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MAA@maa.org
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The Mathematical Association of America (MAA) has announced the recipients of the 2025 awards for expository mathematical writing in MAA publications. The awards recognize outstanding contributions to mathematical literature. Jordan S. Ellenberg was awarded the Chauvenet Prize for his work "Geometry, Inference, Complexity, and Democracy," which appeared in the Bulletin (New Series) of the American Mathematical Society. Ellenberg's work explores the challenge of fairly dividing democratic polities into legislative districts, demonstrating the practical application of mathematics to societal issues. Ismar Volíc of Wellesley College, received the Euler Book Prize for his book "Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation," which brings complex topics, such as voting theory, apportionment, gerrymandering, and the Electoral College, to life.
Awarded individuals are reciving either the Chauvenet Prize, the Euler Book Prize, the Daniel Solow Author’s Award, the George Pólya Awards, the Paul R. Halmos–Lester R. Ford Awards, the Trevor Evans Award, or the Carl B. Allendoerfer Awards. Ellenberg's article, drawn from his 2020 Current Events Bulletin lecture, showcases how mathematical approaches can measure fairness in democratic processes. Volíc's book makes complex topics accessible to readers, highlighting the crucial role of mathematics in collective decision-making, and providing essential insights without political bias. Both works exemplify clear and engaging writing, effectively communicating intricate mathematical ideas to a wider audience. As summer approaches, Denise Gaskins is offering discounts on her math game books at the Playful Math Store. This presents an opportunity for families and educators to enhance mathematical learning through playful activities. Gaskins' "Math You Can Play" series offers math games sorted by topics traditionally taught at various age levels, with teaching tips and advice aimed at parents and teachers. Her new series, "Tabletop Math Games Collection," also covers the same mathematical topics. These books are designed for direct use by players of all ages, making them ideal for spontaneous math play. These books are available in both physical and digital formats, providing flexibility for use in math centers, homeschool co-op classes, or at home.
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Tom Bridges@blogs.surrey.ac.uk
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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.
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