The Mathematician

From τὰ φυσικά (ta physika) to physics – XLVI (thonyc​.wordpress​.com). Giovanni Alfonso Borelli, a pivotal figure in the Galileo-Castelli mathematics school, contributed to astronomy and mechanics, discussing comets, gravity, and fluid dynamics while influencing future scientists like Newton

Travels, 8 (cameroncounts​.wordpress​.com). Peter Cameron describes a journey from Chennai to Puducherry, involving talks on twin reduction and generalized wreath products, and reflections on local experiences including coconut and ice apple tasting

Honoring Peter Cameron (poetrywithmathematics​.blogspot​.com). A tribute to mathematician Peter Cameron, highlighting his contributions to mathematical poetry and announcing the upcoming Conference on Theoretical and Computational Algebra in Evora, Portugal, dedicated to honoring his work

Celebrating 40 years of Elliptic Curves in Cryptography (ECC), August 11, 2025 (ellipticnews​.wordpress​.com). An online event on August 11, 2025, will commemorate 40 years of elliptic curve cryptography (ECC) with reflections from founders Victor Miller and Neal Koblitz, highlighting its unexpected impacts on cryptography

On Coping with the War — and a 1931 Postcard from Akitsugu Kawaguchi to Abraham Fraenkel (gilkalai​.wordpress​.com). The article discusses coping with war through mathematical engagement, citing Edmund Landau's works and personal reflections on public trauma, alongside a postcard from Akitsugu Kawaguchi to Abraham Fraenkel

The Peter Putnam Glossary. (languagehat​.com). Explores Peter Putnam's remarkable yet obscure contributions to physics and philosophy, highlighted through John Archibald Wheeler's introduction at a 1975 MIT conference, including the need for a glossary to understand Putnam's concepts

Zipf genius (languagelog​.ldc​.upenn​.edu). George Kingsley Zipf, the namesake of Zipf's law, discovered that word usage frequencies follow a specific pattern, having broader implications in linguistics and social behavior, despite his dislike for mathematics

Robert Hooke - Undershaft (londonremembers​.com). Robert Hooke (1635-1703), eminent scientist, is commemorated at St Helen’s Bishopsgate, a historic parish church in London, where he was first buried, though his remains are now lost

Can You Pass Harvard’s Remedial Math Class? (mindyourdecisions​.com). Harvard offers a new college-level calculus course, responding to pandemic learning loss. Critics labeled it as 'remedial math.' Sample test questions are available online for evaluation of foundational math skills

A polygon puzzle that really isn’t (leancrew​.com). A polygon puzzle involving eight regular polygons requires finding a missing number, derived from prime numbers associated with polygons. A difference table suggests a solution linked to specific numerical patterns

If you do well in the UMCP HS Math Competition you may win $1,000,000 (blog​.computationalcomplexity​.org). Those excelling in the UMCP HS Math Competition could potentially earn $1,000,000, highlighting the intersection of competitive mathematics and significant financial rewards

Tukey's birthday (languagelog​.ldc​.upenn​.edu). A humorous xkcd comic reflects on the age discrepancy between Randall's future birthday and John Tukey's, highlighting the effects of leap years on day counts and emphasizing the importance of approximate answers in data analysis

The Bride’s Chair (futilitycloset​.com). Euclid's complex proof of the Pythagorean theorem, dubbed the 'bride's chair,' is rooted in a miscommunication between Greek and Arabic translations, showcasing a peculiar intersection of geometry and linguistic confusion

Cracovians: The Twisted Twins of Matrices (marcinciura​.wordpress​.com). Cracovians, an alternative to matrices in linear algebra, were developed by Tadeusz Banachiewicz for computational ease, featuring unique multiplication rules and applications in various fields including astronomy and geodesy

Why the tight clustering of mathematical constants? (thoughtforms​.life). Dr. Michael Levin presents a perplexing observation about the tight clustering of mathematical constants, questioning why they range narrowly between 0.5 and 5, unlike the vast spectrum of physical constants that span 160 orders of magnitude

The mathematical essence of origami blue-and-white porcelain (aperiodical​.com). Exploration of geometric principles in origami and blue-and-white porcelain, unveiling crafting methods, structural transformations, and computational origami techniques

Sinc function approximation (johndcook​.com). Approximation of sinc function in signal processing for small x using (2 + cos(x))/3, highlighting its accuracy and limitations

Curved-Crease Sculpture (erikdemaine​.org). Curved-Crease Sculpture explores the intricate dynamics of self-folding origami, particularly through curved creases, with applications in deployable structures and manufacturing, showcasing various series by Erik and Martin Demaine

2-opt Local Search for the TSP (jmsallan​.netlify​.app). Exploration of 2-opt local search techniques for solving the Traveling Salesman Problem using tabu search and simulated annealing heuristics

Additive FFT: background (blog​.lambdaclass​.com). Exploring Cantor's Additive FFT as an efficient polynomial evaluation method in binary fields, this article delves into linearized polynomials and tower structures crucial for applications like Reed-Solomon encoding

Computing a Matrix Inverse Using Newton Iteration With From-Scratch Python (jamesmccaffrey​.wordpress​.com). Learn to compute a matrix inverse using Newton iteration in Python with NumPy, exploring techniques to set initial matrices and the challenges of numerical programming

Animating Linear Transformations with Quiver (towardsdatascience​.com). Explore how animated quiver plots in Python's Matplotlib help visualize linear transformations and concepts like Singular Value Decomposition, by understanding vector movements and transformations through code snippets

