Top Mathematics discussions
NishMath - #none
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@quantumcomputingreport.com
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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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Miranda Martinengo@Istituto Grothendieck
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Recent developments in the mathematics community showcase notable achievements and career advancements. Ryuya Hora, a doctoral scholar from the University of Tokyo specializing in topos theory and automata theory applications, has been appointed Research Associate of the Centre for Topos Theory and its Applications (CTTA). He is scheduled to collaborate with Olivia Caramello and other researchers at the Centre in Paris between April and June 2025. His appointment signifies a valuable addition to the field, with opportunities to follow his work, including his talk at the "Toposes in Mondovì" conference.
Cesare Tronci has been promoted to Professor of Mathematics at the University of Surrey, effective April 1, 2025. This promotion acknowledges his contributions to the field, and further information about his research can be found on his website. Also at the University of Surrey, Jessica Furber has successfully defended her PhD thesis, "Mathematical Analysis of Fine-Scale Badger Movement Data," marking the completion of her doctoral studies. Her external examiner was Prof Yuliya Kyrychko from Sussex, and the internal examiner was Dr Joaquin Prada from the Vet School, Surrey. In related news, the Mathematics Division at Stellenbosch University in South Africa is seeking a new permanent appointee at the Lecturer or Senior Lecturer level, with consideration potentially given to other levels under specific circumstances. While preference will be given to candidates working in number theory or a related area, applications from those in other areas of mathematics will also be considered. The deadline for applications is April 30, 2025, with detailed information available in the official advertisement. 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:
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Sophia Wood@Fractal Kitty
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The Aperiodical
The 238th Carnival of Mathematics is now available online at Fractal Kitty, rounding up math blog posts from March 2025. This edition, organized by Aperiodical, features a variety of math art and explores interesting facts about the number 238, including that it is 2 × 7 × 17, the sum of the first 13 primes, and a "triprime." The Mathstodon community contributed fun facts about 238, such as its relation to Uranium-238 and its representation in hexadecimal as "EE."
The carnival includes a variety of blog posts and activities from around the mathematical community. Peter Cameron shared thoughts on Compactness, Memories of CFSG, and defending research against government censorship, while other posts covered topics like polyominoes, a modern presentation of Peano Axioms, and the Monty Hall Problem. Karen Campe continued her visual Go For Geometry Series, and Amédée d’Aboville explored Group Theory With Zoombinis. These diverse topics showcase the breadth of interests and engagement within the math world. Beyond traditional blog posts, the carnival highlights creative endeavors like Ayliean's #MathArtMarch, which showcased crochet, coding, painting, and other artistic expressions inspired by mathematics. There's also discussion happening on platforms like Mathstodon, with Terence Tao sharing insights on dynamical systems and the complexities of linear versus nonlinear regimes. Pat's Blog delves into geometry, discussing properties of rhombuses and extensions of concurrency theorems, demonstrating the vibrant and varied nature of mathematical discussions and explorations. Recommended read:
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@aperiodical.com
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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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@lobste.rs
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gilkalai.wordpress.com
, Susam Pal
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Mathematical blogs and platforms are currently buzzing with diverse explorations. Elinor, in a guest post for #MathArtMarch, has curated a collection of favorite mathematical art from the month, providing inspiration for artists and mathematicians alike. Meanwhile, the "exponential sum of the day" page continues to captivate audiences by generating a new figure daily. This figure is created by plotting partial sums and drawing lines between consecutive terms, resulting in visually intriguing patterns that often feature unexpected flat sides.
Recently, Bo’az Klartag has released "Striking new Lower Bounds for Sphere Packing in High Dimensions," which has garnered attention in the mathematical community. Kalai notes that this paper presents a significant breakthrough in the field. Klartag's paper demonstrates that there exists a lattice sphere packing with a density significantly higher than previously known constructions. His proof involves a stochastically evolving ellipsoid designed to accumulate lattice points on its boundary while avoiding them in its interior, a technique rooted in Minkowski's ideas on sphere packing and ellipsoids. Other areas of mathematical interest being explored include Elliptical Python Programming, as discussed on Susam Pal's blog. Also the article "exponential sum of the day" page draws a new figure each day by plotting the partial sums of and drawing a line between consecutive terms. Overall, these diverse explorations highlight the vibrant and dynamic nature of mathematical research and its connections to various fields like art and computer science. Recommended read:
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@primes.utm.edu
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Pat'sBlog
, mathdaypballew.blogspot.com
This week saw a flurry of mathematical activity, highlighted by the 238th Carnival of Mathematics, organized by Aperiodical. The carnival showcases a variety of submissions and mathematical art, focusing on the number 238 itself. Noteworthy facts about 238 include that it is 2 × 7 × 17, the sum of the first 13 primes, and a "triprime". The carnival also encourages exploration beyond pure mathematics, with community members contributing insights linking the number to uranium isotopes, birth minutes, and even hexadecimal representations. It also shines a light on #MathArtMarch, with examples of crochet, coding, and painting from around the world.
