Top Mathematics discussions
NishMath
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@quantumcomputingreport.com
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References:
thequantuminsider.com
, Bitcoin News
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Project Eleven, an open science initiative, has launched the QDay Prize, a global competition offering a reward of one Bitcoin, currently valued around $84,000-$85,000, to the first individual or team that can successfully break elliptic curve cryptography (ECC) using Shor’s algorithm on a quantum computer. The competition aims to assess the current progress in quantum computing and its potential to undermine existing cryptographic systems, emphasizing the transition to post-quantum cryptography. Participants are required to submit a working quantum implementation targeting ECC keys, with no classical shortcuts or hybrid methods allowed, ensuring a pure quantum solution.
The challenge involves breaking the largest ECC key possible using Shor’s algorithm on a quantum computer, focusing on a gate-level implementation of Shor’s algorithm solving the elliptic curve discrete logarithm problem (ECDLP). Project Eleven has prepared a set of ECC keys ranging from 1 to 25 bits for testing, with submissions required to include quantum program code, a written explanation of the method, and details about the hardware used. The quantum machine does not need to be publicly available, but submissions will be shared publicly to ensure transparency. The contest, which runs until April 5, 2026, highlights the real-world cryptographic risks of advancing quantum hardware. Project Eleven believes that even achieving a few bits of a private key would be a significant breakthrough. Experts estimate that a 256-bit ECC key could be cracked with 2,000 logical qubits, potentially within a decade, underscoring the urgency of understanding how close current technologies are to threatening ECC security. The QDay Prize seeks to establish a verifiable and open marker of when practical quantum attacks against widely used encryption systems may emerge. Recommended read:
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@Math Blog
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Math Blog
, denisegaskins.com
Mathematical concepts and their applications are gaining increased attention, with recent explorations into diverse areas. A blog post discusses the fundamental differences between mathematical and statistical reasoning, using the example of predicting days with the fewest noninduced births. Researchers are also delving into methods for eliminating parameters in parametric equations. A podcast delves into the philosophy of mathematics and set theory, examining the nature of mathematics itself.
The article "Eliminating the Parameter in Parametric Equations" provides a guide for expressing relationships between variables `x` and `y` when they are defined in terms of a parameter `t`. It explains the process of removing the parameter to obtain a direct equation between `x` and `y`, showcasing examples and solutions. Furthermore, there is a discussion on Charlotte Mason's approach to mathematics using living books as a method of teaching. Python's dominance in AI and machine learning is a significant development. An article explores the factors behind this, highlighting Python's readability, extensive libraries like NumPy, Pandas, Scikit-learn, TensorFlow, and PyTorch, and the role of AI hype in its rise. The Church of Logic podcast also featured a discussion with Joel David Hamkins on the philosophy of mathematics and set theory, particularly exploring differing perspectives on the nature of mathematics. Recommended read:
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@www.quantamagazine.org
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Recent advancements in mathematics and physics are pushing the boundaries of our understanding of the universe. A decades-old bet between mathematicians Noga Alon and Peter Sarnak regarding the nature of optimal expander graphs has recently been settled, with both mathematicians being proven wrong. This involved tapping into a crucial phenomenon in physics and pushing it to its limits, demonstrating the interconnectedness of mathematics and physics. Also, Researchers have successfully modeled how 'broken' tulips get their stripes, solving a centuries-old floral mystery. The mathematical model explains that the tulip-breaking virus inhibits the production of anthocyanins, leading to the distinctive striped pattern.
Efforts are underway to bridge the gap between quantum mechanics and general relativity, with researchers exploring the possibility of creating quantum gravity in the lab. Monika Schleier-Smith at Stanford University is leading this effort by using laser-cooled atoms to explore whether gravity could emerge from quantum entanglement. NASA is also contributing to this field by developing the first space-based quantum gravity gradiometer. This gradiometer will use ultra-cold rubidium atoms to detect gravitational anomalies with high precision from orbit, with potential applications in water resource management and subsurface geology. Further progress is being made in language model development. Researchers are exploring methods to sidestep language in order to improve how language models work with mathematics. By allowing these models to operate directly in mathematical spaces, they aim to enhance efficiency and reasoning capabilities. This research highlights the potential for artificial intelligence systems to benefit from thinking independently of language, paving the way for more advanced and effective AI applications. Recommended read:
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@medium.com
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References:
IACR News
, thequantuminsider.com
Quantum computing is rapidly advancing, and its potential impact on encryption security is becoming a major concern. Classical encryption methods, such as RSA and Elliptic Curve Cryptography (ECC), rely on mathematical problems that are difficult for traditional computers to solve. However, quantum algorithms, particularly Shor’s algorithm, threaten to break these systems. Shor's algorithm can efficiently factor large integers, which is the foundation of RSA, and solve the elliptic curve discrete logarithm problem (ECDLP), which underpins ECC. Project Eleven has even launched the Q-Day Prize, offering 1 Bitcoin to anyone who can crack a Bitcoin private key using Shor’s algorithm on a quantum computer, underscoring the urgency of addressing this threat.