Productivity and Rate of Profit (constantinides​.net). A mathematical model analyzes Marx's 'Law of the Tendency of the Rate of Profit to Fall' using socially necessary labor time and explores productivity scenarios affecting profit rates across firms

Amplitudes 2025 This Week (4gravitons​.com). Amplitudes 2025 conference in Seoul spotlighted developments in scattering amplitudes with a focus on gravitational waves, QCD, soft theorems, and advanced integration techniques like S-matrix bootstrap and machine learning applications

Stability Regions for Tischer's Formulas (eklausmeier​.goip​.de). Peter Tischer's cyclic multistep formulas, optimized using the ZSYSTM solver, provide stiff stability for differential equations, with codes implemented in ODIOUS that facilitate evaluation against LSODE

How to Explicitly Compute Charts for a Levelset Submanifold (grossack​.site). This blog post explores explicit chart computations for levelset submanifolds, focusing on $SL_2(\mathbbR)$ and hyperboloids, highlighting the use of Jacobians and various charts based on conditions of coordinates

An Easy But Impossible Probability Problem (themathdoctors​.org). Explores an impossible probability problem using conditional probabilities, where P(A) and P(A∩B) lead to contradictions in the context of drawing marbles. Discusses the implications for teaching probability

Practical Techniques in Serial Number Analysis (bruceediger​.com). A review of Leo A. Goodman's 1954 techniques for serial number analysis, focusing on distribution calculations, cumulative distribution comparison, and the significance of estimating total production from limited serial data

Is Mathematics Mostly Chaos or Mostly Order? (quantamagazine​.org). Mathematicians explore new cardinal numbers like exacting and ultraexacting infinities, which challenge existing hierarchies in set theory and suggest unexpected complexities in the mathematical universe, beyond Cantor's original constructs

Potentialist conceptions of infinity, Peking University, June 2025 (jdh​.hamkins​.org). Joel David Hamkins discusses potentialist conceptions of infinity at the Conference on Infinity, focusing on modal logic's role in distinguishing between convergent and radical forms of potentialism

Proving that every program halts (ntietz​.com). The halting problem is explored with a humorous logic proof claiming every program halts, using concepts like disjunctive syllogism and the principle of explosion to illustrate the contradictions in logic

Superimposed codes (blog​.sesse​.net). Exploration of (1,2) superimposed codes using properties of distance and checksum digits, including one-hot encoding and the application of SAT solvers to extend code sets beyond conventional limits

PLDI 2025 and E-Graphs Modulo Theories Talk (philipzucker​.com). Talk on E-graphs Modulo Theories covers bottom-up e-matching, SMT solvers, and implications for algebraic subtyping, with discussions on slotted union finds, group actions, and probabilistic types amidst social interactions at PLDI 2025

Autoformalization: Bridging Human Mathematical Intuition and Machine Precision (medium​.com/intuitionmachine). Autoformalization aims to bridge human mathematical intuition with machine precision by translating informal mathematical content into formal proofs using semantic embedding spaces, guiding exploration, and verification systems to address inherent challenges and ambiguities

Counting with Categories (Part 1) (golem​.ph​.utexas​.edu). John Baez explores categorization in combinatorics, detailing the use of species and generating functions to count derangements and permutations, alongside technical elements like functors and natural transformations in category theory

PhD position in algebraic geometry and representation theory (pbelmans​.ncag​.info). PhD position available in algebraic geometry and representation theory, focusing on computational methods like equivariant vector bundles. Supervised by Karin Melnick and Pieter Belmans, with visits to Utrecht University

Polarities (Part 6) (johncarlosbaez​.wordpress​.com). John Baez and Adittya Chaudhuri explore polarities in graph theory, presenting directed graphs with edges labeled by a monoid to model positive and negative effects, and studying feedback loops via homology

Shakhar Smorodinsky’s Solution to a Radon-Type Problem (gilkalai​.wordpress​.com). Shakhar Smorodinsky solved a Radon-type problem using a VC-dimension argument, shifting the focus on convex sets' intersection properties, promising new directions in discrete geometry

New Bounds for the Ideal Proof System in Positive Characteristic (arxiv:math). Upper and lower bounds for the Ideal Proof System in positive characteristic are established, extending previous results and demonstrating exponential-size lower bounds and efficient refutations for symmetric instances

Lower Bounds against the Ideal Proof System in Finite Fields (arxiv:cs). Establishes lower bounds for fragments of the Ideal Proof System over finite fields, utilizing set-multilinearization and extending results on knapsack instances and algebraic branching programs to demonstrate complexity in proof systems

Cartan's Path Development, the Logarithmic Signature and a Conjecture of Lyons-Sidorova (arxiv:math). Exploration of Lyons-Sidorova conjecture linking BV paths and logarithmic signatures, utilizing Cartan's path development and iterated integrals on complex Lie algebras

Making Non-Negative Polynomials into Sums of Squares (arxiv:math). Investigates linear operators A on polynomials, demonstrating conditions for non-negative polynomials in sums of squares, with applications to closed sets and a proof of Stochel's Theorem within Fréchet Lie groups

A Proof of the Hodge Conjecture for a Special Class of Calabi-Yau 5-Folds via Exceptional Group Constraints (arxiv:math). Proof of (1,1)-type Hodge conjecture for Calabi-Yau 5-folds using exceptional group constraints; connection between representation theory and algebraic geometry

Structured and Punctured Nullstellensätze (arxiv:math). The paper generalizes Nullstellensätze for punctured grids, establishing that certain monomials remain unchanged during polynomial division, enhancing previous results by Schauz and Nica and extending Clark's counting theorem proof

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