Top Mathematics discussions
NishMath
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gasarch (noreply@blogger.com)@Computational Complexity
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Computational Complexity
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Two high school students have achieved a remarkable feat by discovering a novel proof of the Pythagorean Theorem. This new proof, which employs trigonometry, has been accepted for publication after undergoing rigorous scrutiny. The achievement is particularly noteworthy because proving the Pythagorean Theorem using trigonometry is challenging due to the potential for circular reasoning, as trigonometry itself relies on the Pythagorean Theorem. Despite this hurdle, the students' proof has been deemed valid, showcasing their mathematical ingenuity.
The Pythagorean Theorem, a cornerstone of geometry and trigonometry, has been found on clay tablets dating back to 1770 BCE. These tablets, predating Pythagoras by over 1,000 years, reveal that ancient Babylonian mathematicians were aware of the theorem and used it to solve problems. One tablet, IM 67118, demonstrates the application of the theorem to calculate the diagonal length of a rectangle. Another tablet shows a square with triangles and markings, illustrating their understanding of the relationship between the sides of a square and its diagonal. This historical evidence challenges the traditional attribution of the theorem solely to Pythagoras. The newly discovered proof by the high school students and the revelation of the theorem's ancient origins highlight the enduring relevance and evolving understanding of mathematics. While the students' proof demonstrates fresh perspectives on a classical theorem, the historical context emphasizes that mathematical knowledge is often developed and disseminated over centuries and across cultures. As mathematician Bruce Ratner notes, the Babylonians were likely familiar with the Pythagorean Theorem and irrational numbers well before Pythagoras, suggesting a rich and complex history of mathematical discovery. Recommended read:
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@www.marktechpost.com
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Maginative
, MarkTechPost
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Google DeepMind has launched AlphaGenome, a new deep learning framework designed to predict the regulatory consequences of DNA sequence variations. This AI model aims to decode how mutations affect non-coding DNA, which makes up 98% of the human genome, potentially transforming the understanding of diseases. AlphaGenome processes up to one million base pairs of DNA at once, delivering predictions on gene expression, splicing, chromatin accessibility, transcription factor binding, and 3D genome structure.
AlphaGenome stands out by comprehensively predicting the impact of single variants or mutations, especially in non-coding regions, on gene regulation. It uses a hybrid neural network that combines convolutional layers and transformers to digest long DNA sequences. The model addresses limitations in earlier models by bridging the gap between long-sequence input processing and nucleotide-level output precision, unifying predictive tasks across 11 output modalities and handling thousands of human and mouse genomic tracks. This makes AlphaGenome one of the most comprehensive sequence-to-function models in genomics. The AI tool is available via API for non-commercial research to advance scientific research and is planned to be released to the general public in the future. In performance tests, AlphaGenome outperformed or matched the best external models on 24 out of 26 variant effect prediction benchmarks. According to DeepMind's Vice President for Research Pushmeet Kohli, AlphaGenome unifies many different challenges that come with understanding the genome. The model can help researchers identify disease-causing variants and better understand genome function and disease biology, potentially driving new biological discoveries and the development of new treatments. Recommended read:
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Sabine Hossenfelder@backreaction.blogspot.com
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aasnova.org
Recent advancements in physics and astrophysics are focusing on complex simulations and interpretations of celestial phenomena, particularly concerning black holes, gravitational lensing, and active galactic nuclei. A key development is the introduction of new ray-tracing algorithms designed to make these simulations more accessible. These algorithms, like the newly developed "Mahakala," enable researchers to expertly track photons navigating the warped spacetimes around black holes, simulating images of active black holes with greater ease and speed.
