48小时，50年数学谜题就被破解！AI与全球数学家梦幻联动，从游戏分硬币到正方形填充，层层拆解埃尔德什遗留难题，人机协作彻底引爆 了数学研究新范式。 刚刚，AI又破解了一个数学难题！ Erdos#1026问题已经被攻克，且给出了正式证明。 而在此之前，这个问题已经困扰了数学界50年。 陶哲轩在Mastodon上宣布了这一消息，还在一篇博客中详细讲述了这个故事。 他强调，在AI的辅助下，人类团队仅用了48小时，就顺利攻克了这一难题。 并且，AI在此过程中带来的是全新理解，绝非搜索这么简单。 要知道，如果是靠传统方法，只靠数学家使用编程和文献检索，可能会需要数周甚至数月。 在这个过程中，AI实际上是在生成新的数学洞见，而不仅仅是检索现有文献。 Harmonic官网也宣布了这一消息，其AI系统Aristotle参与了此次解题过程。 Erdos#1026问题 1975年，传奇数学家保罗·埃尔德什在一篇论文的角落随手写下一个问题。 半个世纪后，这个问题静静躺在「埃尔德什问题网站」上，编号1026。 谁也没想到，它会在2025年的最后一个月，被一群数学家利用AI工具，在短短48小时内彻底破解。 埃尔德什的原问题，读起来有 ...

生成式AI 一、GPT-5.2上线的24小时，X 大批网友给 GPT-5.2 打差评？ 1. OpenAI十周年发布GPT-5.2系列号称"最强专业知识工作模型"，但上线24小时后X平台和Reddit用户集体差评， 认为其过于平淡、安全审查过度、情商堪忧； 2. SimpleBench测试显示GPT-5.2得分低于一年前的Claude Sonnet 3.7，在garlic有几个r等简单问题上回答错 误，LiveBench得分低于Opus 4.5和Gemini 3.0； 3. 最受诟病的是安全拒绝机制过于严格，用户反馈模型共情力和语境感知能力下降，在情感支持场景中给出机械且脱 离现实的建议。 https://mp.weixin.qq.com/s/xiOX9i6V-yfnn0pyC6ZlTA 二、OpenAI发布同时，谷歌推出Gemini Deep Research Agent 1. 谷歌在GPT-5.2发布前一小时推出全新版Gemini Deep Research Agent，基于Gemini 3 Pro构建并通过多步强 化学习训练提高准确性减少幻觉； 2. 新版在Humanity's Last Exam测试集 ...

Core Viewpoint - The article discusses the emergence of Harmonic, a startup focused on developing a zero-hallucination AI model named Aristotle, which aims to solve the challenges of AI in mathematical reasoning and formal verification [4][5][6]. Group 1: Company Overview - Harmonic is a startup founded by Vlad Tenev and Tudor Achim, focusing on creating AI that can perform mathematical reasoning without hallucinations [9][10]. - The company has rapidly gained attention and investment, achieving a valuation close to $900 million within two years of its establishment [25][26]. - Harmonic's product, Aristotle, is designed to provide rigorous mathematical proofs and reasoning, addressing the common issue of hallucinations in AI outputs [20][21]. Group 2: Technology and Innovation - Aristotle utilizes a formal verification tool called Lean, which ensures that every step in the reasoning process is validated, thus eliminating the possibility of generating false information [36][38]. - The model has demonstrated impressive performance in mathematical competitions, achieving a success rate of 90% in the MiniF2F test, significantly outperforming existing models like OpenAI's GPT-4 [41][42]. - Harmonic's approach emphasizes the importance of rigorous logical constraints in AI, aiming to make AI a reliable assistant in high-stakes fields such as finance and healthcare [21][19]. Group 3: Market Position and Competition - The AI industry is increasingly recognizing the need for more rigorous reasoning capabilities, creating opportunities for companies like Harmonic [27][28]. - Harmonic faces competition from established players like DeepMind and OpenAI, which have their own advanced models and extensive data resources [50][51]. - The startup's unique selling proposition lies in its focus on zero-hallucination outputs, which is a critical requirement in precision-demanding applications [17][19].