The vulnerability of current cryptographic methods has spurred research into post-quantum cryptography (PQC). PQC focuses on developing encryption algorithms that are resistant to attacks from both classical and quantum computers. The National Institute of Standards and Technology (NIST) has already published its first set of post-quantum standards in August 2024, including algorithms like ML-KEM (Kyber) for key encapsulation and ML-DSA (Dilithium) for digital signatures. These standards are intended to be integrated into software and systems over the coming years, with the NSA’s Commercial National Security Algorithm Suite (CNSA 2.0) mandating their use in certain applications by 2030. While commercially viable quantum computers capable of breaking current encryption are still under development, the pace of progress is accelerating. IBM and Google are among the companies racing to build larger and more powerful quantum processors. Experts estimate that a quantum computer with around 20 million physical qubits (approximately 6,000 logical qubits) could factor a 2048-bit RSA modulus in a matter of hours. This has led to a "harvest-now, decrypt-later" strategy, where adversaries collect encrypted data with the intention of decrypting it once quantum computers become powerful enough. The transition to quantum-resistant cryptography is now considered an engineering problem, requiring careful planning and implementation across various systems and infrastructures. Recommended read:
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@www.quantamagazine.org
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References:
pub.towardsai.net
, Sebastian Raschka, PhD
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Recent developments in the field of large language models (LLMs) are focusing on enhancing reasoning capabilities through reinforcement learning. This approach aims to improve model accuracy and problem-solving, particularly in challenging tasks. While some of the latest LLMs, such as GPT-4.5 and Llama 4, were not explicitly trained using reinforcement learning for reasoning, the release of OpenAI's o3 model shows that strategically investing in compute and tailored reinforcement learning methods can yield significant improvements.
Competitors like xAI and Anthropic have also been incorporating more reasoning features into their models, such as the "thinking" or "extended thinking" button in xAI Grok and Anthropic Claude. The somewhat muted response to GPT-4.5 and Llama 4, which lack explicit reasoning training, suggests that simply scaling model size and data may be reaching its limits. The field is now exploring ways to make language models work better, including the use of reinforcement learning. One of the ways that researchers are making language models work better is to sidestep the requirement for language as an intermediary step. Language isn't always necessary, and that having to turn ideas into language can slow down the thought process. LLMs process information in mathematical spaces, within deep neural networks, however, they must often leave this latent space for the much more constrained one of individual words. Recent papers suggest that deep neural networks can allow language models to continue thinking in mathematical spaces before producing any text. Recommended read:
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@arstechnica.com
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References:
arstechnica.com
, www.techrepublic.com
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Microsoft researchers have achieved a significant breakthrough in AI efficiency with the development of a 1-bit large language model (LLM) called BitNet b1.58 2B4T. This model, boasting two billion parameters and trained on four trillion tokens, stands out due to its remarkably low memory footprint and energy consumption. Unlike traditional AI models that rely on 16- or 32-bit floating-point formats for storing numerical weights, BitNet utilizes only three distinct weight values: -1, 0, and +1. This "ternary" architecture dramatically reduces complexity, enabling the AI to run efficiently on a standard CPU, even an Apple M2 chip, according to TechCrunch.
The development of BitNet b1.58 2B4T represents a significant advancement in the field of AI, potentially paving the way for more accessible and sustainable AI applications. This 1-bit model, available on Hugging Face, uses a novel approach of representing each weight with a single bit. While this simplification can lead to a slight reduction in accuracy compared to larger, more complex models, BitNet b1.58 2B4T compensates through its massive training dataset, comprising over 33 million books. The reduction in memory usage is substantial, with the model requiring only 400MB of non-embedded memory, significantly less than comparable models. Comparisons against leading mainstream models like Meta’s LLaMa 3.2 1B, Google’s Gemma 3 1B, and Alibaba’s Qwen 2.5 1.5B have shown that BitNet b1.58 2B4T performs competitively across various benchmarks. In some instances, it has even outperformed these models. However, to achieve optimal performance and efficiency, the LLM must be used with the bitnet.cpp inference framework. This highlights a current limitation as the model does not run on GPU and requires a proprietary framework. Despite this, the creation of such a lightweight and efficient LLM marks a crucial step toward future AI that may not necessarily require supercomputers. Recommended read:
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The Google@The Official Google Blog
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Quantum computing is rapidly advancing, moving beyond a futuristic dream to become a tangible force in solving real-world problems. Experts predict that quantum utility, the point at which quantum computers offer practical advantages over classical computers, is at most 10 years away. This progress is fueled by the potential of quantum computers to optimize finance, discover new drugs, secure networks, and even build better batteries. The industry overwhelmingly agrees that this moment is fast approaching, with some anticipating it could arrive within the next one to five years.