One significant application of these techniques involves studying gravitationally lensed objects, such as the redshift z = 6.2 star Earendel. Researchers are exploring how the presence of dark matter subhalos can alter the interpretation of these lensed sources, highlighting the importance of precise modeling in understanding distant celestial bodies. Furthermore, X-ray observations from missions like XRISM are providing new insights into the structure of low-luminosity active galactic nuclei (LLAGN), a population of accreting black holes that are still poorly understood. XRISM's observations of Messier 81, a nearby galaxy hosting an LLAGN, are helping to determine if these systems conform to the typical model of active galactic nuclei. In a more theoretical realm, some physicists are exploring the intriguing idea that our universe may exist inside a black hole. This hypothesis, while seemingly radical, is being considered as a potential explanation for certain cosmological phenomena. Simultaneously, past findings, such as the unusual particles detected by the ANITA experiment over Antarctica, are being re-evaluated with more conventional explanations, moving away from more exotic theories like parallel universes. These diverse lines of inquiry demonstrate the ongoing efforts to refine our understanding of the universe, from the smallest particles to the largest cosmic structures. Recommended read:
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@Trebor
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Trebor
Recent discussions in theoretical computer science and programming have touched upon diverse topics, ranging from type theory for SDG (Sustainable Development Goals) to the complexities encountered in programming. One thread explored the characteristics a type theory for SDG should possess, suggesting it should include a judgmentally commutative ring, possibly a Q-algebra, where neutral forms of type R are polynomials with other neutral forms as indeterminates. Participants believe such a system would have decidable typechecking.
A common sentiment shared among programmers, particularly those using languages with dependent types like Rust, is the initial hurdle of satisfying the compiler's requirements. Some have described the experience as an engaging puzzle that can involve spending considerable time to prove the validity of their code. The discussion also addressed the subjective nature of "complexity" in programming, suggesting it is a term often used to dismiss unfamiliar concepts rather than a concrete measure of inherent difficulty. In related news, Microsoft’s Krysta Svore has announced geometric error-correcting codes as a potential advancement toward practical quantum computing. These codes utilize high-dimensional geometry to enhance performance, potentially leading to more efficient encoding and logical operations with fewer qubits. The approach builds on topological error correction, employing a mathematical method called Hermite normal form to reshape the grid, resulting in substantial reductions in qubit count and faster logical clock speeds. This geometric reshaping results in substantial reductions in qubit count. In one notable case, they achieved six logical qubits using just 96 physical qubits, which is a 16-to-1 ratio that would mark a significant improvement over standard two-dimensional codes. Recommended read:
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Steve Vandenberg@Microsoft Security Blog
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Microsoft Advances in AI and Data Security - Microsoft's advancements in AI, data security, and computational chemistry include the Responsible AI Transparency Report and AI strategies in higher education.
ImgSrc: techcommunity.m
Microsoft is making significant strides in AI and data security, demonstrated by recent advancements and reports. The company's commitment to responsible AI is highlighted in its 2025 Responsible AI Transparency Report, detailing efforts to build trustworthy AI technologies. Microsoft is also addressing the critical issue of data breach reporting, offering solutions like Microsoft Data Security Investigations to assist organizations in meeting stringent regulatory requirements such as GDPR and SEC rules. These initiatives underscore Microsoft's dedication to ethical and secure AI development and deployment across various sectors.
AI's transformative potential is being explored in higher education, with Microsoft providing AI solutions for creating AI-ready campuses. Institutions are focusing on using AI for unique differentiation and innovation rather than just automation and cost savings. Strategies include establishing guidelines for responsible AI use, fostering collaborative communities for knowledge sharing, and partnering with technology vendors like Microsoft, OpenAI, and NVIDIA. Comprehensive training programs are also essential to ensure stakeholders are proficient with AI tools, promoting a culture of experimentation and ethical AI practices. Furthermore, Microsoft Research has achieved a breakthrough in computational chemistry by using deep learning to enhance the accuracy of density functional theory (DFT). This advancement allows for more reliable predictions of molecular and material properties, accelerating scientific discovery in fields such as drug development, battery technology, and green fertilizers. By generating vast amounts of accurate data and using scalable deep-learning approaches, the team has overcome limitations in DFT, enabling the design of molecules and materials through computational simulations rather than relying solely on laboratory experiments. Recommended read:
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@martinescardo.github.io
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ellipticnews.wordpress.com
The mathematics community is buzzing with activity, including upcoming online events and ongoing discussions about research methodologies. A significant event to watch for is the online celebration marking the 40th anniversary of Elliptic Curve Cryptography (ECC) on August 11, 2025. This event will commemorate the foundational work of Victor Miller and Neal Koblitz in 1985. It is anticipated to be a very important event for those in the cryptography community and to those who work with elliptic curves.