Continuing the daily exploration of numbers, several interesting facts and events were highlighted for April 6th, 7th, 8th and 10th. The number 96, the 96th day of the year, was examined for its unique properties, such as being the smallest number expressible as the difference of two squares in four different ways. Events like Euler's first paper on partitions (April 7th, 1741) and Al-Biruni's observation of a solar eclipse in 1019 were also noted, linking mathematical concepts to historical contexts. Also, the number 97 has been noted as the 97th day of the year, where 97 is the largest prime that we can ever find that is less than the sum of square of its digits. In recreational mathematics, a "Salute" game for reinforcing multiplication and division was featured, emphasizing the inverse relationship between these operations. Additionally, the concept of "truncatable primes" was explored through a game where players create strings of prime numbers by adding digits to either end of a number. The number 91 was discussed as the 91st day of the year where 10 n + 91 and 10 n + 93 are twin primes for n = 1, 2, 3 and 4. Finally, highlighting mathematics beyond academia, James Abram Garfield, a former Congressman and mathematician, was mentioned for his original proof of the Pythagorean Theorem, illustrating the interdisciplinary nature of mathematics. Recommended read:
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@console.cloud.google.com
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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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Unknown (noreply@blogger.com)@Pat'sBlog
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Fractal Kitty
, The Aperiodical
The online mathematics community is buzzing with activity, as evidenced by the 238th Carnival of Mathematics, hosted by Aperiodical. This month's carnival showcases diverse submissions and beautiful math art, starting with an exploration of the number 238 itself. Found to be 2 x 7 x 17 and the sum of the first 13 primes, the number also inspired community contributions, with users pointing out its appearance in uranium isotopes, hexagonal representations, and even birth minute celebrations. The carnival highlights the engaging and creative ways people interact with mathematical concepts online.
The carnival features a collection of blog posts and activities from various math enthusiasts. Number yoga is explored as a technique to develop creative reasoning and comprehension in mathematics. This involves noticing details, wondering about possibilities, and creating explanations or related puzzles. Also featured are posts on polyominoes, a modern presentation of Peano Axioms, practical math for programmers, the Monty Hall Problem, and group theory using Zoombinis. Karen Campe also continues her visual "Go For Geometry" series. Furthermore, the online discussion includes extensions of basic geometry, focusing on pedal triangles and related theorems. A blog post delves into generalizations of perpendiculars from a point in a triangle, highlighting properties of the orthocenter and the orthic triangle. The orthic triangle's perimeter and its connection to the angles of the original triangle are discussed. The community also shares the art from Ayliean's MathArtMarch. Recommended read:
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@x.com
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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:
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Megan Crouse@techrepublic.com
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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:
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@thequantuminsider.com
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medium.com
, mrtecht.medium.com
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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:
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Greg Bock@The Quantum Insider
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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:
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@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:
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Terence Tao@What's new
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References:
beuke.org
, What's new
Terence Tao has recently uploaded a paper to the arXiv titled "Decomposing a factorial into large factors." The paper explores a mathematical quantity, denoted as t(N), which represents the largest value such that N! can be factorized into t(N) factors, with each factor being at least N. This concept, initially introduced by Erdös, delves into how equitably a factorial can be split into its constituent factors.
Erdös initially conjectured that an upper bound on t(N) was asymptotically sharp, implying that factorials could be split into factors of nearly uniform size for large N. However, a purported proof by Erdös, Selfridge, and Straus was lost, leading to the assertion becoming a conjecture. The paper establishes bounds on t(N), recovering a previously lost result. Further conjectures were made by Guy and Selfridge, exploring whether relationships held true for all values of N. On March 30th, mathematical enthusiasts celebrated facts related to the number 89. Eighty-nine is a Fibonacci prime, and patterns emerge when finding it's reciprocal. Also, the number 89 can be obtained by a summation of the first 5 integers to the power of the first 5 Fibonacci numbers. 89 is also related to Armstrong numbers, which are numbers that are the sum of their digits raised to the number of digits in the number. Recommended read:
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Webb Wright@Quanta Magazine
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The Quantum Insider
, Quanta Magazine
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Researchers are making significant strides in reducing the costs associated with quantum randomness, a crucial element for cryptography and simulations. Traditionally, obtaining true quantum randomness has been complex and expensive. However, the exploration of "pseudorandomness" offers a practical alternative, allowing researchers to utilize computational algorithms that mimic randomness, thus sidestepping the high costs of pure quantum randomness. This development broadens the accessibility of randomness, enabling researchers to pursue new scientific investigations.
