Top Mathematics discussions
NishMath - #exploration
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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 :
@lobste.rs
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References:
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:
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 :
@medium.com
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Mathematics is a diverse field with applications spanning multiple disciplines. Recent articles and discussions have highlighted the importance of mathematics in various areas, including Artificial Intelligence (AI), data science, and quantum physics. Linear algebra, calculus, and probability are identified as essential mathematical topics for mastering AI and machine learning, while mathematical tools are enhancing learning in these complex fields.
The exploration of mathematics extends beyond its application in technology, encompassing historical perspectives, number theory, and geometric puzzles. Pi, a fundamental mathematical constant, continues to fascinate mathematicians and enthusiasts, with its presence felt across science, engineering, art, and culture. Discussions also cover the etymology of mathematical terms like logarithms, and the use of math journals and games in education. 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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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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