The ECC celebration will feature personal reflections from Miller and Koblitz, alongside lectures by Dan Boneh and Kristin Lauter, who will explore ECC's broad impact on cryptography and its unforeseen applications. The history of ECC is used as a good example of how fundamental research can lead to unexpected and practical outcomes. This serves as a good way to promote blue skies research. In other news, mathematicians are actively discussing the use of formal methods in their research. One Mathstodon user described using LaTeX and Agda in TypeTopology for writing papers and formalizing mathematical remarks. They found that formalizing remarks in a paper could reveal errors in thinking and improve results, even in meta-mathematical methodology. This shows how computational tools are increasingly being used to verify and explore mathematical ideas, highlighting the practical utility of pure math skills in applied contexts. Recommended read:
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@forge.dyalog.com
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The APL Forge competition is in its final week, with the deadline for submissions set for Monday, June 23, 2024, at 12:00 UTC. This annual event is designed to promote the use and development of the APL programming language within the community. Participants are challenged to create innovative open-source libraries and commercial applications using Dyalog APL. The APL Forge is where developers are rewarded for using Dyalog APL to solve problems and develop libraries, applications, and tools.
Whether you're an individual, a group, or a company, if you have a passion for problem-solving in APL, this competition is for you. The APL Forge competition is rewarding participants for using Dyalog APL to solve problems and develop libraries, applications, and tools. The winner of the APL Forge competition will receive £2,500 (GBP) and an expenses-paid trip to present at our next user meeting. Those looking for inspiration are encouraged to check out the project ideas listed on the APL Forge website, where they can also find eligibility and judging criteria, submission guidelines, and frequently asked questions. For more information and to enter the APL Forge, visit forge.dyalog.com. Recommended read:
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@phys.org
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bigthink.com
, phys.org
Recent research is challenging previous assumptions about the composition and structure of the smallest galaxies. Traditionally believed to be dominated by dark matter due to the expulsion of normal matter through stellar winds and radiation during star formation, new evidence suggests that supermassive black holes may play a more significant role than previously thought. A recent study indicates that Segue 1, known as the most dark matter-dominated galaxy, might harbor a supermassive black hole at its center, potentially altering our understanding of galactic dynamics in low-mass systems. This proposition offers an alternative explanation for the observed gravitational effects, suggesting that these central black holes could be anchoring these tiny galaxies.
The realm of statistical analysis is also undergoing significant advancements. Mathematician Tyron Lardy has pioneered a novel approach to hypothesis testing, utilizing e-values instead of the conventional p-values. E-values, representing 'expected value', provide greater flexibility, particularly during mid-study analysis when adjustments to data collection or analysis plans are necessary. Unlike p-values, which require conclusions to be drawn only after all data is gathered to maintain statistical validity, e-values remain statistically sound even with modifications to the research process. This advancement holds promise for fields like medicine and psychology, where complex situations often demand adaptable data handling techniques. The development of e-values is based on the concept of betting, where the e-value signifies the potential earnings from such bets, offering quantifiable evidence against the initial assumption. This approach allows researchers to assess whether an assumption still holds true. While the general method for calculating optimal e-values can be intricate, its flexibility and robustness in handling data adjustments offer a valuable tool for scientific research, enhancing the reliability and adaptability of hypothesis testing in various disciplines. Recommended read:
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@www.marktechpost.com
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Google has unveiled a new AI model designed to forecast tropical cyclones with improved accuracy. Developed through a collaboration between Google Research and DeepMind, the model is accessible via a newly launched website called Weather Lab. The AI aims to predict both the path and intensity of cyclones days in advance, overcoming limitations present in traditional physics-based weather prediction models. Google claims its algorithm achieves "state-of-the-art accuracy" in forecasting cyclone track and intensity, as well as details like formation, size, and shape.
The AI model was trained using two extensive datasets: one describing the characteristics of nearly 5,000 cyclones from the past 45 years, and another containing millions of weather observations. Internal testing demonstrated the algorithm's ability to accurately predict the paths of recent cyclones, in some cases up to a week in advance. The model can generate 50 possible scenarios, extending forecast capabilities up to 15 days. This breakthrough has already seen adoption by the U.S. National Hurricane Center, which is now using these experimental AI predictions alongside traditional forecasting models in its operational workflow. Google's AI's ability to forecast up to 15 days in advance marks a significant improvement over current models, which typically provide 3-5 day forecasts. Google made the AI accessible through a new website called Weather Lab. The model is available alongside two years' worth of historical forecasts, as well as data from traditional physics-based weather prediction algorithms. According to Google, this could help weather agencies and emergency service experts better anticipate a cyclone’s path and intensity. Recommended read:
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@www.marktechpost.com
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Apple researchers are challenging the perceived reasoning capabilities of Large Reasoning Models (LRMs), sparking debate within the AI community. A recent paper from Apple, titled "The Illusion of Thinking," suggests that these models, which generate intermediate thinking steps like Chain-of-Thought reasoning, struggle with fundamental reasoning tasks. The research indicates that current evaluation methods relying on math and code benchmarks are insufficient, as they often suffer from data contamination and fail to assess the structure or quality of the reasoning process.
