Top Mathematics discussions
NishMath - #mathematics
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@Latest from Tom's Guide
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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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msaul@mathvoices.ams.org
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Researchers at the Technical University of Munich (TUM) and the University of Cologne have developed an AI-based learning system designed to provide individualized support for schoolchildren in mathematics. The system utilizes eye-tracking technology via a standard webcam to identify students’ strengths and weaknesses. By monitoring eye movements, the AI can pinpoint areas where students struggle, displaying the data on a heatmap with red indicating frequent focus and green representing areas glanced over briefly.
This AI-driven approach allows teachers to provide more targeted assistance, improving the efficiency and personalization of math education. The software classifies the eye movement patterns and selects appropriate learning videos and exercises for each pupil. Professor Maike Schindler from the University of Cologne, who has collaborated with TUM Professor Achim Lilienthal for ten years, emphasizes that this system is completely new, tracking eye movements, recognizing learning strategies via patterns, offering individual support, and creating automated support reports for teachers. Recommended read:
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@techcrunch.com
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DeepMind's artificial intelligence, AlphaGeometry2, has achieved a remarkable feat by solving 84% of the geometry problems from the International Mathematical Olympiad (IMO) over the past 25 years. This performance surpasses the average gold medalist in the prestigious competition for gifted high school students. The AI's success highlights the growing capabilities of AI in handling sophisticated mathematical tasks.
AlphaGeometry2 represents an upgraded system from DeepMind, incorporating advancements such as the integration of Google's Gemini large language model and the ability to reason by manipulating geometric objects. This neuro-symbolic system combines a specialized language model with abstract reasoning coded by humans, enabling it to generate rigorous proofs and avoid common AI pitfalls like hallucinations. This could potentially impact fields that heavily rely on mathematical expertise. Recommended read:
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vishnupriyan@Verdict
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Google's AI mathematics system, known as AlphaGeometry2 (AG2), has surpassed the problem-solving capabilities of International Mathematical Olympiad (IMO) gold medalists in solving complex geometry problems. This second-generation system combines a language model with a symbolic engine, enabling it to solve 84% of IMO geometry problems, compared to the 81.8% solved by human gold medalists. Developed by Google DeepMind, AG2 can engage in both pattern matching and creative problem-solving, marking a significant advancement in AI's ability to mimic human reasoning in mathematics.
This achievement comes shortly after Microsoft released its own advanced AI math reasoning system, rStar-Math, highlighting the growing competition in the AI math domain. While rStar-Math uses smaller language models to solve a broader range of problems, AG2 focuses on advanced geometry problems using a hybrid reasoning model. The improvements in AG2 represent a 30% performance increase over the original AlphaGeometry, particularly in visual reasoning and logic, essential for solving complex geometry challenges. Recommended read:
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Matt Marshall@AI News | VentureBeat
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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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Tom Bridges@blogs.surrey.ac.uk
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blogs.surrey.ac.uk
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The London Mathematical Society has awarded Polina Vytnova a Research in Pairs grant, dated February 14th. The grant will enable Vytnova to host Victor Kleptsyn, a CNRS Researcher from the University of Rennes, at the University of Surrey. Together, they will collaborate on a joint research project focusing on the "Arithmetic of Cantor sets."
Also, Terry Tao has announced a collaboration with Grant Sanderson of 3blue1brown, along with Tanya Klowden, to produce a two-part video about the history of the cosmic distance ladder. This project builds upon a previous public lecture by Tao and is related to their forthcoming book. The first part of the video is already available, with Sanderson currently editing the second part. Recommended read:
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Tom Bridges@blogs.surrey.ac.uk
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Math Department
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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@artsci.washington.edu
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Recent News
, artsci.washington.edu
University of Washington professors Xiaodong Xu, Cynthia Vinzant, and Shayan Oveis Gharan have been honored by the National Academy of Sciences (NAS) for their outstanding research achievements. The NAS awards program has been recognizing outstanding achievement in the physical, biological, and social sciences since 1866. The annual awards ceremony will honor the major contributions made by 20 researchers.
Xu received the NAS Award for Scientific Discovery for his experimental observation of the fractional quantum anomalous Hall effect. This award, presented every two years, recognizes an accomplishment or discovery in basic research within the previous five years that is expected to have a significant impact on astronomy, biochemistry, biophysics, chemistry, materials science, or physics. Xu's research explores new quantum phenomena in layered two-dimensional materials and engineered quantum systems. Vinzant and Oveis Gharan, along with Nima Anari and Kuikui Liu, will receive the Michael and Sheila Held Prize for breakthrough work advancing the theory of matroids and mixing rates of Markov chains. The Michael and Sheila Held Prize is presented annually to honor outstanding, innovative, creative, and influential research in the areas of combinatorial and discrete optimization, or related parts of computer science, such as the design and analysis of algorithms and complexity theory. This $100,000 prize is intended to recognize recent work. Recommended read:
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@Department of mathematics
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www.ams.org
, ams.org
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The American Mathematical Society (AMS) is actively advocating for mathematics, particularly concerning the National Science Foundation (NSF). The AMS has started a page to coordinate support for professional mathematics, focusing on executive orders impacting the NSF. Recently, the NSF has seen significant changes, including the firing of 168 employees, which raises concerns about the potential impact on quantum funding and artificial intelligence research. These layoffs, occurring in response to a presidential executive order aimed at reducing the federal workforce, have affected both probationary employees and part-time experts in physics-related fields.
