Top Mathematics discussions
NishMath - #NumberTheory
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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:
References :
@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:
References :
@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:
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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