The US military is taking a proactive approach by launching an initiative spearheaded by the Defense Advanced Research Projects Agency (DARPA) to identify the most promising quantum computer technologies. DARPA aims to discern which of the numerous quantum computers currently under development have the greatest potential to revolutionize American industries and the broader economy. This initiative underscores the strategic importance of quantum computing and the desire to be at the forefront of its development and application. However, challenges remain in achieving widespread quantum utility. Misconceptions about quantum computing are hindering advancement, highlighting the need for improved public and business education. Overcoming technical hurdles, particularly error correction, and acquiring sufficient talent are also key concerns. Despite these challenges, the collective progress and the focused efforts of both industry and government suggest that quantum computing is poised to make a significant impact in the near future. Recommended read:
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@www.analyticsvidhya.com
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OpenAI recently unveiled its groundbreaking o3 and o4-mini AI models, representing a significant leap in visual problem-solving and tool-using artificial intelligence. These models can manipulate and reason with images, integrating them directly into their problem-solving process. This unlocks a new class of problem-solving that blends visual and textual reasoning, allowing the AI to not just see an image, but to "think with it." The models can also autonomously utilize various tools within ChatGPT, such as web search, code execution, file analysis, and image generation, all within a single task flow.
These models are designed to improve coding capabilities, and the GPT-4.1 series includes GPT-4.1, GPT-4.1 mini, and GPT-4.1 nano. GPT-4.1 demonstrates enhanced performance and lower prices, achieving a 54.6% score on SWE-bench Verified, a significant 21.4 percentage point increase from GPT-4o. This is a big gain in practical software engineering capabilities. Most notably, GPT-4.1 offers up to one million tokens of input context, compared to GPT-4o's 128k tokens, making it suitable for processing large codebases and extensive documentation. GPT-4.1 mini and nano also offer performance boosts at reduced latency and cost. The new models are available to ChatGPT Plus, Pro, and Team users, with Enterprise and education users gaining access soon. While reasoning alone isn't a silver bullet, it reliably improves model accuracy and problem-solving capabilities on challenging tasks. With Deep Research products and o3/o4-mini, AI-assisted search-based research is now effective. Recommended read:
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@Martin Escardo
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www.johndcook.com
, Martin Escardo
A new approach to defining interval objects in category theory is being explored, focusing on the universal characterization of the Euclidean interval. This research, a collaboration between Martin Escardo and Alex Simpson, aims to establish a definition of interval objects applicable to general categories, capturing both geometrical and computational aspects. The goal is to find a definition that works across diverse categorical settings, allowing for a more abstract and unified understanding of intervals. This work builds upon their previous research, aiming for a broader mathematical foundation for interval objects.
The work by Escardo and Simpson delves into defining arithmetic operations within this abstract framework. Given an interval object [-1,1] in a category with finite products, they demonstrate how to define operations such as negation and multiplication using the universal property of the interval. Negation, denoted as -x, is defined as the unique automorphism that maps -1 to 1 and 1 to -1, ensuring that -(-x) = x. Similarly, multiplication x × (-) is defined as the unique automorphism mapping -1 to -x and 1 to x, resulting in commutative and associative multiplication. This research has already produced significant results, including two joint papers: "A universal characterization of the closed Euclidean interval (extended abstract)" from LICS 2001 and "Abstract Datatypes for Real Numbers in Type Theory" from RTA/TLCA'2014. A third paper, focused more on the mathematical aspects, is currently in preparation. This work aims to provide a robust and universal characterization of interval objects, impacting both theoretical mathematics and practical applications in computer science and related fields. Recommended read:
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@www.quantamagazine.org
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finance.yahoo.com
, Quanta Magazine
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Researchers are exploring innovative methods to enhance the performance of artificial intelligence language models by minimizing their reliance on direct language processing. This approach involves enabling models to operate more within mathematical or "latent" spaces, reducing the need for constant translation between numerical representations and human language. Studies suggest that processing information directly in these spaces can improve efficiency and reasoning capabilities, as language can sometimes constrain and diminish the information retained by the model. By sidestepping the traditional language-bound processes, AI systems may achieve better results by "thinking" independently of linguistic structures.
Meta has announced plans to resume training its AI models using publicly available content from European users. This move aims to improve the capabilities of Meta's AI systems by leveraging a vast dataset of user-generated information. The decision comes after a period of suspension prompted by concerns regarding data privacy, which were raised by activist groups. Meta is emphasizing that the training will utilize public posts and comments shared by adult users within the European Union, as well as user interactions with Meta AI, such as questions and queries, to enhance model accuracy and overall performance. A new method has been developed to efficiently safeguard sensitive data used in AI model training, reducing the traditional tradeoff between privacy and accuracy. This innovative framework maintains an AI model's performance while preventing attackers from extracting confidential information, such as medical images or financial records. By focusing on the stability of algorithms and utilizing a metric called PAC Privacy, researchers have shown that it's possible to privatize almost any algorithm without needing access to its internal workings, potentially making privacy more accessible and less computationally expensive in real-world applications. Recommended read:
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@teorth.github.io
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leanprover.zulipchat.com
, Terence Tao
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The Equational Theories Project has achieved a major breakthrough, formalizing all possible implications between a test list of 4694 equational laws in the Lean theorem prover. This involved verifying a staggering 22,033,636 implications (4694 squared) over a period of just over 200 days. The project's success is attributed to a substantial and diverse collection of code, data, and text, highlighting the complexity and scale of the formalization effort. This milestone marks a significant advancement in the field of automated theorem proving, with potential applications in formal verification of mathematical theories and software.
