Top Mathematics discussions
NishMath - #mathematics
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Tom Bridges@blogs.surrey.ac.uk
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References:
phys.org
, www.sciencedaily.com
Recent mathematical explorations have focused on a variety of intriguing number patterns and historical mathematical context. One notable discovery comes from UNSW Sydney mathematician Norman Wildberger, who has revealed a new algebraic solution to higher polynomial equations, a problem considered unsolvable since the 19th century. Polynomials are equations with variables raised to powers, and while solutions for lower-degree polynomials are well-known, a general method for those of degree five or higher has remained elusive. Wildberger's method, detailed in a publication with computer scientist Dr. Dean Rubine in The American Mathematical Monthly, uses novel number sequences to "reopen a previously closed book in mathematics history."
Wildberger's approach challenges the traditional use of radicals, which often involve irrational numbers. Irrational numbers, with their infinite, non-repeating decimal expansions, are seen by Wildberger as problematic. He argues that assuming their existence in formulas implies treating infinite decimals as complete objects, an assumption he rejects. His solution involves discarding irrational numbers, a move that may redefine how certain algebraic problems are approached. Critics may find the claims overstated, as one commentary notes the article never specifies what "algebra's oldest problem" actually is, but indicates that solving it requires discarding irrational numbers. In addition to advancements in solving polynomial equations, mathematicians continue to explore other number sequences, such as Recamán’s sequence, a favorite of N. J. A. Sloane, founder of the Online Encyclopedia of Integer Sequences. The sequence starts at 0, and each subsequent number is derived by moving forward or backward a specific number of steps from the previous number, based on certain conditions. Recamán’s sequence can be visualized using circular arcs and even represented as music, associating each number with a note on the chromatic scale, showcasing the diverse ways in which mathematical concepts can be explored and interpreted. Recommended read:
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@sciencedaily.com
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Dan Drake ?
, phys.org
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A mathematician from UNSW Sydney has reportedly solved one of algebra's oldest and most challenging problems: finding a general algebraic solution for higher polynomial equations. These equations, which involve a variable raised to powers, are fundamental in mathematics and science, with broad applications ranging from describing planetary movement to writing computer programs. While solutions for lower-degree polynomials (up to degree four) have been known for centuries, a general method for solving equations of degree five or higher had remained elusive, until now.
Professor Norman Wildberger, along with computer scientist Dr. Dean Rubine, developed a new approach using novel number sequences to tackle this problem. Their solution, recently published in The American Mathematical Monthly journal, challenges established mathematical assumptions and potentially "reopens a previously closed book in mathematics history," according to Professor Wildberger. The breakthrough centers around rethinking the use of radicals (roots of numbers) in classical formulas, traditionally used to solve lower-order polynomials. Wildberger argues that radicals, often representing irrational numbers with infinite, non-repeating decimal expansions, introduce incompleteness into calculations. He claims that since these irrational numbers can never be fully calculated, assuming their 'existence' in a formula is problematic. This perspective led him to develop an alternative method based on number sequences, potentially offering a purely algebraic solution to higher-degree polynomial equations, bypassing the limitations of traditional radical-based approaches. Recommended read:
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@quantumcomputingreport.com
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Metadata
, Quantum Computing Report
Universities worldwide are engaging in a diverse range of mathematics-related activities, from exploring quantum communication to using origami for hands-on learning. Heriot-Watt University in Edinburgh recently inaugurated a £2.5 million ($3.3 million USD) Optical Ground Station (HOGS) to foster advancements in satellite-based quantum-secure communication. This facility, equipped with a 70-cm precision telescope, aims to conduct quantum key distribution (QKD) experiments with satellites, monitor space debris, and test high-speed optical communications for next-generation networks. The project is a significant step in the UK's ambition to establish a quantum-secure internet, offering a unique platform for industry and academia to collaborate on secure communications across various sectors.