The AMS provides tools for the mathematical community to engage with government representatives, ensuring that the voices of mathematicians are heard in policy discussions. The AMS also actively supports mathematics on a global stage, as demonstrated by the US team earning third place at the 2025 Romanian Master of Mathematics, a challenging international high school mathematics competition, with team members earning individual awards. Penn State also rose in the NSF Higher Education Research and Development rankings. The AMS is dedicated to advancing research and connecting the diverse global mathematical community through publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs. Recommended read:
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@medium.com
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The year 2025 is gaining attention not just for marking a new year but also for its unique mathematical properties. It's a perfect square, specifically 45 squared (45 x 45 = 2025). This means it can be represented as a square shape with 45 units on each side. Perfect square years are not common, with the last one being 1936 and the next one not until 2116, making 2025 mathematically special and a rare occurrence. Beyond being a perfect square 2025 also has other interesting traits that are being noted.
Another unusual property of 2025 is that it's linked to the concept of Kaprekar numbers, with 45 fitting the criteria. When 2025 is split into 20 and 25, their sum is 45. Furthermore, 2025 can be expressed as the sum of the cubes of all single-digit numbers from one to nine, and is also a sum of three squares, 40², 20², and 5². The number also happens to be the product of squares, and the sum of two consecutive triangular numbers. These properties highlight the complex and intriguing nature of the number 2025 within mathematical theory. 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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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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@medium.com
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Pat'sBlog
, medium.com
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March 14th marks the annual celebration of Pi Day, honoring the mathematical constant π (pi), which represents the ratio of a circle’s circumference to its diameter. Pi, an irrational number approximately equal to 3.14159, holds significance across various scientific disciplines, including geometry, physics, engineering, and even music theory. Its infinite, non-repeating decimal expansion symbolizes infinity and mystery, captivating mathematicians and enthusiasts alike.
Pi Day 2025 presents an opportunity to engage students with interactive activities like Ratio Riddles, PiCraft, and Math Progress. Ratio Riddles, a lesson from Minecraft Education, introduces concepts of ratio, proportion, fractions, and scale through engaging games. PiCraft offers a student workbook blending gaming and learning, allowing students to estimate and calculate the area of a circle within the Minecraft universe, applying mathematical concepts through coding with Microsoft MakeCode. These hands-on experiences aim to make math more meaningful and strengthen students' confidence in the subject. Recommended read:
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Tom Bridges@blogs.surrey.ac.uk
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Joel David Hamkins
Professor Dame Alison Etheridge from Oxford University, who is also the first President of the Academy for the Mathematical Sciences and former Chair of the REF mathematical sciences sub-panel, visited Mathematics at Surrey on March 7, 2025. She presented a colloquium talk titled "The forwards and backwards of population models," discussing a class of models suitable for modelling plant populations, which includes a novel explicit modelling of the juvenile phase and its implications for inferring data from genetics.
Tom Bridges visited the Courant Institute of Mathematical Sciences in New York on March 5, 2025, for research interaction with Yuri Latushkin. Their work focused on various research problems related to the Maslov index, Fredholm operators, and the stability of solitary waves. Additionally, Joel David Hamkins is scheduled to present a talk on modal model theory at the Panglobal Algebra and Logic Seminar at the University of Colorado Boulder on March 12, 2025, which will be available live on Zoom. The International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) 2025 features a session on "Mathematical modeling applied to epidemics and the spread of bioaerosols indoors." Organized by António F. Miguel and Murat Aydin, this session highlights the importance of mathematical modeling in predicting, assessing, and controlling disease outbreaks, with a focus on indoor viral bioaerosol transmission patterns. ICNAAM aims to gather leading scientists in numerical and applied mathematics to discuss original research. 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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Michael Weiss@Diagonal Argument
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Diagonal Argument
Recent discussions in mathematical concepts and programming tools cover a range of topics, including theoretical foundations and practical applications. Peter Cameron highlighted the Compactness Theorem for first-order logic, explaining its consequences and connections to topology. Also, a beginner's guide to sets has been published to explain how they work and some applications.
