Top Mathematics discussions
NishMath - #geometry
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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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@primes.utm.edu
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Pat'sBlog
, mathdaypballew.blogspot.com
This week saw a flurry of mathematical activity, highlighted by the 238th Carnival of Mathematics, organized by Aperiodical. The carnival showcases a variety of submissions and mathematical art, focusing on the number 238 itself. Noteworthy facts about 238 include that it is 2 × 7 × 17, the sum of the first 13 primes, and a "triprime". The carnival also encourages exploration beyond pure mathematics, with community members contributing insights linking the number to uranium isotopes, birth minutes, and even hexadecimal representations. It also shines a light on #MathArtMarch, with examples of crochet, coding, and painting from around the world.
Continuing the daily exploration of numbers, several interesting facts and events were highlighted for April 6th, 7th, 8th and 10th. The number 96, the 96th day of the year, was examined for its unique properties, such as being the smallest number expressible as the difference of two squares in four different ways. Events like Euler's first paper on partitions (April 7th, 1741) and Al-Biruni's observation of a solar eclipse in 1019 were also noted, linking mathematical concepts to historical contexts. Also, the number 97 has been noted as the 97th day of the year, where 97 is the largest prime that we can ever find that is less than the sum of square of its digits. In recreational mathematics, a "Salute" game for reinforcing multiplication and division was featured, emphasizing the inverse relationship between these operations. Additionally, the concept of "truncatable primes" was explored through a game where players create strings of prime numbers by adding digits to either end of a number. The number 91 was discussed as the 91st day of the year where 10 n + 91 and 10 n + 93 are twin primes for n = 1, 2, 3 and 4. Finally, highlighting mathematics beyond academia, James Abram Garfield, a former Congressman and mathematician, was mentioned for his original proof of the Pythagorean Theorem, illustrating the interdisciplinary nature of mathematics. Recommended read:
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Unknown (noreply@blogger.com)@Pat'sBlog
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Fractal Kitty
, The Aperiodical
The online mathematics community is buzzing with activity, as evidenced by the 238th Carnival of Mathematics, hosted by Aperiodical. This month's carnival showcases diverse submissions and beautiful math art, starting with an exploration of the number 238 itself. Found to be 2 x 7 x 17 and the sum of the first 13 primes, the number also inspired community contributions, with users pointing out its appearance in uranium isotopes, hexagonal representations, and even birth minute celebrations. The carnival highlights the engaging and creative ways people interact with mathematical concepts online.
The carnival features a collection of blog posts and activities from various math enthusiasts. Number yoga is explored as a technique to develop creative reasoning and comprehension in mathematics. This involves noticing details, wondering about possibilities, and creating explanations or related puzzles. Also featured are posts on polyominoes, a modern presentation of Peano Axioms, practical math for programmers, the Monty Hall Problem, and group theory using Zoombinis. Karen Campe also continues her visual "Go For Geometry" series. Furthermore, the online discussion includes extensions of basic geometry, focusing on pedal triangles and related theorems. A blog post delves into generalizations of perpendiculars from a point in a triangle, highlighting properties of the orthocenter and the orthic triangle. The orthic triangle's perimeter and its connection to the angles of the original triangle are discussed. The community also shares the art from Ayliean's MathArtMarch. Recommended read:
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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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Denise Gaskins@denisegaskins.com
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Recent studies and educational resources are focusing on enhancing math education through innovative approaches. Denise Gaskins' "Let's Play Math" blog offers resources for families to learn and enjoy math together, including playful math books and internet resources suitable for various age groups. Math journaling and games have been highlighted as effective tools to engage students, promote problem-solving skills, and foster a richer mathematical mindset.
Numerous games and activities can make learning fun. For instance, "Make a Square" is a game that builds 2-D visualization skills and strategic thinking. Quick number games that can be played anywhere. The divisibility rules for numbers, particularly divisibility by 2, are being emphasized to help students easily identify even and odd numbers. A megastudy also revealed that behaviorally informed email messages improved students' math progress, demonstrating how simple interventions can positively impact learning outcomes. Recommended read:
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munizao@Puzzle Zapper Blog
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mathvoices.ams.org
, John D. Cook
Math enthusiasts and educators are exploring a variety of topics on blogs and websites. Puzzlezapper features geometrical puzzles like polyiamond path puzzles, while other platforms share insights into math education and mathematical concepts. Alexandre Muñiz, on Puzzle Zapper Blog, explores variations on polyiamond tiles with marked paths, constrained to straight lines connecting the midpoints of cell edges.
Donna Fernandez, Co-Director of Alliance of Indigenous Math Circles, highlights the power of indigenous approaches to math education, using the example of the Navajo Prep Math Camp and ICME-15. John D. Cook discusses the practical consequences of tokenization, noting how subtle changes in prompts can significantly impact Large Language Models (LLMs), referencing an article about LLMs and chess, and illustrating how tokenization differences can confuse the model, affecting its ability to play effectively. 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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