Top Mathematics discussions
NishMath - #programming
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@lobste.rs
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Mathematical blogs and platforms are currently buzzing with diverse explorations. Elinor, in a guest post for #MathArtMarch, has curated a collection of favorite mathematical art from the month, providing inspiration for artists and mathematicians alike. Meanwhile, the "exponential sum of the day" page continues to captivate audiences by generating a new figure daily. This figure is created by plotting partial sums and drawing lines between consecutive terms, resulting in visually intriguing patterns that often feature unexpected flat sides.
Recently, Bo’az Klartag has released "Striking new Lower Bounds for Sphere Packing in High Dimensions," which has garnered attention in the mathematical community. Kalai notes that this paper presents a significant breakthrough in the field. Klartag's paper demonstrates that there exists a lattice sphere packing with a density significantly higher than previously known constructions. His proof involves a stochastically evolving ellipsoid designed to accumulate lattice points on its boundary while avoiding them in its interior, a technique rooted in Minkowski's ideas on sphere packing and ellipsoids. Other areas of mathematical interest being explored include Elliptical Python Programming, as discussed on Susam Pal's blog. Also the article "exponential sum of the day" page draws a new figure each day by plotting the partial sums of and drawing a line between consecutive terms. Overall, these diverse explorations highlight the vibrant and dynamic nature of mathematical research and its connections to various fields like art and computer science.
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Michael Weiss@Diagonal Argument
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Recent discussions in mathematical concepts and programming tools cover a range of topics, including theoretical foundations and practical applications. Peter Cameron highlighted the Compactness Theorem for first-order logic, explaining its consequences and connections to topology. Also, a beginner's guide to sets has been published to explain how they work and some applications.
Noel Welsh presented a talk at Imperial College on dualities in programming, exploring the relationships between data and codata, calls and returns, and ASTs and stack machines. The use of adjoints in boolean operations was justified, and Daniel Lemire published an overview of parallel programming using Go. These discussions bridge the gap between abstract mathematical principles and their concrete uses in software development and programming paradigms.
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