To address these shortcomings, Apple researchers introduced controllable puzzle environments, including the Tower of Hanoi, River Crossing, Checker Jumping, and Blocks World, allowing for precise manipulation of problem complexity. These puzzles require diverse reasoning abilities, such as constraint satisfaction and sequential planning, and are free from data contamination. The Apple paper concluded that state-of-the-art LRMs ultimately fail to develop generalizable problem-solving capabilities, with accuracy collapsing to zero beyond certain complexities across different environments. However, the Apple research has faced criticism. Experts, like Professor Seok Joon Kwon, argue that Apple's lack of high-performance hardware, such as a large GPU-based cluster comparable to those operated by Google or Microsoft, could be a factor in their findings. Some argue that the models perform better on familiar puzzles, suggesting that their success may be linked to training exposure rather than genuine problem-solving skills. Others, such as Alex Lawsen and "C. Opus," argue that the Apple researchers' results don't support claims about fundamental reasoning limitations, but rather highlight engineering challenges related to token limits and evaluation methods. Recommended read:
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@quantumcomputingreport.com
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thequantuminsider.com
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The quantum computing industry is experiencing a surge in activity, marked by significant acquisitions and technological advancements. IonQ has announced its intent to acquire UK-based Oxford Ionics for $1.075 billion in stock and cash, uniting two leaders in trapped-ion quantum computing. This deal aims to accelerate the development of scalable and reliable quantum systems, targeting 256 high-fidelity qubits by 2026 and over 10,000 physical qubits by 2027. The acquisition combines IonQ's quantum computing stack with Oxford Ionics' semiconductor-compatible ion-trap technology, strengthening IonQ's technical capabilities and expanding its European presence. CEO of IonQ, Niccolo de Masi, highlighted the strategic importance of this acquisition, uniting talent from across the world to become the world’s best quantum computing, quantum communication and quantum networking ecosystem.
Recent advancements also include the activation of Europe’s first room-temperature quantum accelerator by Fraunhofer IAF, featuring Quantum Brilliance’s diamond-based QB-QDK2.0 system. This system utilizes nitrogen-vacancy (NV) centers and operates without cryogenic requirements, seamlessly integrating into existing high-performance computing environments. It's co-located with classical processors and NVIDIA GPUs to support hybrid quantum-classical workloads. Moreover, IBM has announced plans to build the world’s first large-scale, error-corrected quantum computer named Starling, aiming for completion by 2028 and cloud availability by 2029. IBM claims it has cracked the code for quantum error correction, moving from science to engineering. Further bolstering the industry's growth, collaborative projects are demonstrating the potential of quantum computing in various applications. IonQ, in partnership with AstraZeneca, AWS, and NVIDIA, has showcased a quantum-accelerated drug discovery workflow that drastically reduces simulation time for key pharmaceutical reactions. Their hybrid system, integrating IonQ’s Forte quantum processor with NVIDIA CUDA-Q and AWS infrastructure, achieved over a 20-fold improvement in time-to-solution for the Suzuki-Miyaura reaction. Additionally, the Karnataka State Cabinet has approved the second phase of the Quantum Research Park at the Indian Institute of Science (IISc) in Bengaluru, allocating ₹48 crore ($5.595 million USD) to expand the state’s quantum technology infrastructure and foster collaboration between academia, startups, and industry. Recommended read:
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Sophia Chen@technologyreview.com
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IBM Aims to Build First Large-Scale Error-Corrected Quantum Computer by 2028 - IBM plans to build a large-scale, error-corrected quantum computer by 2028, with cloud access anticipated by 2029.
ImgSrc: wp.technologyre
IBM has announced ambitious plans to construct a large-scale, error-corrected quantum computer, aiming for completion by 2028. This initiative, known as IBM Quantum Starling, represents a significant step forward in quantum computing technology. The project involves a modular architecture, with components being developed at a new IBM Quantum Data Center in Poughkeepsie, New York. IBM hopes to make the computer available to users via the cloud by 2029.
