Top Mathematics discussions
NishMath - #research
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@martinescardo.github.io
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The mathematics community is buzzing with activity, including upcoming online events and ongoing discussions about research methodologies. A significant event to watch for is the online celebration marking the 40th anniversary of Elliptic Curve Cryptography (ECC) on August 11, 2025. This event will commemorate the foundational work of Victor Miller and Neal Koblitz in 1985. It is anticipated to be a very important event for those in the cryptography community and to those who work with elliptic curves.
The ECC celebration will feature personal reflections from Miller and Koblitz, alongside lectures by Dan Boneh and Kristin Lauter, who will explore ECC's broad impact on cryptography and its unforeseen applications. The history of ECC is used as a good example of how fundamental research can lead to unexpected and practical outcomes. This serves as a good way to promote blue skies research. In other news, mathematicians are actively discussing the use of formal methods in their research. One Mathstodon user described using LaTeX and Agda in TypeTopology for writing papers and formalizing mathematical remarks. They found that formalizing remarks in a paper could reveal errors in thinking and improve results, even in meta-mathematical methodology. This shows how computational tools are increasingly being used to verify and explore mathematical ideas, highlighting the practical utility of pure math skills in applied contexts.
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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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@www.quantamagazine.org
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Recent breakthroughs have significantly advanced the "Core of Fermat's Last Theorem," a concept deeply rooted in number theory. Four mathematicians have extended the key insight behind Fermat's Last Theorem, which states there are no three positive integers that, when raised to a power greater than two, can be added together to equal another number raised to the same power. Their work involves applying this concept to other mathematical objects, notably elliptic curves. This extension represents a major step towards building a "grand unified theory" of mathematics, a long-sought goal in the field.
This achievement builds upon the groundwork laid by Andrew Wiles's famous 1994 proof of Fermat's Last Theorem. Wiles, with assistance from Richard Taylor, demonstrated that elliptic curves and modular forms, seemingly distinct mathematical entities, are interconnected. This discovery revealed a surprising "modularity," where these realms mirror each other in a distorted way. Mathematicians can now leverage this connection, translating problems about elliptic curves into the language of modular forms, solving them, and then applying the results back to the original problem. This new research goes beyond elliptic curves, extending the modularity connection to more complicated mathematical objects. This breakthrough defies previous expectations that such extensions would be impossible. The Langlands program, a set of conjectures aiming to develop a grand unified theory of mathematics, hinges on such correspondences. The team's success provides strong support for the Langlands program and opens new avenues for solving previously intractable problems in various areas of mathematics, solidifying the power and reach of the "Core of Fermat's Last Theorem."
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