The project leverages the Lean theorem prover, a powerful tool for formalizing mathematics and verifying software. The formalization effort required managing a large volume of code, data, and textual descriptions. Now that the formalization is complete, the project team is focusing on documenting their methodologies and results in a comprehensive paper. This paper will detail the techniques used to tackle the challenge of formalizing such a vast number of implications, offering insights for future research in automated reasoning and formal verification. The next key step for the Equational Theories Project is drafting the accompanying paper. The current draft is in an incomplete state, but is now the central focus of the project. This paper will serve as a crucial resource for understanding the project's accomplishments and methodologies. While the code and data are essential, the paper will provide the necessary context and explanation to make the formalization accessible and useful to the broader research community. Recommended read:
References :
Igor Konnov@Protocols Made Fun
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Protocols Made Fun
, Protocols Made Fun
Model checking is increasingly recognized as a valuable tool in the design of distributed protocols, offering both technical improvements and measurable benefits. Independent researcher Igor Konnov highlights the importance of embracing various methods like testing, property-based testing, simulation, fuzzing, and model checking to enhance correctness and security in critical systems. The focus on model checking stems from its potential to uncover bugs that have economic impact and demonstrate system properties, ultimately leading to better protocol design and implementation. Real value is added when a technical improvement of a protocol is seen, preferably in a measurable way.
Recently, Konnov published two technical papers demonstrating the application of model checkers in verifying fault-tolerant distributed algorithms. These works include the ChonkyBFT consensus protocol for ZKsync and an exploration of automatic model checking of the Ethereum specification, supported by the Ethereum Foundation. The experience gained from these projects highlights the practical advantages of model checking, especially in identifying potential issues and improving overall system reliability. The ZKsync governance protocol was also the topic of a talk at the DeFi Security Summit 2024. Specifically, the application of Quint and Apalache model checkers to the ZKsync governance protocol revealed several benefits, including the identification of code fragments that could be improved and the refinement of freezability logic. The process also demonstrated that legal documents could be translated into state invariants, which were used to specify the protocol. This resulted in the creation of over 50 invariants, all tested with randomized simulation and symbolic model checking, showcasing the ability of model checking to contribute to the verification process, even with bounded model checking and randomized symbolic execution. Recommended read:
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@www.newtonproject.sussex.ac.uk
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Recent blog posts are delving into a variety of mathematical topics, offering insights and explorations across different areas of the field. These posts cover historical aspects of mathematics, examine specific mathematical concepts, and explore the connections between mathematics and other disciplines. This collection of diverse content aims to provide readers with a broader understanding and appreciation of mathematics.
The blog posts include diverse mathematical items. For example, one post references Gemma Frisius' "Arithmeticae Practicae Methodus Facilis" (1540) and its entry in *MAA Mathematical Treasures. Another commemorates April 13 as "On This Day in Math," highlighting mathematical facts associated with the number 103. This includes its unique properties as a prime number and its presence in Ramanujan's mathematical explorations. Furthermore, the blog explores historical events like the coining of the word "microscope" in 1620 and Lord Brouncker's published mathematical result in 1668. From statistical physics to number theory, these blogs showcase the versatility and interdisciplinary nature of mathematical thought. One blog even mentions using statistical physics concepts to analyze election results. These blog postings aim to engage readers with a range of mathematical subjects, from historical figures and publications to contemporary applications and connections. Recommended read:
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@aperiodical.com
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Exploring Number Theory and Recreational Mathematics - The 238th Carnival of Mathematics highlights properties of the number 238, features math art, blog posts on diverse topics, and explores prime numbers.
ImgSrc: www.fractalkitt
References:
Fractal Kitty
The 238th Carnival of Mathematics, organized by Aperiodical, has been celebrated with a diverse range of submissions and mathematical artwork. The carnival highlights interesting properties of the number 238, which is the product of three primes (2 × 7 × 17) and the sum of the first 13 primes. It's also noted as a "triprime." The event showcases the beauty and fun in mathematics, encouraging exploration and engagement with numbers and their unique attributes. Various individuals from the Mathstodon community contributed interesting facts about 238, further enriching the carnival's celebration of mathematics.
The Carnival features engaging math art and thoughtful blog posts covering diverse topics. Ayliean's #MathArtMarch initiative inspired creative works including crochet, coding, painting, and structural designs. Blog posts include Peter Cameron's reflections on Compactness, Memories of CFSG, and research defense strategies. Further topics discussed were polyominoes, a modern presentation of Peano Axioms, practical math for programmers, the Monty Hall Problem, communication failures, a visual Go For Geometry series, and group theory with Zoombinis. Prime numbers and their curiosities were also explored, inviting mathematicians and enthusiasts to discover and share interesting properties. The Prime Pages maintain an evolving collection of prime numbers with unique characteristics. "Prime Curios!" is an exciting collection of curiosities, wonders and trivia related to prime numbers. There are currently 31951 curios corresponding to 22773 different numbers in their database. One post highlighted truncatable primes and a game based on creating prime number strings. The goal is to list the small primes that are especially curious and provide explanations understandable to a general audience, fostering further interest and investigation in prime numbers. Recommended read:
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@console.cloud.google.com
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References:
Compute
, BigDATAwire
Google Cloud is empowering global scientific discovery and innovation by integrating Google DeepMind and Google Research technologies with its cloud infrastructure. This initiative aims to provide researchers with advanced, cloud-scale tools for scientific computing. The company is introducing supercomputing-class infrastructure, including H4D VMs powered by AMD CPUs and A4/A4X VMs powered by NVIDIA GPUs, which boast low-latency networking and high memory bandwidth. Additionally, Google Cloud Managed Lustre offers high-performance storage I/O, enabling scientists to tackle large-scale and complex scientific problems.