Core Viewpoint - The article discusses the emergence of Harmonic, a startup focused on developing a zero-hallucination AI model named Aristotle, which aims to excel in mathematical reasoning and formal verification, attracting significant investment and attention in the AI industry [2][5][46]. Group 1: Company Overview - Harmonic is a two-year-old startup that has rapidly gained attention from top-tier investment firms, achieving a valuation close to $900 million [5][23]. - The company has attracted nearly $200 million in investments from prominent firms such as Sequoia Capital, Kleiner Perkins, and Paradigm [5][29][27]. - Founders Vlad Tenev and Tudor Achim bring unique backgrounds in mathematics and AI, respectively, with Tenev being the CEO of Robinhood and Achim having experience in autonomous driving [11][12][16]. Group 2: Product Development - Harmonic's flagship product, Aristotle, is designed to perform mathematical reasoning without hallucinations, utilizing a formal verification tool called Lean [18][30]. - Aristotle has demonstrated impressive performance in mathematical problem-solving, achieving a success rate of 90% in the MiniF2F test, significantly outperforming existing models like OpenAI's GPT-4 [37][38]. - The model addresses three main issues: hallucination, unclear reasoning processes, and lack of rigor in traditional AI models [19][20][21]. Group 3: Market Context - The AI industry is increasingly recognizing the need for rigorous reasoning capabilities, creating opportunities for startups like Harmonic [25][24]. - Competitors in the space include DeepSeek and Google DeepMind, both of which are also developing advanced mathematical AI models [40][45]. - The competitive landscape is intensifying as major players seek to enhance their AI models' reasoning capabilities, particularly in high-stakes applications [26][46].

Core Viewpoint - Harmonic, an AI startup co-founded by Robinhood CEO Vlad Tenev, has launched a beta version of its AI chatbot application, Aristotle, which aims to provide reliable answers to mathematical reasoning problems without hallucinations [1][2]. Group 1: Company Overview - Harmonic recently completed a $100 million Series B funding round led by Kleiner Perkins, achieving a valuation of $875 million [1]. - The company is focused on creating "Mathematical Super Intelligence" (MSI) to assist users in fields reliant on mathematics, such as physics, statistics, and computer science [1]. Group 2: Product Features - Aristotle is claimed to be the first public product capable of reasoning and formally verifying its outputs, ensuring no hallucinations in quantitative reasoning [2]. - The model has reportedly achieved gold medal level in the International Mathematical Olympiad (IMO) through formal testing, contrasting with other AI models that used informal testing methods [2]. Group 3: Technical Approach - Harmonic utilizes the open-source programming language Lean to generate responses, ensuring high precision by double-verifying solutions through non-AI algorithms before presenting them to users [3]. - The technology employed by Harmonic is similar to that used in high-stakes fields like medical devices and aviation for output verification [3]. Group 4: Industry Context - Many leading tech companies are focusing on training AI models to solve mathematical problems, as mathematical capability is seen as a unique and verifiable domain requiring core reasoning skills [3]. - Achieving hallucination-free performance in AI models, even in narrow domains, is recognized as a challenging task, with leading models frequently producing hallucinations [4][5].

Group 1 - Harmonic AI, co-founded by Robinhood Markets CEO Vlad Tenev, has raised $100 million in funding to address challenges in mathematical operations faced by AI models [1][2] - The recent Series B funding round was led by Kleiner Perkins, with participation from Sequoia Capital, Index Ventures, and Paradigm, bringing the company's valuation to $875 million, just below the $1 billion "unicorn" threshold [1] - The CEO of Harmonic AI, Tudor Achim, aims to develop an AI system capable of solving complex mathematical problems, referred to as "mathematical superintelligence" [1][2] Group 2 - Harmonic plans to release its flagship AI model, Aristotle, to researchers and the public later this year, with the goal of creating an AI that surpasses human-level mathematical problem-solving abilities [2] - The ultimate objective is to tackle significant unsolved problems in mathematics and extend the capabilities to physics and computer science [2] - Harmonic's math-first strategy is expected to give it an edge over large language models that typically struggle with complex mathematical tasks [2][3] Group 3 - The company employs formal verification methods to ensure the correctness of its AI system's outputs and reasoning steps, which is a distinct approach to AI model construction [3] - Tenev emphasizes that maximizing valuation is not always wise, reflecting a strategic mindset in the company's growth and funding approach [3]

