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Maximilian Schreiner@THE DECODER
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Google's Gemini 2.5 Pro: A Breakthrough in AI Reasoning - Google DeepMind introduced Gemini 2.5 Pro, its most intelligent AI model with advanced reasoning, securing the top position on the Arena leaderboard.
ImgSrc: the-decoder.com
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:
References :
@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:
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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 :
@The Cryptography Caffe? ?
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The UK's National Cyber Security Centre (NCSC) has released a roadmap for transitioning to post-quantum cryptography (PQC), establishing key dates for organizations to assess risks, define strategies, and fully transition by 2035. This initiative aims to mitigate the future threat of quantum computers, which could potentially break today's widely used encryption methods. The NCSC’s guidance recognizes that PQC migration is a complex and lengthy process requiring significant planning and investment.
By 2028, organizations are expected to complete a discovery phase, identifying systems and services reliant on cryptography that need upgrades, and draft a migration plan. High-priority migration activities should be completed by 2031, with infrastructure prepared for a full transition. The NCSC emphasizes that these steps are essential for addressing quantum threats and improving overall cyber resilience. Ali El Kaafarani, CEO of PQShield, noted that these timelines give clear instructions to protect the UK’s digital future. Researchers have also introduced ZKPyTorch, a compiler that integrates ML frameworks with ZKP engines to simplify the development of zero-knowledge machine learning (ZKML). ZKPyTorch automates the translation of ML operations into optimized ZKP circuits and improves proof generation efficiency. Through case studies, ZKPyTorch successfully converted VGG-16 and Llama-3 models into ZKP-compatible circuits. 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 :
Matt Swayne@The Quantum Insider
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D-Wave Quantum Inc. has made a splash by claiming its Advantage2 annealing quantum computer achieved quantum supremacy in complex materials simulations, publishing their study in the journal Science. The company states that its system can perform simulations in minutes that would take the Frontier supercomputer nearly a million years and consume more than the world’s annual electricity consumption. According to D-Wave CEO Alan Baratz, this achievement validates quantum annealing's practical advantage and represents a major milestone in quantum computational supremacy and materials discovery.
However, D-Wave's claim has faced criticism, with researchers suggesting that classical algorithms can rival or even exceed quantum methods in these simulations. Some researchers say that they performed similar calculations on a normal laptop in just two hours. Concerns have been raised about the real-world applicability and practical benefits of D-Wave's quantum supremacy claims in computational tasks. Despite the criticisms, D-Wave is standing by the claims from the study. 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:
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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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Webb Wright@Quanta Magazine
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References:
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:
References :
Tom Bridges@blogs.surrey.ac.uk
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References:
blogs.surrey.ac.uk
, The Quantum Insider
,
Recent breakthroughs are pushing the boundaries of quantum theory and quantum randomness, paving the way for commercial applications and more reliable quantum technologies. A paper by Dorje Brody, along with collaborators Eva-Maria Graefe and Rishindra Melanathuru, has been published in Physical Review Letters, exploring decoherence resulting from phase-space measurements. Their work addresses the question of decoherence resulting from a monitoring of position and momentum, i.e., a phase-space measurement, by the environment.
Researchers have also made strides in protecting quantum information from environmental disruptions, offering hope for more stable quantum computers and networks. Scientists have demonstrated how certain quantum states can maintain their critical information even when disturbed by environmental noise. This could lead to more reliable quantum technology, enhanced medical imaging techniques, improved AI-driven diagnostics, and stronger data security. Simultaneously, a joint research team consisting of members from JPMorgan Chase, Quantinuum, multiple national labs, and UT Austin, has achieved certified quantum randomness, turning once theoretical experiments into first commercial applications for quantum computing. The team demonstrated a certified randomness protocol using Quantinuum's 56-qubit H2 trapped-ion system, showcasing a quantum computer's ability to generate entropy beyond classical reach. Furthermore, the high cost of quantum randomness is dropping due to advancements in pseudorandomness techniques, which may open new doors for quantum computing and cryptography research. Recommended read:
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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 :
@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 :
@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 :
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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@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:
References :
Stephen Ornes@Quanta Magazine
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References:
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:
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:
References :
@thequantuminsider.com
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References:
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:
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:
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@www.newtonproject.sussex.ac.uk
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References:
Xi'an's Og
, Pat'sBlog
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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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@teorth.github.io
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References:
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 :
@gilkalai.wordpress.com
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References:
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:
References :
@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:
References :
Igor Konnov@Protocols Made Fun
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References:
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:
References :
Amir Najmi@unofficialgoogledatascience.com
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Data scientists and statisticians are continuously exploring methods to refine data analysis and modeling. A recent blog post from Google details a project focused on quantifying the statistical skills necessary for data scientists within their organization, aiming to clarify job descriptions and address ambiguities in assessing practical data science abilities. The authors, David Mease and Amir Najmi, leveraged their extensive experience conducting over 600 interviews at Google to identify crucial statistical expertise required for the "Data Scientist - Research" role.