Google Cloud is also rolling out advanced scientific applications powered by AI models. These include AlphaFold 3 for predicting the structure and interactions of biomolecules, and WeatherNext models for weather forecasting. Moreover, the company is introducing AI agents designed to accelerate scientific discovery. As an example, Google Cloud and Ai2 are investing $20 million in the Cancer AI Alliance to accelerate cancer research using AI, advanced models, and cloud computing power. Google Cloud will provide the AI infrastructure and security, while Ai2 will deliver the training and development of cancer models. In addition to these advancements, Google unveiled its seventh-generation Tensor Processing Unit (TPU), Ironwood. The company claims Ironwood delivers 24 times the computing power of the world’s fastest supercomputer when deployed at scale. Ironwood is specifically designed for inference workloads, marking a shift in Google's AI chip development strategy. When scaled to 9,216 chips per pod, Ironwood delivers 42.5 exaflops of computing power, and each chip comes with 192GB of High Bandwidth Memory. Recommended read:
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@gilkalai.wordpress.com
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Combinatorics and more
, grossack.site
Recent breakthroughs in mathematics have captured the attention of researchers, spanning both theoretical and practical domains. Bo’az Klartag has released a new paper detailing findings on lower bounds for sphere packing in high dimensions. This is a significant achievement as it surpasses previously known constructions. Additionally, advancements are being made in understanding analytic combinatorics and its application to problems such as counting ternary trees.
Klartag's paper presents a novel approach to sphere packing. It proves that in any dimension, there exists an origin-symmetric ellipsoid of specific volume that contains no lattice points other than the origin. This leads to a lattice sphere packing with a density significantly higher than previously achieved, marking a substantial leap forward in this area of study. Gil Kalai, who lives in the same neighborhood as Klartag, was among the first to acknowledge and celebrate this significant accomplishment. Beyond sphere packing, researchers are also exploring analytic combinatorics and its applications. One specific example involves determining the asymptotic formula for the number of ternary trees with *n* nodes. A recent blog post delves into this problem, showcasing how to derive the surprising formula. Furthermore, incremental computation and dynamic dependencies are being addressed in blog build systems, demonstrating the broad impact of these mathematical and computational advancements. Recommended read:
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@hubblesite.org
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Cosmology has undergone significant changes from 2000 to 2025, marked by an increased understanding of dark matter and dark energy's dominance in the Universe. Evidence gathered in the late 1990s pointed towards these mysterious components making up the majority of the cosmic energy budget, with normal matter contributing a mere 5%. Subsequent data from projects like the Hubble key project, WMAP, and Planck's Cosmic Microwave Background (CMB) observations, alongside extensive supernova and large-scale structure surveys, appeared to solidify this picture. However, tensions have emerged as these different data sets reveal inconsistencies, hinting at a potential need for a breakthrough in cosmological understanding.
The core issue revolves around the Hubble constant, a measure of the Universe's expansion rate. Measurements derived from supernova data, CMB observations, and large-scale structure surveys are not mutually compatible, leading to a significant debate within the scientific community. While some propose a crisis in cosmology, questioning the foundations of the Big Bang and the ΛCDM model, others argue that the situation is less dire. Alterations or modifications to the current cosmological model might be necessary to reconcile the discrepancies and restore order. The DESI survey, designed to measure the evolution of large-scale structure, is crucial in understanding how dark energy affects this evolution. Furthermore, recent research indicates that dark energy may not be constant, challenging our established cosmological history. Astronomers are also finding the sky brighter than previously thought, necessitating a reanalysis of existing data. Studies involving Type Ia supernovae at high redshifts, as highlighted by the Union2 compilation of 557 supernovae, provide crucial data for refining the understanding of dark energy's equation-of-state parameter. These observations, made possible by telescopes such as the Hubble Space Telescope, Gemini, and the Very Large Telescope, are instrumental in probing the expansion history of the Universe and revealing potential variations in dark energy's behavior over cosmic time. Recommended read:
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@x.com
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References:
IEEE Spectrum
The integration of Artificial Intelligence (AI) into coding practices is rapidly transforming software development, with engineers increasingly leveraging AI to generate code based on intuitive "vibes." Inspired by the approach of Andrej Karpathy, developers like Naik and Touleyrou are using AI to accelerate their projects, creating applications and prototypes with minimal prior programming knowledge. This emerging trend, known as "vibe coding," streamlines the development process and democratizes access to software creation.