The company's approach to fault tolerance involves a novel architecture using quantum low-density parity check (qLDPC) codes. This method is projected to drastically reduce the number of physical qubits required for error correction, potentially cutting overhead by around 90% compared to other leading codes. IBM says it's cracked the code to quantum error correction and this will significantly enhance the computational capability of the new machine compared to existing quantum computers. IBM also released two technical papers outlining how qLDPC codes can improve instruction processing and operational efficiency, and describes how error correction and decoding can be handled in real-time using classical computing resources. IBM anticipates that Starling will be capable of executing 100 million quantum operations using 200 logical qubits. This lays the foundation for a follow-up system, IBM Quantum Blue Jay, which will operate with 2,000 logical qubits and run 1 billion operations. According to IBM, storing the computational state of Starling would require memory exceeding that of a quindecillion (10⁴⁸) of today’s most powerful supercomputers. This project aims to solve real-world challenges and unlock immense possibilities for business in fields such as drug development, materials science, chemistry, and optimisation. Recommended read:
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Carl Franzen@AI News | VentureBeat
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Mistral AI has launched its first reasoning model, Magistral, signaling a commitment to open-source AI development. The Magistral family features two models: Magistral Small, a 24-billion parameter model available with open weights under the Apache 2.0 license, and Magistral Medium, a proprietary model accessible through an API. This dual release strategy aims to cater to both enterprise clients seeking advanced reasoning capabilities and the broader AI community interested in open-source innovation.
Mistral's decision to release Magistral Small under the permissive Apache 2.0 license marks a significant return to its open-source roots. The license allows for the free use, modification, and distribution of the model's source code, even for commercial purposes. This empowers startups and established companies to build and deploy their own applications on top of Mistral’s latest reasoning architecture, without the burdens of licensing fees or vendor lock-in. The release serves as a powerful counter-narrative, reaffirming Mistral’s dedication to arming the open community with cutting-edge tools. Magistral Medium demonstrates competitive performance in the reasoning arena, according to internal benchmarks released by Mistral. The model was tested against its predecessor, Mistral-Medium 3, and models from Deepseek. Furthermore, Mistral's Agents API's Handoffs feature facilitates smart, multi-agent workflows, allowing different agents to collaborate on complex tasks. This enables modular and efficient problem-solving, as demonstrated in systems where agents collaborate to answer inflation-related questions. Recommended read:
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@www.marktechpost.com
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A new framework called AlphaOne, developed by researchers at the University of Illinois Urbana-Champaign and the University of California, Berkeley, offers AI developers a novel method to modulate the reasoning processes of large language models (LLMs). This test-time scaling technique improves model accuracy and efficiency without requiring costly retraining. AlphaOne essentially provides a new "dial" to control LLM 'thinking,' allowing developers to boost performance on complex tasks in a more controlled and cost-effective manner compared to existing approaches. The framework dynamically manages slow-to-fast reasoning transitions, optimizing accuracy on real-world datasets like AMC23 and LiveCodeBench.
One persistent issue with large reasoning models is their inability to self-regulate shifts between fast and slow thinking, leading to either premature conclusions or excessive processing. AlphaOne addresses this by providing a universal method for modulating the reasoning process of advanced LLMs. Previous solutions, such as parallel scaling (running a model multiple times) or sequential scaling (modulating thinking during a single run), often lack synchronization between the duration of reasoning and the scheduling of slow-to-fast thinking transitions. AlphaOne aims to overcome these limitations by effectively adapting reasoning processes. In addition to AlphaOne, Amazon Nova provides a solution for data consistency in generative AI through Text-to-SQL. Businesses rely on precise, real-time insights to make critical decisions, and Text-to-SQL bridges the gap by generating precise, schema-specific queries that empower faster decision-making and foster a data-driven culture. Unlike Retrieval Augmented Generation (RAG) which is better suited for extracting insights from unstructured data and Generative Business Intelligence, Text-to-SQL excels in querying structured organizational data directly from relational schemas and provides deterministic, reproducible results for specific, schema-dependent queries. Recommended read:
References :
Mark Tyson@tomshardware.com
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OpenAI has recently launched its newest reasoning model, o3-pro, making it available to ChatGPT Pro and Team subscribers, as well as through OpenAI’s API. Enterprise and Edu subscribers will gain access the following week. The company touts o3-pro as a significant upgrade, emphasizing its enhanced capabilities in mathematics, science, and coding, and its improved ability to utilize external tools.