HOGS is connected to Heriot-Watt’s quantum labs via dark fibre, enabling real-time simulation and validation of optical quantum networks. This infrastructure will serve as a valuable R&D platform for secure communications in financial services, healthcare, and critical infrastructure, aiming to mitigate the UK's estimated £27 billion annual cost of cybercrime. The university also intends to expand Scotland’s space economy and workforce through partnerships and STEM programs, emphasizing the educational outreach aspect of the new facility. The Integrated Quantum Networks (IQN) Hub also considers the station part of Heriot-Watt's role as a leader in the development of quantum-secure communications. Meanwhile, ETH Zürich is promoting practical mathematics through its goMATH funding program, exemplified by the Origami Challenge. ETH students visited schools to introduce origami mathematics in a fun and engaging way, encouraging pupils to create geometric origami artworks from paper without using glue. This initiative aims to make mathematics more accessible and enjoyable for young students. At the TLA+ Community Event in Hamilton, Ontario, discussions revolved around integrating TLA+ into tooling for fuzzers, trace validators, and compilers, emphasizing its evolving role beyond just specifications. Attendees observed that TLA+ is increasingly being used to build bridges from models to real-world applications. Recommended read:
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Katie Steckles@The Aperiodical
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The Aperiodical
, D-MATH News
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The Carnival of Mathematics, a monthly gathering of mathematical blog posts, continues to connect the global math community. For over a decade, this event has been hosted by various math bloggers, showcasing a wide range of mathematical topics, from recreational puzzles to advanced research. It serves as a valuable resource for mathematicians and enthusiasts alike, offering a way to stay informed about current trends and innovative ideas within the field.
The latest edition, Carnival of Maths 239, is now available at Reflections and Tangents, featuring blog posts from April 2025. This edition, like its predecessors, aims to broaden the accessibility of diverse mathematical discussions to a larger audience. Readers can expect to find explorations of topics like origami mathematics, as well as discussions of mathematical concepts relevant to daily life. Besides the Carnival of Mathematics, other events are taking place within the math community. An Origami Challenge was undertaken in schools by ETH students, who visited schools and taught about origami and its relationship to the mathematical world, and a simple way to generate random points on a sphere was recently highlighted. These varied activities showcase the dynamic and engaging nature of mathematics and its diverse applications. Recommended read:
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@phys.org
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A mathematician from UNSW Sydney has made a significant breakthrough in addressing a longstanding problem in algebra: solving higher polynomial equations. Honorary Professor Norman Wildberger has developed a novel method that utilizes intriguing number sequences to tackle equations where variables are raised to the power of five or higher, a challenge that has eluded mathematicians for centuries. The findings are outlined in a recent publication co-authored with computer scientist Dr. Dean Rubine, and could lead to advancements in various mathematical disciplines. This new approach has the potential to reshape mathematical problem-solving techniques.
Professor Wildberger's approach challenges traditional methods that rely on radicals, which often represent irrational numbers—decimals that extend infinitely without repeating. He argues that these irrational numbers introduce imprecision, and that a real answer to a polynomial equation can never be completely calculated because it would need an infinite amount of work. The mathematician suggests this solution "reopens a previously closed book in mathematics history." Prior to this discovery, French mathematician Évariste Galois demonstrated in 1832 that it's impossible to resolve higher polynomial equations with a general formula, such as the quadratic formula. Approximate solutions for higher-degree polynomials have been used, but are not pure algebra. Wildberger's radical rejection has lead to a new method for solving this decades old problem. Recommended read:
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@Greg Egan
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References:
jcarroll.com.au
Modulo arithmetic is being explored as a technique for rotation, inspired by a post from Greg Egan on Mastodon. Jonathan Carroll implemented Egan's formula in various languages. The formula, rot(n, j, k) = (n * 10^k) mod (10^j-1), efficiently rotates a j-digit number n by k digits. Carroll highlighted the importance of understanding fundamental operators across different languages while implementing this seemingly simple mathematical concept.
This exploration is beneficial for fortifying knowledge of basic functionalities in different programming languages. As Carroll wrote in his blog, implementing this simple math "means I’ll be working with some basic functionality and I believe it’s very important to have that locked in comfortably." Carroll demonstrated the implementation in R, utilizing the power operator '^' and the modulo operator '%%'. He also showed how to determine the number of digits in a number using the 'nchar()' function, showcasing practical application of these operators. The R implementation allows for the cyclic rotation of digits within a number. While R doesn't have a built-in function for this specific purpose, Carroll demonstrated the usage of his '{vec}' package for a similar ring-buffer effect on vectors. This involved using modulo on the indices to achieve the desired rotation. The formula subtracts (10^j-1) times the leftmost k digits of n*10^k, removing them from the left and adding them to the right. Recommended read:
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@sciencedaily.com
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www.sciencedaily.com
Researchers are employing advanced mathematical techniques to tackle complex problems in diverse fields. A recent study highlights the application of the hinge function in fluvial geomorphology, providing a solution for predicting bedload sediment transport in rivers. Additionally, mathematicians have used mathematical modeling to unravel the mystery behind the striped patterns of "broken" tulips, a phenomenon that has puzzled scientists for centuries. These examples demonstrate the power of mathematical methods in understanding and predicting phenomena across various scientific disciplines.