Open-source AI is playing a crucial role in these advancements, particularly among younger developers who are quick to embrace new technologies. A recent Stack Overflow survey of over 1,000 developers and technologists reveals a strong preference for open-source AI, driven by a belief in transparency and community collaboration. While experienced developers recognize the benefits of open-source due to their existing knowledge, younger developers are leading the way in experimenting with these emerging technologies, fostering trust and accelerating the adoption of open-source AI tools. To further enhance the capabilities and reliability of AI models, particularly in complex reasoning tasks, Microsoft researchers have introduced inference-time scaling techniques. In addition, Amazon Bedrock Evaluations now offers enhanced capabilities to evaluate Retrieval Augmented Generation (RAG) systems and models, providing developers with tools to assess the performance of their AI applications. The introduction of "bring your own inference responses" allows for the evaluation of RAG systems and models regardless of their deployment environment, while new citation metrics offer deeper insights into the accuracy and relevance of retrieved information. Recommended read:
References :
Megan Crouse@techrepublic.com
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References:
hlfshell
, www.techrepublic.com
Researchers from DeepSeek and Tsinghua University have recently made significant advancements in AI reasoning capabilities. By combining Reinforcement Learning with a self-reflection mechanism, they have created AI models that can achieve a deeper understanding of problems and solutions without needing external supervision. This innovative approach is setting new standards for AI development, enabling models to reason, self-correct, and explore alternative solutions more effectively. The advancements showcase that outstanding performance and efficiency don’t require secrecy.
Researchers have implemented the Chain-of-Action-Thought (COAT) approach in these enhanced AI models. This method leverages special tokens such as "continue," "reflect," and "explore" to guide the model through distinct reasoning actions. This allows the AI to navigate complex reasoning tasks in a more structured and efficient manner. The models are trained in a two-stage process. DeepSeek has also released papers expanding on reinforcement learning for LLM alignment. Building off prior work, they introduce Rejective Fine-Tuning (RFT) and Self-Principled Critique Tuning (SPCT). The first method, RFT, has a pre-trained model produce multiple responses and then evaluates and assigns reward scores to each response based on generated principles, helping the model refine its output. The second method, SPCT, uses reinforcement learning to improve the model’s ability to generate critiques and principles without human intervention, creating a feedback loop where the model learns to self-evaluate and improve its reasoning capabilities. Recommended read:
References :
@thequantuminsider.com
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References:
medium.com
, mrtecht.medium.com
,
The rise of quantum computing is creating a new era of strategic competition, with nations and organizations racing to prepare for the potential disruption to modern encryption. Quantum computers, leveraging qubits that can exist in multiple states simultaneously, have the potential to break current encryption standards, revolutionize fields like medicine and finance, and reshape global power dynamics. Governments and businesses are acutely aware of this threat, with the U.S. scrambling to implement quantum-resistant cryptography and China investing heavily in quantum networks. This competition extends to technology controls, with the U.S. restricting China's access to quantum technology, mirroring actions taken with advanced semiconductors.
The urgency stems from the fact that a cryptanalytically relevant quantum computer capable of breaking common public key schemes like RSA or ECC is anticipated by 2030. To address this, the National Institute of Standards and Technology (NIST) has standardized quantum-secure algorithms and set a 2030 deadline for their implementation, alongside the depreciation of current cryptographic methods. Companies like Utimaco are launching post-quantum cryptography (PQC) application packages such as Quantum Protect for its u.trust General Purpose HSM Se-Series, enabling secure migration ahead of the quantum threat. This package supports NIST-standardized PQC algorithms like ML-KEM and ML-DSA, as well as stateful hash-based signatures LMS and XMSS. Efforts are also underway to secure blockchain technology against quantum attacks. Blockchains rely on cryptography techniques like public-key cryptography and hashing to keep transactions secure, however, quantum computers could potentially weaken these protections. Post-quantum cryptography focuses on developing encryption methods resistant to quantum attacks. Key approaches include Lattice-Based Cryptography, which uses complex mathematical structures that quantum computers would struggle to solve. The transition to a quantum-resistant future presents challenges, including the need for crypto-agility and the development of secure migration strategies. Recommended read:
References :
Tom Bridges@blogs.surrey.ac.uk
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References:
Computational Complexity
Mathematical research and discoveries have been highlighted recently through several avenues. Vanderbilt University is hosting a series of workshops focused on "Groups in Geometry, Analysis and Logic," emphasizing the central role of group theory in mathematics and its connections to other fields. The workshops aim to foster collaboration and provide educational opportunities for graduate students and early-career mathematicians. The initial workshop, scheduled for May 28 through June 1, 2025, will specifically address Groups in Logic. In other news, Cesare Tronci delivered a PAP/MAS Colloquium at Nanyang Technological University on "Koopman trajectories in nonadiabatic quantum-classical dynamics."
The mathematical community is also celebrating the 238th Carnival of Mathematics, organized by Aperiodical. This event showcases a variety of mathematical art and engaging content. This month's carnival dives into the number 238, noting it is 2 × 7 × 17, the sum of the first 13 primes, and a "triprime." The community has contributed interesting facts about 238, including its connection to Uranium-238 and its representation as "EE" in Hex. The carnival also highlights mathematical blog posts and activities, such as Peter Cameron's reflections on compactness and government censorship in research, and Jeremy Kun's announcement of a new book on practical math for programmers. In related news, PDQ Shor, described as the smarter brother of Peter Shor and a Physicist/Computer Scientist/Mathematician/Astrologer/Psychic, has reportedly passed away. Known for his concept of unnatural proofs and contributions to quantum computing theory, PDQ Shor is credited with creating the perpetual Turing machine and reverse engineering his brother’s quantum space work. Despite his contributions to the field, there are some discrepancies with his actual existence and this could be an April Fools day joke. Recommended read:
References :
@phys.org
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References:
phys.org
, The Quantum Insider
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A research team of statisticians from Cornell University has developed a novel data representation method inspired by quantum mechanics. This innovative approach aims to address the growing challenges posed by big, noisy data, which often overwhelms traditional data analysis techniques. The method works by simplifying large data sets and effectively filtering out noise, leading to more efficient data handling.