Noel Welsh presented a talk at Imperial College on dualities in programming, exploring the relationships between data and codata, calls and returns, and ASTs and stack machines. The use of adjoints in boolean operations was justified, and Daniel Lemire published an overview of parallel programming using Go. These discussions bridge the gap between abstract mathematical principles and their concrete uses in software development and programming paradigms. Recommended read:
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Unknown (noreply@blogger.com)@Pat'sBlog
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Infinite nested radicals, a fascinating area of mathematical exploration, involve iterated square roots and cube roots. These radicals are studied to discover integer solutions and their connections to other mathematical concepts. A key focus is on using basic algebraic manipulations to solve for these iterated roots, offering insights into the relationships between infinite radicals and various number sequences.
The exploration extends to finding integer values from iterated square roots and cube roots and how these connect to specific sequences like oblong or hexonic numbers. By squaring and simplifying the expressions, one can derive quadratic or cubic equations. This allows for the calculation of values that produce integer results. Recommended read:
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Megan Murphy@STATTRAK
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STATTRAK
The Causality in Statistics Education Award, established by Judea Pearl, is seeking nominations. This award acknowledges the growing importance of incorporating causal inference into undergraduate and lower-division graduate statistics courses. The award provides a $5,000 cash prize annually, and nominations are due by April 5th. Further details regarding selection criteria and nomination requirements can be found on the American Statistical Association's STATtr@k website.
In other news, the Carnival of Maths 237, which rounds up various mathematics blog posts, is now available online. A mathematics conference organized by DEA SCUOLA is scheduled for secondary school mathematics teachers which aims to enhance mathematics teaching through innovative strategies and the integration of AI. Musically, Day 30 of a practice series features bass drum exercises from Mark Guiliana's book, highlighting complex coordination challenges in alternating snare and bass drum strokes. Recommended read:
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John@John D. Cook
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The Mathematician Coder
, blogs.surrey.ac.uk
Recent mathematical discussions and events showcase the field's dynamism. The European Universities Cup (EUC) mathematics competition will be held in 2025. This event brings together top teams from European regionals, providing them with a qualification path to the ICPC World Finals and an opportunity to participate in a significant onsite competition.
Also of note is a seminar given by Cesare Tronci at the University of Sussex on March 3, 2025. The seminar, part of the Theoretical and Mathematical Physics Seminar, was titled "Koopman trajectories in nonadiabatic quantum-classical dynamics." In addition, a blog post discussed how changing our perspective on mathematics has expanded its possibilities, particularly with imaginary numbers and Cantor's work on set theory and infinity. Recommended read:
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@Thony Christie
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Pat'sBlog
Several blogs and articles delve into the historical development and conceptual understanding of mathematics. One area of focus includes the cosmic distance ladder, a method for measuring distances to astronomical objects. This is explored in a blog post discussing a video featuring commentary and corrections to the topic, referencing a collaboration between Grant Sanderson and others. This content clarifies inaccuracies and omissions present in the video, offering valuable insights for viewers.
Mathematical history is further enriched by discussions on geometric vanishes, the history of the factorial function, and mathematical induction. Geometric vanishes, often presented as puzzles, date back to the 16th century. One blog explores their history, referencing examples from the Renaissance era. A blog post and external links also explore the evolution of factorial notation and the concept of mathematical induction, explaining how it works like dominoes, cascading through a series of logical steps to prove mathematical statements. Recommended read:
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@uk.bookshop.org
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Now Appearing
, www.brianclegg.net
Popular science author Brian Clegg is offering a bonus puzzle related to his book, "Conundrum," a collection of 200 puzzles and ciphers. Participants who solve the puzzle will be entered into a draw for a free signed copy of the book. The puzzle requires solvers to combine different elements, with the solution needing to be submitted via a form on the Conundrum Book Site by the end of February 28, 2025.
Solving the bonus puzzle involves interpreting clues such as "Passing under the seventh Duke, take the date of the crocodile, add the psalm number and divide by the verse to get the answer." Hints are available on the website for those needing assistance. "Conundrum" challenges readers with general knowledge and lateral thinking skills across various subjects. More information about the book, including purchase options and a Facebook page, can be found on Brian Clegg's website. Recommended read:
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@medium.com
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medium.com
, medium.com
Recent explorations in probability, statistics, and data analysis have highlighted the significance of the z-score as a tool for understanding data distribution. The z-score, a standard way of comparing data points across different distributions, helps identify outliers and make data-driven decisions. This statistical method is crucial for understanding how unusual or typical a particular data point is in relation to the average and is a fundamental element in making sound inferences from data. Researchers are emphasizing the importance of mastering these fundamentals for anyone involved in data science or analytical fields.
The study of distributions plays a key role in both probability and generalized function theories. Understanding how these distributions are related enhances our insights into patterns and randomness in the natural world. The normal distribution, often represented by a bell curve, illustrates how many phenomena tend to cluster around an average, with rarer events falling at the extremes. Moreover, the essential mathmatics behind these theories, including descriptive statistics, basic probability, inferential statistics, and regression analysis, form the heart and soul of data science, allowing data scientists to analyze and make sense of raw data. Recommended read:
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