Statistical testing remains a cornerstone of data analysis, guiding analysts in transforming raw numbers into actionable insights. One must also keep in mind bias-variance tradeoff and how to choose the right statistical test to ensure the validity of analyses. These tools are critical for both traditional statistical roles and the evolving field of AI/ML, where responsible practices are paramount, as highlighted in discussions about the relevance of statistical controversies to ethical AI/ML development at an AI ethics conference on March 8. Recommended read:
References :
Mike Watts@computational-intelligence.blogspot.com
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References:
computational-intelligence.blo
, computational-intelligence.blo
Recent developments highlight advancements in quantum computing, artificial intelligence, and cryptography. Classiq Technologies, in collaboration with Sumitomo Corporation and Mizuho-DL Financial Technology, achieved up to 95% compression of quantum circuits for Monte Carlo simulations used in financial risk analysis. This project explored the use of Classiq’s technology to generate more efficient quantum circuits for a novel quantum Monte Carlo simulation algorithm incorporating pseudo-random numbers proposed by Mizuho-DL FT, evaluating the feasibility of implementing quantum algorithms in financial applications.
Oxford researchers demonstrated a fast, 99.8% fidelity two-qubit gate using a simplified circuit design, achieving this using a modified coaxmon circuit architecture. Also, a collaborative team from JPMorganChase, Quantinuum, Argonne National Laboratory, Oak Ridge National Laboratory, and the University of Texas at Austin demonstrated a certified randomness protocol using a 56-qubit Quantinuum System Model H2 trapped-ion quantum computer. This is a major milestone for real-world quantum applications, with the certified randomness validated using over 1.1 exaflops of classical computing power, confirming the quantum system’s ability to generate entropy beyond classical reach. The 2025 IEEE International Conference on Quantum Artificial Intelligence will be held in Naples, Italy, from November 2-5, 2025, with a paper submission deadline of May 15, 2025. Vanderbilt University will host a series of workshops devoted to Groups in Geometry, Analysis and Logic starting May 28, 2025. Recommended read:
References :
Yvonne Smit@Qusoft
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References:
Qusoft
Koen Groenland's book, "Introduction to Quantum Computing for Business," is gaining attention as a key resource for guiding companies on leveraging quantum advancements. As the Dutch quantum ecosystem expands, experts like Groenland are playing a vital role in making quantum knowledge accessible to the business world. The book aims to demystify this technology for business professionals without a technical background, focusing on the capabilities and applications of quantum computers rather than the underlying technical details. Groenland hopes the book will become a standard work for anyone starting a quantum journey, emphasizing the importance of understanding quantum algorithms for business value.
Classiq Technologies, in collaboration with Sumitomo Corporation and Mizuho-DL Financial Technology, achieved significant compression of quantum circuits for Monte Carlo simulations used in financial risk analysis. The study compared traditional and pseudo-random number-based quantum Monte Carlo methods, optimizing circuit depth and qubit usage using Classiq’s high-level quantum design platform, Qmod. The results showed efficient circuit compression is possible without compromising accuracy, supporting the feasibility of scalable, noise-tolerant quantum applications in financial risk management. The Open Source Initiative (OSI) and Apereo Foundation have jointly responded to the White House Office of Science & Technology Policy's (OSTP) request for information on an AI Action Plan. Their comment emphasizes the benefits of Open Source and positions the Open Source community as a valuable resource for policymakers. The OSI highlighted its history of stewarding the Open Source Definition and its recent work in co-developing the Open Source AI Definition (OSAID), recommending that the White House rely on the OSAID as a foundational piece of any future AI Action Plan. Recommended read:
References :
Tom Bridges@blogs.surrey.ac.uk
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Recent activity in the mathematical community has highlighted the enduring fascination with mathematical constants and visual representations of mathematical concepts. A blog post on March 23, 2025, discussed a remarkably accurate approximation for pi, noting that π ≈ 3 log(640320) / √163 is exact within the limits of floating-point arithmetic, achieving accuracy to 15 decimal places. This discovery builds upon historical efforts to approximate pi, from ancient Babylonian and Egyptian calculations to Archimedes' method of exhaustion and the achievements of Chinese mathematicians like Liu Hui and Zu Chongzhi.
Visual insights in mathematics continue to be explored. A blog called Visual Insight shares striking images that help explain topics in mathematics. The creator gave a talk about it at the Illustrating Math Seminar. The blog features images created by people such as Refurio Anachro, Greg Egan, and Roice Nelson, and individual articles are available on the AMS website. Recommended read:
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