiconductors, energy, and robotics. The government estimates total public and private investment in 62 key technologies could exceed 370 trillion yen by 2040. The market reaction has been mixed and cautious. While equity markets may respond to policy signals, bond markets are focused on fiscal credibility. Concerns center on whether the weakening of the clear primary balance anchor could lead to looser fiscal discipline. If investors doubt that these strategic investments will generate sufficient productivity gains, tax revenue, and nominal growth to outpace rising interest costs, they may demand higher yields on Japanese Government Bonds (JGBs). Recent volatility in the yen and JGB yields, with the 10-year yield briefly reaching 2.9%, reflects this skepticism. The success of this new framework hinges on two factors: whether Japan can achieve a nominal growth rate consistently higher than its long-term interest rates, and whether future budgets demonstrate disciplined control over bond issuance. The government's narrative is that strategic investment is essential to break Japan's cycle of low growth, aging, and labor shortages. However, the bond market will continuously assess the credibility of this plan, pricing the risk that it may represent fiscal expansion rather than a viable growth strategy.

Bitcoin mines are transforming into AI factories. This shift is driven by the convergence of three key assets from the previous crypto cycle: infrastructure, talent, and capital. Crypto mining companies like Crusoe, CoreWeave, and Bitdeer are repurposing their core competency—securing power, land, and grid connections in remote locations—to build data centers for AI clients. These firms are signing multi-billion dollar, long-term contracts with companies like Anthropic, AWS, and Microsoft, as AI's demand for reliable, high-capacity compute surpasses the profitability of Bitcoin mining. Simultaneously, crypto entrepreneurs and engineers are applying their skills to new AI ventures. Examples include OpenSea's co-founder launching OpenRouter (an AI model aggregator), and former Coinbase engineers building Fal.ai (a generative media infrastructure platform). Their experience in building scalable, global software networks translates effectively to the AI space. Furthermore, capital accumulated during the crypto boom is now fueling AI. Figures like Jed McCaleb (co-founder of Ripple) funded Voltage Park, a large-scale GPU cloud provider. Notably, some crypto investments, like FTX's early bets on Anthropic and Cursor, have generated astronomical paper returns, demonstrating how high-risk crypto capital flowed into AI before it became mainstream. The transition is not just about repurposing hardware, but about redirecting critical resources—power infrastructure, distributed systems expertise, and venture funding—to the next technological frontier: artificial intelligence.

Feeding "Noise" to AI Can Improve Performance: A Method Enables Positive Transfer from Noise This work, Semi-Supervised Noise Adaptation (SSNA), introduces a Noise Adaptation Framework (NAF) that challenges traditional transfer learning. Instead of requiring a labeled source domain of real data (e.g., images, text), NAF uses randomly generated Gaussian noise as the source. For a target task with C classes, it constructs C noise clusters by sampling from Gaussian distributions. Although this synthetic noise contains no semantic meaning, NAF trains it to form a discriminative class structure in a shared representation space—clustering same-class noise and separating different classes. The key is aligning this learned structure from the noise domain to the real, sparsely labeled target domain. A small number of target labels are still essential to establish the correspondence between noise clusters and actual classes. The training objective combines: 1) supervised loss on the few labeled target samples, 2) classification loss for the noise to build its structure, and 3) a distribution alignment loss (using Negative Domain Similarity) to minimize the gap between the noise and target domains in the shared space. Experiments show significant gains in few-label settings. With just 4 labels per class, NAF with a ResNet-18 backbone improves accuracy over a standard supervised baseline (ERM) by +12.35% on CIFAR-10, +7.61% on CIFAR-100, +4.38% on DTD-47, and +2.74% on Caltech-101. It also benefits fine-grained datasets and scales to ImageNet-1K (with 100 labels/class) and text classification (AG News). NAF can be integrated into existing semi-supervised methods like FixMatch for further gains. Ablation studies confirm the transferred benefit comes from the discriminative structure of the noise, not randomness itself. Collapsing all noise into a single point causes negative transfer, while increasing separation between noise cluster centers improves performance. The amount of noise per class is less critical once a basic structure forms. In conclusion, this work demonstrates that for positive transfer, the semantic content of source data may not be necessary. What can be effectively transferred is the *organizational structure* of categories within a representation space. This offers a promising alternative for scenarios where real source data is unavailable due to privacy, copyright, or procurement constraints.