This breakthrough leverages the mathematical structures of quantum mechanics to better understand the underlying structure of complex data. According to Martin Wells, a professor of Statistical Sciences at Cornell, physicists have developed quantum mechanics-based tools that offer concise mathematical representations of complex data and the team is borrowing from these tools to understand the structure of data. Unlike conventional intrinsic dimension estimation techniques, which can be easily disrupted by noise and complexity, this quantum-inspired approach is more robust and accurate. The potential applications of this method are vast, particularly in data-rich fields like healthcare and epigenetics, where traditional methods have struggled. While quantum computing promises unprecedented speed, some experts debate its true potential, with efforts focused on "dequantizing" quantum algorithms to achieve comparable speeds using classical counterparts. This new data representation method offers a practical and accessible way to harness the principles of quantum mechanics on classical computers, potentially unlocking new insights from previously intractable data sets. Recommended read:
References :
@phys.org
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References:
phys.org
Recent research has spotlighted the diverse applications of mathematical and computational methods across multiple critical fields. One notable study, published in ACM Transactions on the Web, details the use of advanced mathematical techniques and software to investigate the collapse of the TerraUSD stablecoin and its associated currency, LUNA. Led by Dr. Richard Clegg at Queen Mary University of London, the research team employed temporal multilayer graph analysis to uncover suspicious trading patterns indicative of a coordinated attack, which led to the loss of $3.5 billion. The study highlights the power of mathematical tools in unraveling complex financial events.
Scientists have also made significant strides in fluid dynamics through the development of AI-powered simulation models. Researchers at Osaka Metropolitan University have created a machine learning model that dramatically reduces computation time for fluid simulations while maintaining accuracy. This innovation, which utilizes graph neural networks, has potential applications in offshore power generation, ship design, and real-time ocean monitoring, offering a scalable solution that balances accuracy with efficiency. The new model cuts simulation time from 45 minutes to just three minutes. The 23rd International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2025) also focuses on the integration of mathematical and computational methods across science and engineering. A session within the conference aims to unite researchers and practitioners in discussing novel ideas, methodologies, and applications that bridge the gap between mathematics and its practical implementations. The session welcomes contributions focusing on analytical and numerical techniques, algorithm development, and computational modeling, particularly those providing new insights into solving complex systems. Recommended read:
References :
Greg Bock@The Quantum Insider
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References:
The Quantum Insider
Quantum computing has taken a significant leap forward with Phasecraft's development of a novel quantum simulation method called THRIFT (Trotter Heuristic Resource Improved Formulas for Time-dynamics). This breakthrough, detailed in a recent *Nature Communications* publication, drastically improves simulation efficiency and lowers computational costs, bringing real-world quantum applications closer to reality. THRIFT optimizes quantum simulations by prioritizing interactions with different energy scales within quantum systems, streamlining their implementation into smaller, more manageable steps.
This approach allows for larger and longer simulations to be executed without the need for increased quantum circuit size, thereby reducing computational resources and costs. In benchmarking tests using the 1D transverse-field Ising model, a widely used benchmark in quantum physics, THRIFT achieved a tenfold improvement in both simulation estimates and circuit complexities, enabling simulations that are ten times larger and run ten times longer compared to traditional methods. This development holds immense promise for advancements in materials science and drug discovery. Separately, mathematicians have achieved a breakthrough in understanding and modeling melting ice and other similar phenomena through a new proof that resolves long-standing issues related to singularities. A powerful mathematical technique used to model melting ice and other phenomena had been hampered by “nightmare scenarios.” A new proof has removed that obstacle. This new proof addresses concerns about "nightmare scenarios" that previously hindered the analysis of these processes, ensuring that singularities do not impede the continued evolution of the surface being modeled. The resolution, described in Quanta Magazine, allows mathematicians to more effectively assess the surface's evolution even after a singularity appears. Finally, researchers at Cornell University have introduced a novel data representation method inspired by quantum mechanics that tackles the challenge of handling big, noisy data sets. This quantum statistical approach simplifies large data sets and filters out noise, allowing for more efficient analysis than traditional methods. By borrowing mathematical structures from quantum mechanics, this technique enables a more concise representation of complex data, potentially revolutionizing innovation in data-rich fields such as healthcare and epigenetics where traditional methods have proven insufficient. Recommended read:
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@simonwillison.net
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Google has broadened access to its advanced AI model, Gemini 2.5 Pro, showcasing impressive capabilities and competitive pricing designed to challenge rival models like OpenAI's GPT-4o and Anthropic's Claude 3.7 Sonnet. Google's latest flagship model is currently recognized as a top performer, excelling in Optical Character Recognition (OCR), audio transcription, and long-context coding tasks. Alphabet CEO Sundar Pichai highlighted Gemini 2.5 Pro as Google's "most intelligent model + now our most in demand." Demand has increased by over 80 percent this month alone across both Google AI Studio and the Gemini API.