A team at Washington State University has developed a new forecasting model that helps businesses predict customer demand more accurately, even when key data is missing. This model, published in Production and Operations Management, uses a mathematical modeling method to estimate customer interest beyond just completed transactions and traditional forecasting techniques. By analyzing real-world sales data, the model provides a clearer view of how many customers considered a purchase but ultimately did not buy due to factors like pricing or timing. The researchers utilized a computational technique called the sequential minorization-maximization algorithm to improve forecasting accuracy. Furthermore, researchers at the University of Alberta have solved a centuries-old floral mystery by using a mathematical model to explain how striped tulips get their distinctive pattern. The study, published in Nature Communications Biology, reveals that the tulip-breaking virus inhibits the production of anthocyanins, the pigments that give tulips their vibrant colors. The mathematical model incorporates two key mechanisms—the substrate-activator mechanism and Wolpert's positional information mechanism—to simulate the interaction between the virus, pigment production, and cellular resources within the plant, ultimately creating the striped pattern. Recommended read:
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@Math Blog
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Math Blog
, denisegaskins.com
Mathematical concepts and their applications are gaining increased attention, with recent explorations into diverse areas. A blog post discusses the fundamental differences between mathematical and statistical reasoning, using the example of predicting days with the fewest noninduced births. Researchers are also delving into methods for eliminating parameters in parametric equations. A podcast delves into the philosophy of mathematics and set theory, examining the nature of mathematics itself.
The article "Eliminating the Parameter in Parametric Equations" provides a guide for expressing relationships between variables `x` and `y` when they are defined in terms of a parameter `t`. It explains the process of removing the parameter to obtain a direct equation between `x` and `y`, showcasing examples and solutions. Furthermore, there is a discussion on Charlotte Mason's approach to mathematics using living books as a method of teaching. Python's dominance in AI and machine learning is a significant development. An article explores the factors behind this, highlighting Python's readability, extensive libraries like NumPy, Pandas, Scikit-learn, TensorFlow, and PyTorch, and the role of AI hype in its rise. The Church of Logic podcast also featured a discussion with Joel David Hamkins on the philosophy of mathematics and set theory, particularly exploring differing perspectives on the nature of mathematics. Recommended read:
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@www.quantamagazine.org
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Recent advancements in mathematics and physics are pushing the boundaries of our understanding of the universe. A decades-old bet between mathematicians Noga Alon and Peter Sarnak regarding the nature of optimal expander graphs has recently been settled, with both mathematicians being proven wrong. This involved tapping into a crucial phenomenon in physics and pushing it to its limits, demonstrating the interconnectedness of mathematics and physics. Also, Researchers have successfully modeled how 'broken' tulips get their stripes, solving a centuries-old floral mystery. The mathematical model explains that the tulip-breaking virus inhibits the production of anthocyanins, leading to the distinctive striped pattern.
Efforts are underway to bridge the gap between quantum mechanics and general relativity, with researchers exploring the possibility of creating quantum gravity in the lab. Monika Schleier-Smith at Stanford University is leading this effort by using laser-cooled atoms to explore whether gravity could emerge from quantum entanglement. NASA is also contributing to this field by developing the first space-based quantum gravity gradiometer. This gradiometer will use ultra-cold rubidium atoms to detect gravitational anomalies with high precision from orbit, with potential applications in water resource management and subsurface geology. Further progress is being made in language model development. Researchers are exploring methods to sidestep language in order to improve how language models work with mathematics. By allowing these models to operate directly in mathematical spaces, they aim to enhance efficiency and reasoning capabilities. This research highlights the potential for artificial intelligence systems to benefit from thinking independently of language, paving the way for more advanced and effective AI applications. Recommended read:
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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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@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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@www.newtonproject.sussex.ac.uk
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Recent blog posts are delving into a variety of mathematical topics, offering insights and explorations across different areas of the field. These posts cover historical aspects of mathematics, examine specific mathematical concepts, and explore the connections between mathematics and other disciplines. This collection of diverse content aims to provide readers with a broader understanding and appreciation of mathematics.