OpenAI has also slashed the price of o3 by 80% and o3-pro by 87%, positioning the model as a more accessible option for developers seeking advanced reasoning capabilities. This price adjustment comes at a time when AI providers are competing more aggressively on both performance and affordability. Experts note that evaluations consistently prefer o3-pro over the standard o3 model across all categories, especially in science, programming, and business tasks. O3-pro utilizes the same underlying architecture as o3, but it’s tuned to be more reliable, especially on complex tasks, with better long-range reasoning. The model supports tools like web browsing, code execution, vision analysis, and memory. While the increased complexity can lead to slower response times, OpenAI suggests that the tradeoff is worthwhile for the most challenging questions "where reliability matters more than speed, and waiting a few minutes is worth the tradeoff.” Recommended read:
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Carl Franzen@AI News | VentureBeat
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Mistral AI has launched Magistral, its inaugural reasoning large language model (LLM), available in two distinct versions. Magistral Small, a 24 billion parameter model, is offered with open weights under the Apache 2.0 license, enabling developers to freely use, modify, and distribute the code for commercial or non-commercial purposes. This model can be run locally using tools like Ollama. The other version, Magistral Medium, is accessible exclusively via Mistral’s API and is tailored for enterprise clients, providing traceable reasoning capabilities crucial for compliance in highly regulated sectors such as legal, financial, healthcare, and government.
Mistral is positioning Magistral as a powerful tool for both professional and creative applications. The company highlights Magistral's ability to perform "transparent, multilingual reasoning," making it suitable for tasks involving complex calculations, programming logic, decision trees, and rule-based systems. Additionally, Mistral is promoting Magistral for creative writing, touting its capacity to generate coherent or, if desired, uniquely eccentric content. Users can experiment with Magistral Medium through the "Thinking" mode within Mistral's Le Chat platform, with options for "Pure Thinking" and a high-speed "10x speed" mode powered by Cerebras. Benchmark tests reveal that Magistral Medium is competitive in the reasoning arena. On the AIME-24 mathematics benchmark, the model achieved an impressive 73.6% accuracy, comparable to its predecessor, Mistral Medium 3, and outperforming Deepseek's models. Mistral's strategic release of Magistral Small under the Apache 2.0 license is seen as a reaffirmation of its commitment to open source principles. This move contrasts with the company's previous release of Medium 3 as a proprietary offering, which had raised concerns about a shift towards a more closed ecosystem. Recommended read:
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@machinelearning.apple.com
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Apple researchers have released a new study questioning the capabilities of Large Reasoning Models (LRMs), casting doubt on the industry's pursuit of Artificial General Intelligence (AGI). The research paper, titled "The Illusion of Thinking," reveals that these models, including those from OpenAI, Google DeepMind, Anthropic, and DeepSeek, experience a 'complete accuracy collapse' when faced with complex problems. Unlike existing evaluations primarily focused on mathematical and coding benchmarks, this study evaluates the reasoning traces of these models, offering insights into how LRMs "think".
Researchers tested various models, including OpenAI's o3-mini, DeepSeek-R1, and Claude 3.7 Sonnet, using puzzles like the Tower of Hanoi, Checker Jumping, River Crossing, and Blocks World. These environments allowed for the manipulation of complexity while maintaining consistent logical structures. The team discovered that standard language models surprisingly outperformed LRMs in low-complexity scenarios, while LRMs only demonstrated advantages in medium-complexity tasks. However, all models experienced a performance collapse when faced with highly complex tasks. The study suggests that the so-called reasoning of LRMs may be more akin to sophisticated pattern matching, which is fragile and prone to failure when challenged with significant complexity. Apple's research team identified three distinct performance regimes: low-complexity tasks where standard models outperform LRMs, medium-complexity tasks where LRMs show advantages, and high-complexity tasks where all models collapse. Apple has begun integrating powerful generative AI into its own apps and experiences. The new Foundation Models framework gives app developers access to the on-device foundation language model. Recommended read:
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@medium.com
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Medium is currently hosting a series of articles that delve into the core concepts and practical applications of cryptography. These articles aim to demystify complex topics such as symmetric key cryptography, also known as secret key or private key cryptography, where a single shared key is used for both encryption and decryption. This method is highlighted for its speed and efficiency, making it suitable for bulk data encryption, though it primarily provides confidentiality and requires secure key distribution. The resources available are designed to cater to individuals with varying levels of expertise, offering accessible guides to enhance their understanding of secure communication and cryptographic systems.
