Top Mathematics discussions
NishMath - #mathematics
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Tom Bridges@blogs.surrey.ac.uk
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In the academic world, there's a notable discussion ongoing regarding the perceived political leanings of university professors. Joshua May, a philosophy and psychology professor, posits that many liberal professors, while advocating for societal change and government intervention in the broader world, often exhibit a more conservative stance within their own university settings. This apparent inconsistency is characterized by a resistance to administrative mandates, a defense of academic traditions, and a hesitancy towards adopting new technologies or pedagogical approaches like online learning or AI tools. May suggests this might stem from a comfortable adherence to established academic structures that protect their own autonomy and expertise, creating a potential double standard between their public advocacy and their institutional behavior.
Amidst these discussions, the field of mathematics is seeing significant recognition and activity. Maryna Viazovska's formalization of her E8 lattice sphere packing proof marks a significant mathematical achievement. Additionally, the Mathematical Association of America (MAA) has become an Affiliate Member of the International Association of Scientific, Technical & Medical Publishers (STM), signaling a commitment to advancing research integrity and innovation in scholarly publishing. The MAA's leadership believes this affiliation will allow them to contribute their unique perspective to the wider publishing community. In other news, André Seznec has been named the recipient of the 2025 ACM-IEEE CS Eckert-Mauchly Award for his pioneering contributions to computing, specifically in branch prediction and cache memories. The university landscape also highlights student and faculty achievements. Jessica Furber, a PhD student, has won the university-wide 3-minute thesis competition, showcasing her ability to communicate complex research concisely. This competition, known as 3MT, challenges PhD students to present their work to a non-specialist audience in under three minutes, with Furber advancing to the national competition. Furthermore, Ravi Boppana's mathematical video channel, "Boppana Math," is being featured as part of a series highlighting online mathematics content creators, focusing on pure mathematics. The University of Washington's math students have also received accolades, being recognized in the Husky 100, a program that honors outstanding students across the university. Recommended read:
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@Martin Escardo
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Recent discussions and advancements in mathematics reveal a dynamic intersection of theoretical concepts and practical applications. In the realm of type theory, the concept of dependent equality is a significant topic, particularly within the framework of Martin-Löf Type Theory (MLTT). This area explores how equality is handled when types themselves depend on other types, with a particular focus on the implications of the K rule. This foundational work in type theory is crucial for formalizing mathematics and is seeing increasing adoption in proof assistants.
Further exploration into abstract mathematical structures is evident with discussions on semi-adjunctions, a concept extending the idea of adjunctions to semicategories. Alexander S. Sergeev's work also highlights the geometric aspects of vector bundles in relation to topological insulators. This research connects sophisticated mathematical ideas with the study of solid-state physics, illustrating how abstract geometry can illuminate complex physical phenomena such as surface states in topological materials. Beyond theoretical explorations, recent mathematical discourse touches upon applied problems and historical context. A fun project aims to optimize shapes for specific rolling statistics, essentially turning any object into a fair die or creating dice that mimic other statistical outcomes. Furthermore, reflections on the impact of war on the mathematical community, drawing parallels from historical figures like Akitsugu Kawaguchi and Abraham Fraenkel, underscore the resilience and enduring nature of mathematical pursuit even in challenging times. The ongoing evolution of tools for mathematicians, such as improvements in interactive search and replace functionalities in Emacs, also reflects the field's continuous adaptation. Recommended read:
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@www.dailykos.com
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Computational Complexity
, www.iflscience.com
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Two high school students have achieved a remarkable feat by discovering a novel proof of the Pythagorean Theorem. This new proof, which employs trigonometry, has been accepted for publication after undergoing rigorous scrutiny. The achievement is particularly noteworthy because proving the Pythagorean Theorem using trigonometry is challenging due to the potential for circular reasoning, as trigonometry itself relies on the Pythagorean Theorem. Despite this hurdle, the students' proof has been deemed valid, showcasing their mathematical ingenuity.
