Top Mathematics discussions
NishMath - #knowledge
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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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Sophia Wood@Fractal Kitty
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References:
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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References:
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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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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@medium.com
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References:
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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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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Karina Cuevas@PBS NewsHour - The Latest
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References:
NASA Science
, PBS NewsHour - The Latest
NASA's partnership with the private sector achieved a major milestone with the successful lunar landing of Firefly Aerospace's Blue Ghost lander. The spacecraft touched down safely early Sunday, marking the first commercial spacecraft to achieve this feat after previous attempts by others resulted in crashes or tip-overs. Blue Ghost is carrying several experiments for NASA as part of a broader initiative to utilize private companies for lunar deliveries in support of the Artemis program. This mission is designed to scout the lunar surface, evaluate the radiation environment, and develop solutions for navigating the challenging lunar dust.
NASA's Hubble Space Telescope also achieved a significant accomplishment, completing the largest galactic mosaic of all-time, imaging the full extent of the Andromeda galaxy. This mosaic consists of over 600 overlapping snapshots, creating a 2.5+ billion pixel image filled with a wealth of astronomical data. Furthermore, NASA's Spectro-Photometer for the History of the Universe, Epoch of Reionization and Ices Explorer (SPHEREx) is scheduled to launch this week. SPHEREx will map the entire sky four times over two years to uncover insights into the infant universe, the formation of early galaxies, and the location of building blocks of life in the Milky Way. Recommended read:
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