The published materials offer detailed explorations of cryptographic techniques, including AES-256 encryption and decryption. AES-256, which stands for Advanced Encryption Standard with a 256-bit key size, is a symmetric encryption algorithm renowned for its high level of security. Articles break down the internal mechanics of AES-256, explaining the rounds of transformation and key expansion involved in the encryption process. These explanations are presented in both technical terms for those with a deeper understanding and in layman's terms to make the concepts accessible to a broader audience. In addition to theoretical explanations, the Medium articles also showcase the practical applications of cryptography. One example provided is the combination of OSINT (Open Source Intelligence), web, crypto, and forensics techniques in CTF (Capture The Flag) challenges. These challenges offer hands-on experience in applying cryptographic principles to real-world scenarios, such as identifying the final resting place of historical figures through OSINT techniques. The series underscores the importance of mastering cryptography in the evolving landscape of cybersecurity, equipping readers with the knowledge to secure digital communications and protect sensitive information. Recommended read:
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@medium.com
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Recent advancements in math education are focusing on making mathematics more accessible and intuitive for all learners. Universal Design for Learning (UDL) is gaining traction as a framework to optimize teaching and learning by acknowledging the varied needs of students. This approach aims to eliminate barriers and foster a belief that every student is capable of excelling in math. Educators are encouraged to offer multiple modalities for interacting with content, addressing the "why," "what," and "how" of learning to ensure every student has a successful access point.
Mathz AI is emerging as a powerful tool extending beyond traditional homework help. It emphasizes conceptual clarity by guiding users through multiple solution paths with interactive explanations. Features include versatile input methods, clear problem displays, hints, step-by-step solutions, and auto-generated practice questions. It offers targeted revision plans and breakdowns the logic behind each solution. This AI-driven approach promotes active engagement, enabling students to see patterns, connect concepts, and build confidence. It also acts as a resource for parents and tutors, offering intuitive ways to assist learners. Machine learning is becoming more accessible to individuals without advanced math backgrounds. While concepts like linear algebra, calculus, and probability are relevant, a strong understanding of fundamental principles, critical thinking, and the ability to apply appropriate tools are sufficient to start. Linear Regression is a fundamental machine learning model to grasp and implement, allowing us to find relationships between data and make predictions. Interactive tools are also enhancing the learning experience, providing visual and intuitive ways to understand complex machine learning and mathematical concepts. Recommended read:
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@www.iansresearch.com
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The increasing capabilities of quantum computers are posing a significant threat to current encryption methods, potentially jeopardizing the security of digital assets and the Internet of Things. Researchers at Google Quantum AI are urging software developers and encryption experts to accelerate the implementation of next-generation cryptography, anticipating that quantum computers will soon be able to break widely used encryption standards like RSA. This urgency is fueled by new estimates suggesting that breaking RSA encryption may be far easier than previously believed, with a quantum computer containing approximately 1 million qubits potentially capable of cracking it. Experts recommend that vulnerable systems should be deprecated after 2030 and disallowed after 2035.
Last week, Craig Gidney from Google Quantum AI published research that significantly lowers the estimated quantum resources needed to break RSA-2048. Where previous estimates projected that cracking RSA-2048 would require around 20 million qubits and 8 hours of computation, the new analysis reveals that it could be done in under a week using fewer than 1 million noisy qubits. This more than 95% reduction in hardware requirements is a seismic shift in the projected timeline for "Q-Day," the hypothetical moment when quantum computers can break modern encryption. RSA encryption, used in secure web browsing, email encryption, VPNs, and blockchain systems, relies on the difficulty of factoring large numbers into their prime components. Quantum computers, leveraging Shor's algorithm, can exponentially accelerate this process. Recent innovations, including Approximate Residue Arithmetic, Magic State Cultivation, Optimized Period Finding with Ekerå-Håstad Algorithms, and Yoked Surface Codes & Sparse Lookups, have collectively reduced the physical qubit requirement to under 1 million and allow the algorithm to complete in less than 7 days. Recommended read:
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@www.quantamagazine.org
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Fermilab has announced the final results from its Muon g-2 experiment, aiming to resolve a long-standing anomaly regarding the magnetic moment of muons. This experiment delves into the quantum realm, exploring how short-lived particles popping in and out of existence influence the magnetic properties of muons. The initial results from this experiment suggested that the Standard Model of physics might be incomplete, hinting at the presence of undiscovered particles or forces.