The Pythagorean Theorem, a cornerstone of geometry and trigonometry, has been found on clay tablets dating back to 1770 BCE. These tablets, predating Pythagoras by over 1,000 years, reveal that ancient Babylonian mathematicians were aware of the theorem and used it to solve problems. One tablet, IM 67118, demonstrates the application of the theorem to calculate the diagonal length of a rectangle. Another tablet shows a square with triangles and markings, illustrating their understanding of the relationship between the sides of a square and its diagonal. This historical evidence challenges the traditional attribution of the theorem solely to Pythagoras. The newly discovered proof by the high school students and the revelation of the theorem's ancient origins highlight the enduring relevance and evolving understanding of mathematics. While the students' proof demonstrates fresh perspectives on a classical theorem, the historical context emphasizes that mathematical knowledge is often developed and disseminated over centuries and across cultures. As mathematician Bruce Ratner notes, the Babylonians were likely familiar with the Pythagorean Theorem and irrational numbers well before Pythagoras, suggesting a rich and complex history of mathematical discovery. Recommended read:
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@Martin Escardo
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The Aperiodical
, denisegaskins.com
Recent activity on Mathstodon, the mathematics-focused corner of Mastodon, has sparked discussions across a variety of mathematical topics. Users such as MartinEscardo and Ddrake have been active, contributing to the vibrant exchange of ideas within the community. The Aperiodical, a website dedicated to recreational mathematics, has also been a key source of content, highlighting events like the "Big Internet Math-Off" competitions from previous years and teasing the upcoming "Big Internet Math-Off 2024." Denise Gaskins' "Playful Math for the Summer" blog post was shared, showcasing engaging math resources and games.
These online platforms provide a space for mathematicians and enthusiasts to share insights, puzzles, and announcements. One example is a post from Ngons highlighting a tiling pattern involving dodecagon rings, squares, and triangles, which can be connected to form a Koch snowflake, demonstrating the intersection of geometry, fractals, and math art. Another post referenced an issue of Double Maths First Thing by Colin, who discusses his mission to the moon and spreading joy for math. In addition to sharing interesting mathematical concepts, some Mastodon users are addressing platform-specific issues. MartinEscardo proposed a feature request aimed at improving the reply system, suggesting that users should have more control over who is notified in a thread to avoid irrelevant notifications. The Mathstodon community continues to be a hub for mathematical exploration, resource sharing, and discussions on improving the online experience for its members. Recommended read:
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@Trebor
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Trebor
Recent discussions in theoretical computer science and programming have touched upon diverse topics, ranging from type theory for SDG (Sustainable Development Goals) to the complexities encountered in programming. One thread explored the characteristics a type theory for SDG should possess, suggesting it should include a judgmentally commutative ring, possibly a Q-algebra, where neutral forms of type R are polynomials with other neutral forms as indeterminates. Participants believe such a system would have decidable typechecking.
A common sentiment shared among programmers, particularly those using languages with dependent types like Rust, is the initial hurdle of satisfying the compiler's requirements. Some have described the experience as an engaging puzzle that can involve spending considerable time to prove the validity of their code. The discussion also addressed the subjective nature of "complexity" in programming, suggesting it is a term often used to dismiss unfamiliar concepts rather than a concrete measure of inherent difficulty. In related news, Microsoft’s Krysta Svore has announced geometric error-correcting codes as a potential advancement toward practical quantum computing. These codes utilize high-dimensional geometry to enhance performance, potentially leading to more efficient encoding and logical operations with fewer qubits. The approach builds on topological error correction, employing a mathematical method called Hermite normal form to reshape the grid, resulting in substantial reductions in qubit count and faster logical clock speeds. This geometric reshaping results in substantial reductions in qubit count. In one notable case, they achieved six logical qubits using just 96 physical qubits, which is a 16-to-1 ratio that would mark a significant improvement over standard two-dimensional codes. Recommended read:
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@martinescardo.github.io
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ellipticnews.wordpress.com
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. Recommended read:
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MAA@maa.org
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maa.org
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. Recommended read:
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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." Recommended read:
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