The blog posts include diverse mathematical items. For example, one post references Gemma Frisius' "Arithmeticae Practicae Methodus Facilis" (1540) and its entry in *MAA Mathematical Treasures. Another commemorates April 13 as "On This Day in Math," highlighting mathematical facts associated with the number 103. This includes its unique properties as a prime number and its presence in Ramanujan's mathematical explorations. Furthermore, the blog explores historical events like the coining of the word "microscope" in 1620 and Lord Brouncker's published mathematical result in 1668. From statistical physics to number theory, these blogs showcase the versatility and interdisciplinary nature of mathematical thought. One blog even mentions using statistical physics concepts to analyze election results. These blog postings aim to engage readers with a range of mathematical subjects, from historical figures and publications to contemporary applications and connections. Recommended read:
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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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Tom Bridges@blogs.surrey.ac.uk
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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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@phys.org
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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:
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Terence Tao@What's new
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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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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 has unveiled Gemini 2.5 Pro, its latest and "most intelligent" AI model to date, showcasing significant advancements in reasoning, coding proficiency, and multimodal functionalities. According to Google, these improvements come from combining a significantly enhanced base model with improved post-training techniques. The model is designed to analyze complex information, incorporate contextual nuances, and draw logical conclusions with unprecedented accuracy. Gemini 2.5 Pro is now available for Gemini Advanced users and on Google's AI Studio.
Google emphasizes the model's "thinking" capabilities, achieved through chain-of-thought reasoning, which allows it to break down complex tasks into multiple steps and reason through them before responding. This new model can handle multimodal input from text, audio, images, videos, and large datasets. Additionally, Gemini 2.5 Pro exhibits strong performance in coding tasks, surpassing Gemini 2.0 in specific benchmarks and excelling at creating visually compelling web apps and agentic code applications. The model also achieved 18.8% on Humanity’s Last Exam, demonstrating its ability to handle complex knowledge-based questions. Recommended read:
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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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Tom Bridges@blogs.surrey.ac.uk
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Department of Mathematics
Academic institutions are hosting a variety of mathematics-related events and activities. The Department of Mathematics hosted its first annual "Pi Your Professor" event on March 20, 2025, a belated celebration of Pi Day. Undergraduate students were invited to throw pies made of paper plates with Reddi Wip at participating professors, including Maddie Brandt, Spencer Dowdall, and Dan Margalit.
Math Game Monday featured "Make a Square," a strategic game designed to build 2-D visualization skills for all ages. The game involves players marking symbols on a grid, aiming to form a square with their marks. Additionally, the One World Approximate Bayesian Inference (OWABI) Seminar is scheduled for March 27th, featuring Meïli Baragatti from the Université de Montpellier discussing Approximate Bayesian Computation with Deep Learning and Conformal Prediction. Recommended read:
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Unknown (noreply@blogger.com)@Pat'sBlog
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Pat'sBlog
Recent discussions have highlighted the diverse applications and historical roots of mathematics. A blog post explored the history of mathematical terms such as billion, trillion, and others, tracing their origins back to figures like Nicholas Chuquet, a French physician from the 15th century. The evolution of these terms and their varying definitions across different countries demonstrate the rich history and changing conventions within mathematical nomenclature. This information has recently resurfaced in a post from earlier this year.
Alongside the history of math, practical math applications are being discussed. For example, recent word problems are now available that focuses on division suitable for fourth-grade students. The step-by-step solutions for problems involving dividing quantities among groups can help students improve their comprehension of division and problem solving. Mathematics continues to be the basis for many algorithms in a variety of modern technological applications and is not widely recognized as a science. Recommended read:
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Unknown (noreply@blogger.com)@Pat'sBlog
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Pat'sBlog
A recent discussion has emerged regarding the use of specific mathematical terminology in educational settings. A young educator expressed concern over a visiting math teacher's use of the term "reduce fractions" during a lesson. The educator questioned whether it was appropriate to correct the more experienced teacher for using what they perceived as outdated or imprecise "edu-speak." This situation has sparked debate about the evolution of mathematical language and its implications for teaching practices.
Many modern elementary teachers get upset by the use of the term "reduce a fraction". Some argue that the term "reduce" can be misinterpreted by students as solely meaning "make smaller," potentially leading to confusion. However, historical context reveals that the term "reduction" in mathematics once had a broader meaning, encompassing the transformation of a quantity from one denomination to another without altering its value. This broader definition was prevalent in arithmetic textbooks until the late 1930s and 40s, when the term became primarily associated with fractions in "lowest terms" or "simplest terms." Recommended read:
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Blogs
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