The experiment's findings continue to show a discrepancy between experimental measurements and the predictions of the Standard Model. However, the statistical significance of this discrepancy has decreased due to improvements in theoretical calculations. This implies that while the Standard Model may not fully account for the behavior of muons, the evidence for new physics is not as strong as previously thought. The result is at 4.2σ (standard deviations) away from what's calculated using the Standard Model, which is a bit short of the 5 sigma normally used to declare a discovery. There's about a 1 in 40,000 chance that this is a fluke. Despite the reduced statistical significance, the results remain intriguing and motivate further research. The possibility of undiscovered particles influencing muons still exists, pushing physicists to explore new theoretical models and conduct additional experiments. Fermilab shared first results from their "g-2" experiment showing the Standard Model of physics is even more incomplete than we thought. If the universe includes particles we don't yet know about, these too will show up as fluctuations around particles, influencing the properties we can measure. Recommended read:
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@www.quantamagazine.org
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Recent breakthroughs have significantly advanced the "Core of Fermat's Last Theorem," a concept deeply rooted in number theory. Four mathematicians have extended the key insight behind Fermat's Last Theorem, which states there are no three positive integers that, when raised to a power greater than two, can be added together to equal another number raised to the same power. Their work involves applying this concept to other mathematical objects, notably elliptic curves. This extension represents a major step towards building a "grand unified theory" of mathematics, a long-sought goal in the field.
This achievement builds upon the groundwork laid by Andrew Wiles's famous 1994 proof of Fermat's Last Theorem. Wiles, with assistance from Richard Taylor, demonstrated that elliptic curves and modular forms, seemingly distinct mathematical entities, are interconnected. This discovery revealed a surprising "modularity," where these realms mirror each other in a distorted way. Mathematicians can now leverage this connection, translating problems about elliptic curves into the language of modular forms, solving them, and then applying the results back to the original problem. This new research goes beyond elliptic curves, extending the modularity connection to more complicated mathematical objects. This breakthrough defies previous expectations that such extensions would be impossible. The Langlands program, a set of conjectures aiming to develop a grand unified theory of mathematics, hinges on such correspondences. The team's success provides strong support for the Langlands program and opens new avenues for solving previously intractable problems in various areas of mathematics, solidifying the power and reach of the "Core of Fermat's Last Theorem." Recommended read:
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Nvidia's Blackwell GPUs have achieved top rankings in the latest MLPerf Training v5.0 benchmarks, demonstrating breakthrough performance across various AI workloads. The NVIDIA AI platform delivered the highest performance at scale on every benchmark, including the most challenging large language model (LLM) test, Llama 3.1 405B pretraining. Nvidia was the only vendor to submit results on all MLPerf Training v5.0 benchmarks, highlighting the versatility of the NVIDIA platform across a wide array of AI workloads, including LLMs, recommendation systems, multimodal LLMs, object detection, and graph neural networks.
The at-scale submissions used two AI supercomputers powered by the NVIDIA Blackwell platform: Tyche, built using NVIDIA GB200 NVL72 rack-scale systems, and Nyx, based on NVIDIA DGX B200 systems. Nvidia collaborated with CoreWeave and IBM to submit GB200 NVL72 results using a total of 2,496 Blackwell GPUs and 1,248 NVIDIA Grace CPUs. The GB200 NVL72 systems achieved 90% scaling efficiency up to 2,496 GPUs, improving time-to-convergence by up to 2.6x compared to Hopper-generation H100. The new MLPerf Training v5.0 benchmark suite introduces a pretraining benchmark based on the Llama 3.1 405B generative AI system, the largest model to be introduced in the training benchmark suite. On this benchmark, Blackwell delivered 2.2x greater performance compared with the previous-generation architecture at the same scale. Furthermore, on the Llama 2 70B LoRA fine-tuning benchmark, NVIDIA DGX B200 systems, powered by eight Blackwell GPUs, delivered 2.5x more performance compared with a submission using the same number of GPUs in the prior round. These performance gains highlight advancements in the Blackwell architecture and software stack, including high-density liquid-cooled racks, fifth-generation NVLink and NVLink Switch interconnect technologies, and NVIDIA Quantum-2 InfiniBand networking. Recommended read:
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