Core Viewpoint - Harmonic AI, co-founded by Vlad Tenev and Tudor Achim, aims to develop an AI system capable of solving complex mathematical problems, striving for Mathematical Superintelligence (MSI) [3][20]. Group 1: Company Overview - Harmonic AI has successfully raised $100 million in Series B funding, bringing its valuation to approximately $875 million [4][17]. - The company was co-founded by Vlad Tenev, who previously established Robinhood Markets, and Tudor Achim, an expert in AI and large model training [5][15]. - Robinhood, under Tenev's leadership, achieved a market cap of around $22.7 billion and reported a revenue of $927 million with a net profit of $336 million in Q1 2025 [8][12]. Group 2: Funding and Valuation - Harmonic AI's Series A funding raised $75 million, led by Sequoia Capital, with a post-money valuation of $325 million [15]. - The recent Series B funding was led by Kleiner Perkins, with participation from Paradigm and Ribbit Capital, among others [16]. - The company intentionally set its valuation below the "unicorn" threshold of $1 billion, focusing on long-term growth rather than short-term valuation targets [18][19]. Group 3: Product Development - Harmonic AI announced its first model, Aristotle, which can formalize natural language problems into formal representations, enhancing collaboration with mathematicians [20]. - The model's performance improved from 83% to 90% on the MiniF2F benchmark, which includes various levels of mathematical problems [23]. - The ultimate goal is to create an AI system with mathematical capabilities surpassing human abilities, addressing challenges like the "hallucination" problem in AI [26][28].

Core Viewpoint - Harmonic.fun, co-founded by Vlad Tenev and Tudor Achim, focuses on developing an AI model based on Mathematical Superintelligence (MSI) to address reliability issues in AI applications, particularly in high-stakes fields like finance and healthcare [1][2][3]. Group 1: Company Overview - Harmonic.fun recently completed a $100 million Series B funding round, led by KP, with participation from Paradigm, Ribbit Capital, Sequoia Capital, and Index Ventures, achieving a valuation of nearly $900 million [1]. - The company previously raised $75 million in a Series A round led by Sequoia, with a valuation of $325 million at that time [1]. Group 2: Technology and Methodology - The core concept of MSI is rooted in formal mathematical reasoning, which allows for verifiable outputs and eliminates the "hallucination" phenomenon common in traditional AI models [2][3]. - Traditional AI models rely on probabilistic predictions and pattern recognition, which can lead to inaccuracies when faced with unfamiliar situations or complex reasoning tasks [2][3]. - Harmonic's flagship model, Aristotle, is designed to solve complex mathematical problems and is applicable in fields requiring zero-tolerance for errors, such as aerospace, chip design, and healthcare [3][4]. Group 3: Advantages of MSI - MSI provides verifiable accuracy, ensuring that every logical step in the reasoning process is rigorous and correct, contrasting with the "black box" nature of traditional AI [5]. - The model eliminates hallucinations by adhering strictly to mathematical and logical rules, ensuring the authenticity of its results [5]. - Aristotle can transparently identify and mark errors in the reasoning process, which is crucial for debugging and understanding AI decision-making, especially in high-risk applications [5]. Group 4: Applications and Impact - In high-security industries like blockchain, financial services, and aerospace, Aristotle can generate formally verified software code, enhancing system safety and reliability [5]. - In finance, Aristotle can handle complex data for rigorous risk assessment and model validation, aiding institutions in making informed investment and risk management decisions [5]. - The model also has potential applications in scientific research and engineering design, accelerating breakthroughs in fields like theoretical physics and materials science [5]. - Although primarily aimed at enterprise applications, the interpretability and accuracy of MSI could enhance mathematics education by helping students understand complex concepts through verifiable reasoning steps [5]. Group 5: Training Methodology - Harmonic employs a unique approach of using synthetic data generation for training, allowing the system to autonomously create formal problem proofs for recursive self-improvement [8][9].