The team from JPMorganChase, Quantinuum, multiple national labs, and UT Austin demonstrated a certified quantum randomness protocol. They showcased the first successful demonstration of a quantum computing method to generate certified randomness. Using a 56-qubit quantum machine, they output more randomness than they initially put in. What makes this truly remarkable is that this feat is considered impossible for even the most powerful classical supercomputers. This groundbreaking achievement could open new doors for quantum computing and cryptography research. Recommended read:
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Ryan Daws@www.artificialintelligence-news.com
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Anthropic has unveiled groundbreaking insights into the 'AI biology' of their advanced language model, Claude. Through innovative methods, researchers have been able to peer into the complex inner workings of the AI, demystifying how it processes information and learns strategies. This research provides a detailed look at how Claude "thinks," revealing sophisticated behaviors previously unseen, and showing these models are more sophisticated than previously understood.
These new methods allowed scientists to discover that Claude plans ahead when writing poetry and sometimes lies, showing the AI is more complex than previously thought. The new interpretability techniques, which the company dubs “circuit tracing” and “attribution graphs,” allow researchers to map out the specific pathways of neuron-like features that activate when models perform tasks. This approach borrows concepts from neuroscience, viewing AI models as analogous to biological systems. This research, published in two papers, marks a significant advancement in AI interpretability, drawing inspiration from neuroscience techniques used to study biological brains. Joshua Batson, a researcher at Anthropic, highlighted the importance of understanding how these AI systems develop their capabilities, emphasizing that these techniques allow them to learn many things they “wouldn’t have guessed going in.” The findings have implications for ensuring the reliability, safety, and trustworthiness of increasingly powerful AI technologies. Recommended read:
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Matt Marshall@AI News | VentureBeat
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References:
Microsoft Security Blog
, www.zdnet.com
Microsoft is enhancing its Copilot Studio platform with AI-driven improvements, introducing deep reasoning capabilities that enable agents to tackle intricate problems through methodical thinking and combining AI flexibility with deterministic business process automation. The company has also unveiled specialized deep reasoning agents for Microsoft 365 Copilot, named Researcher and Analyst, to help users achieve tasks more efficiently. These agents are designed to function like personal data scientists, processing diverse data sources and generating insights through code execution and visualization.
Microsoft's focus includes securing AI and using it to bolster security measures, as demonstrated by the upcoming Microsoft Security Copilot agents and new security features. Microsoft aims to provide an AI-first, end-to-end security platform that helps organizations secure their future, one example being the AI agents designed to autonomously assist with phishing, data security, and identity management. The Security Copilot tool will automate routine tasks, allowing IT and security staff to focus on more complex issues, aiding in defense against cyberattacks. Recommended read:
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Maximilian Schreiner@THE DECODER
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Google DeepMind has announced Gemini 2.5 Pro, its latest and most advanced AI model to date. This new model boasts enhanced reasoning capabilities and improved accuracy, marking a significant step forward in AI development. Gemini 2.5 Pro is designed with built-in 'thinking' capabilities, enabling it to break down complex tasks into multiple steps and analyze information more effectively before generating a response. This allows the AI to deduce logical conclusions, incorporate contextual nuances, and make informed decisions with unprecedented accuracy, according to Google.
The Gemini 2.5 Pro has already secured the top position on the LMArena leaderboard, surpassing other AI models in head-to-head comparisons. This achievement highlights its superior performance and high-quality style in handling intricate tasks. The model also leads in math and science benchmarks, demonstrating its advanced reasoning capabilities across various domains. This new model is available as Gemini 2.5 Pro (experimental) on Google’s AI Studio and for Gemini Advanced users on the Gemini chat interface. Recommended read:
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Stephen Ornes@Quanta Magazine
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Quanta Magazine
, medium.com
A novel quantum algorithm has demonstrated a speedup over classical computers for a significant class of optimization problems, according to a recent report. This breakthrough could represent a major advancement in harnessing the potential of quantum computers, which have long promised faster solutions to complex computational challenges. The new algorithm, known as decoded quantum interferometry (DQI), outperforms all known classical algorithms in finding good solutions to a wide range of optimization problems, which involve searching for the best possible solution from a vast number of choices.
Classical researchers have been struggling to keep up with this quantum advancement. Reports of quantum algorithms often spark excitement, partly because they can offer new perspectives on difficult problems. The DQI algorithm is considered a "breakthrough in quantum algorithms" by Gil Kalai, a mathematician at Reichman University. While quantum computers have generated considerable buzz, it has been challenging to identify specific problems where they can significantly outperform classical machines. This new algorithm demonstrates the potential for quantum computers to excel in optimization tasks, a development that could have broad implications across various fields. Recommended read:
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