Google's expansion includes a tiered pricing structure for the Gemini 2.5 Pro API, offering a more affordable option compared to competitors. Prompts with less than 200,000 tokens are priced at $1.25 per million for input and $10 per million for output, while larger prompts increase to $2.50 and $15 per million tokens, respectively. Although prompt caching is not yet available, its future implementation could potentially lower costs further. The free tier allows 500 free grounding queries with Google Search per day, with an additional 1,500 free queries in the paid tier, with costs per 1,000 queries set at $35 beyond that. The AI research group EpochAI reported that Gemini 2.5 Pro scored 84% on the GPQA Diamond benchmark, surpassing the typical 70% score of human experts. This benchmark assesses challenging multiple-choice questions in biology, chemistry, and physics, validating Google's benchmark results. The model is now available as a paid model, along with a free tier option. The free tier can use data to improve Google's products while the paid tier cannot. Rates vary by tier and range from 150-2,000/minute. Google will retire the Gemini 2.0 Pro preview entirely in favor of 2.5. Recommended read:
References :
@www.quantamagazine.org
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Quantum computing faces the challenge of demonstrating a consistent advantage over classical computing. Ewin Tang's work on "dequantizing" quantum algorithms has questioned the assumption that quantum computers can always outperform classical ones. Tang designed classical algorithms to match the speed of quantum algorithms in solving certain problems, initiating an approach where researchers seek classical counterparts to quantum computations. This raises fundamental questions about the true potential and future trajectory of quantum computing, especially considering the resources required.
The discussion extends to the costs associated with quantum randomness, exploring pseudorandomness as a practical alternative. Researchers at the University of the Witwatersrand have found a method to shield quantum information from environmental disruptions, which could lead to more stable quantum computers and networks. Despite the potential of quantum computing to revolutionize fields like science, pharmaceuticals, and healthcare, limitations in energy demands and computing power suggest that it will likely be applied selectively to areas where it offers the most significant advantage, rather than replacing classical computing across all applications. Recommended read:
References :
Charlie Fink,@Charlie Fink
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Sourcetable Launches AI Spreadsheets With New Funding - Sourcetable launched AI-powered spreadsheets, securing $4.3 million in funding to transform data analysis using natural language.
ImgSrc: imageio.forbes.
Sourcetable has launched its AI-powered spreadsheet, securing $4.3 million in funding. This new platform aims to revolutionize data analysis, allowing users to interact with and analyze data using natural language, eliminating the need for complex formulas. The funding round was led by Bee Partners, with participation from figures such as Hugging Face CTO Julien Chaumond and GitHub co-founder Tom Preston-Werner. The company aims to make data analysis more accessible, and empower more people to become spreadsheet power users.
The "self-driving spreadsheet" can understand data context without the need for users to pre-select ranges, interpreting multiple ranges across different tabs. Users can issue commands via text or voice, creating financial models, generating pivot tables, cleaning data, and creating charts and graphs. Sourcetable CEO Eoin McMillan says that AI is the biggest platform shift since the browser. Recommended read:
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@sciencedaily.com
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Recent advancements in quantum computing research have yielded promising results. Researchers at the University of the Witwatersrand in Johannesburg, along with collaborators from Huzhou University in China, have discovered a method to shield quantum information from environmental disruptions, potentially leading to more reliable quantum technologies. This breakthrough involves manipulating quantum wave functions to preserve quantum information, which could enhance medical imaging, improve AI diagnostics, and strengthen data security by providing ultra-secure communication.
UK startup Phasecraft has announced a new algorithm, THRIFT, that improves the ability of quantum computers to model new materials and chemicals by a factor of 10. By optimizing quantum simulation, THRIFT enables scientists to model new materials and chemicals faster and more accurately, even on today’s slower machines. Furthermore, Oxford researchers have demonstrated a 25-nanosecond controlled-Z gate with 99.8% fidelity, combining high speed and accuracy in a simplified superconducting circuit. This achievement advances fault-tolerant quantum computing by improving raw gate performance without relying heavily on error correction or added hardware. Recommended read:
References :
Maximilian Schreiner@THE DECODER
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Google's Gemini 2.5 Pro is making waves as a top-tier reasoning model, marking a leap forward in Google's AI capabilities. Released recently, it's already garnering attention from enterprise technical decision-makers, especially those who have traditionally relied on OpenAI or Claude for production-grade reasoning. Early experiments, benchmark data, and developer reactions suggest Gemini 2.5 Pro is worth serious consideration.
Gemini 2.5 Pro distinguishes itself with its transparent, structured reasoning. Google's step-by-step training approach results in a structured chain of thought that provides clarity. The model presents ideas in numbered steps, with sub-bullets and internal logic that's remarkably coherent and transparent. This breakthrough offers greater trust and steerability, enabling enterprise users to validate, correct, or redirect the model with more confidence when evaluating output for critical tasks. Recommended read:
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