Top Mathematics discussions
NishMath - #knowledge
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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.
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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.
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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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