Top Mathematics discussions
NishMath - #history
|
Tom Bridges@blogs.surrey.ac.uk
//
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.
Share:
References :
Classification:
Tom Bridges@blogs.surrey.ac.uk
//
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.
Share:
References :
Classification:
@Thony Christie
//
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.
Share:
References :
Classification:
|
Blogs
|